Performance of Information and Communication Systems: IFIP TC6 / WG6.3 Seventh International Conference on Performance of Information and Communication Systems (PICS â€™98) 25â€“28

Performance of Information and Communication Systems

Visit the IT & Applied Computing resource centre www.IT-CH.com

IFIP - The International Federation for Information Processing

IFIP was founded in 1960 under the auspices of UNESCO, following the First World Computer Congress held in Paris the previous year. An umbrella organization for societies working in information processing, IFIP's aim is two-fold: to support information processing within its member countries and to encourage technology transfer to developing nations. As its mission statement clearly states,

IFIP's mission is to be the leading, truly international, apolitical organization which encourages and assists in the development, exploitation and application of information technology for the benefit of all people.

IFIP is a non-profitmaking organization, run almost solely by 2500 volunteers. It operates through a number of technical committees, which organize events and publications. IFIP's events range from an international congress to local seminars, but the most important are:

• the IFIP World Computer Congress, held every second year; • open conferences; • working conferences.

The flagship event is the IFIP World Computer Congress, at which both invited and contributed papers are presented. Contributed papers are rigorously refereed and the rejection rate is high.

As with the Congress, participation in the open conferences is open to all and papers may be invited or submitted. Again, submitted papers are stringently refereed.

The working conferences are structured differently. They are usually run by a working group and attendance is small and by invitation only. Their purpose is to create an atmosphere conducive to innovation and development. Refereeing is less rigorous and papers are subjected to extensive group discussion.

Publications arising from IFIP events vary. The papers presented at the IFIP World Computer Congress and at open conferences are published as conference proceedings, while the results of the working conferences are often published as collections of selected and edited papers.

Any national society whose primary activity is in information may apply to become a full member of IFIp, although full membership is restricted to one society per country. Full members are entitled to vote at the annual General Assembly, National societies preferring a less committed involvement may apply for associate or corresponding membership. Associate members enjoy the same benefits as full members. but without voting rights. Corresponding members are not represented in IFIP bodies. Affiliated membership is open to non-national societies, and individual and honorary membership schemes are also offered.

Performance of Information and Communication Systems IFIP 1C6 / WG6.3 Seventh International Conference on Performance of Information and Communication Systems (PICS '98) 25-28 May 1998, Lund, Sweden

Edited by Ulf Korner Department of Communication Systems Lund University Sweden

and

Arne A. Nilsson Dept of Electrical & Computer Engineering North Carolina State University USA

SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.

First edition 1998

o 1998 Springer Science+Business Media Dordrecht Originally published by Chapman & HalI in 1998

Thomson Science is a division of International Thomson Publishing I(!)P'

ISBN 918-1-4151-6166-5 ISBN 918-0-381-35355-5 (eBook) DOI 10.1001/918-0-381-35355-5

AII rigbts reserved. No part of tbis publication may be reprodueed, slored in a retrieval system or transmitted in any form or by any means, electtooic, mecbanical, pbotocopying, reconliog or otherwise, witboul tbe prior permission of tbe publisbers. Applicatioos for permissioo sbould be addressed ro tbe rigbts manager al tbe Loodoo address of tbe publisber.

The publisber makes no representation, express or implied, witb regard 10 tbe accuracy of tbe information contaioed in tbis book aod canoot accept any legal respoosibUity or Iiability for any errors or omissions tbat may be made.

A cataIogue record for this book is available from the British Library

8 Printed on permanent acid-free text paper, manufactured in accordance with ANSIINISO Z39.48-1992 (Permanence ofPaper).

Preface

Committees

CONTENTS

PART ONE ATM Switch Performance

1 Paradigm shift in reliability monitoring M. Perry, P. Schroeder; D. Vuncannon, R. Dipper; T. Bull, A. Nilsson and B. Peters

2 Performance analysis of multipath ATM switches under correlated and uncorrelated IBP traffic patterns A.-L. Beylot and M. Becker

3 Performance of the neural network controlled ATM switch V.M. Sku lie and ZR. Petrovic

4 A new method for assessing the performances in ATM networks H.Lee

PART TWO ATM Network Performance

5 Overload generated by signalling message flows in ATM networks S. Szekely, I. Moldowin and C. Simon

6 Quantitative evaluation of scalability in broadband intelligent networks G. Karagiannis, v.F. Nicola and I.G.M.M. Niemegeers

7 Hop-by-hop option based flow-handling compared to other IP over ATM protocols M. V. Loukola and 1.0. Skyttii

PART THREE Traffic Characteristics

8 Peakedness characterization in teletraffic S. Molnar and G. Miklos

9 On the combined effect of self-similarity and flow control in Quality of Service for transactional internet services 1. Aracil, D. Morato and M. hal

PART FOUR Multicast

lOAn analysis of retransmission strategies for reliable multicast protocols M. Schuba and P. Reichl

ix

xi

3

14

26

38

49

51

65

83

95

97

111

123

125

vi Contents

11 Scheduling combined unicast and multicast traffic in WDM Z. Ortiz, C.N. Rouskas and H.C. Perros

PART FIVE Admission and Trame Control

12 A family of measurement-based admission control algorithms Z. Tur6nyi, A. Veres and A. 0l6h

13 Resource reservation in a connectionless network A. Eriksson

14 Buffer analysis of the explicit rate congestion control mechanism for the ABR service category in ATM networks C. Blondia, O. Casals and B. Van Houdt

15 A new traffic control algorithm for ABR service A. Bak and W Burakowski

PART SIX Video over ATM

16 On the efficiency of statistical-bitrate service for video C. Karlsson

17 Predictive shaping for VBR MPEG video traffic transmission over ATM networks L de la Cruz, J.J. Alins and J. Mata

18 Circulant matching method for multiplexing ATM traffic applied to video sources K. Spaey and C. Blondia

PART SEVEN Applied Queueing Theory

19 Approximate analysis of a dynamic priority queueing method for ATM networks A. Chanwani and E. Celenbe

20 Using Gibbs sampler in simulating multiservice loss systems P. Lassila and J. Virtamo

PART EIGHT Mobility and Wireless Networks

21 Effects of user mobility on a TCP transmission A. Fladenmuller and R. De Silva

22 Achievable QoS in an interface/resource-limited shared wireless channel J.M. Capone and l. Stavrakakis

23 Call connection control in CDMA-based mobile networks with Multiple frequency assignments S.-H. Lee, S.-H. Kim and S.-W Park

PART NINE Multimedia Applications

24 Authoring and E-LOTOS conception of interactive networked multimedia applications in MUSE environment L.P. Caspary and M.J. Almeida

137

151

153

165

177

189

203

205

216

234

247

249

261

273

275

283

295

307

309

Contents

25 Simple integrated media access-a comprehensive service for future internet J. Ruutu and K. Kilkki

26 Performance evaluation of an inter-stream adaptation algorithm for multimedia communications A. Youssef, H. Abdel-Wahab and K. Maly

Index of contributors

Keyword index

vii

321

333

345

347

PREFACE

During the last two decades we have seen a tremendous development within the computer and communication industry. The ever increasing density on silicon, the increasing transmission speeds on fiber based systems as well as twisted pairs, the revolutionary development in the wireless area and of course the Internet have all led to many opportunities for new service developments. It is interesting to note that the last time this conference was held three years ago, the Web really did not fully exist.

We are now ready to face new interesting challenges. It is an utmost importance for the performance community to focus on the modeling and analysis of the Internet, the multimedia applications and the untethered applications that are coming to the forefront. There will be a need for new and better simulation methods, new analytical tools and a much better understanding of measurement techniques.

"Performance of Information and Communication Systems", PICS'98, which takes place in Lund, Sweden, May 25-28, 1998, is the seventh conference in a series on performance of communication systems organized by IFIP TC 6, WG 6.3.

In response to our call for papers, we have received nearly fifty submissions. Each paper was distributed to three reviewers for judgment. As a result the Program Committee accepted 26 papers for presentation. In addition, we have invited Mr. Lars-Erik Eriksson, Technical Director at Ericsson Telecom in Stockholm, to give a keynote address entitled ''The changing customer interface". We are grateful to the authors of the papers, the members of the Program Committee, the referees and all the participants in the conference. Without their dedication and active involvement, the conference would not have achieved its current quality.

Ulf Korner and Arne A. Nilsson

Editors

GENERAL CONFERENCE CHAIR Lars-Erik Eriksson, Ericsson, Sweden

CO-CHAIR Ulf Korner, Lund University, Sweden

EDITORS

Ulf Korner Arne A. Nilsson

Lund University, Sweden North Carolina State University, USA

PROGRAM COMMITTEE Ake Arvidsson Chris Blondia Miklos Boda Olga Casals Serge Fdida Bjarne Helvik Villy B Iversen Johan M Karlsson Konosuke Kawashima. UlfKorner Paul Kuehn Karl Lindberger Arne A Nilsson Christian Nyberg Harry Perros Michal Pioro Ramon Puigjaner Guy Pujolle Anders Rudberg Michael Rumsewicz Ioannis Stavrakakis Yutaka Takahashi Don Towsley Jorma Virtamo

University of KarlskronaIRonneby, Sweden University of Antwerp, Belgium Ericsson Traffic Lab., Hungary Politechnic University of Catalonia, Spain University Pierre et Marie Curie, France Norwegian University of Science and Technology, Norway Technical University of Denmark, Denmark Lund University, Sweden NTT,Japan Lund University, Sweden University of Stuttgart, Germany Telia Research, Sweden North Carolina State University, USA Lund University, Sweden North Carolina State University, USA Warsaw University of Technology, Poland Universitat de les Illes Balears, Spain University of Versailles, France Ericsson Telcom, Sweden Software Engineering Research Centre, Australia Northeastern University, USA Nara Institute of Science and Technology, Japan University of Massachusetts, USA Helsinki University of Technology, Finland

LOCAL COMMITTEE Johan M Karlsson UlfKorner Christian Nyberg Michal Pioro

PART ONE

ATM Switch Performance

1 Paradigm Shift in Reliability Monitoring

M. pe~, P. Schroeder, D. Vuncannon, R. Dipper, T. Bull Nortel orthern Telecom) RTP, C 27709-3478, USA, [email protected]

A. Nilsson North Carolina State University Dept. ofECE, Raleigh, NC 27695, USA, [email protected]

B. Peters Ameritech 220 N. Meridian, Room 910, Indianapolis, IN 46204, USA

Abstract

Reliability and maintenance of telecommunications equipment is evolving and continues to evolve. Improved hardware, development of software engineering principles, and better understanding of procedures have reduced system downtime. This is reflected in more stringent downtime specifications in the telecommunications industry. The makeup of failures leading to downtime has also changed. Advances in digital equipment have dramatically reduced hardware problems. Although software has also improved, more is demanded of it, and it has not improved at the same rate as hardware. Procedural techniques have also improved--better user interfaces, and improvements in process have led to fewer failures. However, maintenance personnel maintain more equipment than before, and in consequence, procedural failure rates have not improved as fast as those for hardware. Software and procedural problems--not hardware--are now the dominant reasons for outages. Not only do they cause most outages, but the public perceives these outages to be worse. Yet the current in-service auditing of telecommunications equipment may still be based on a paradigm of preventing outages caused by relatively unreliable hardware. Auditing--the inspection and testing of communications equipment--is performed on a regular basis. The purpose of auditing telecommunications switching equipment is to improve system reliability. For duplex equipment (equipment consisting of two identical units, one of which takes over if the other breaks down) auditing takes place on both the active and inactive units. If problems are found, repairs can be made before service is impacted. Despite this clear benefit, audits also incur costs. Auditing invokes software which itself has a failure rate. Audit testing can lead to two types of incorrect conclusion, both of which can lead to unnecessary repairs, or to a dangerous misperception that the equipment is working properly. The first type of incorrect conclusion is a false positive--the audit shows there is a problem

Performance of Information and Communication Systems U. Komer & A. Nilsson (Eds.) @ 1998 IFIP. Published by Chapman & Hall

4 Part One ArM Switch Performance

when none exists. The second is a false negative--the audit shows there is no problem when one exists. Reducing the incorrect audit conclusions will reduce the dominant failures of today--software and procedural. Since audits incur both costs and benefits, the natural conclusion is that audits should be run neither too frequently nor too infrequently. Yet there is a lack of guidelines on how often to perform audits. Our hypothesis is that audits are run too frequently for today's mix of failures. We develop a detailed reliability model of a generic duplex module for switching equipment. Our intent is to provide a useful methodology and some results that are independent of any manufacturer's equipment. The model shows that selecting the correct audit frequency saves significantly on downtime and maintenance costs. The results of this modeling were then applied to live equipment in the field. The reported results are very encouraging--81 % less outages, 79% less software traps, and 39% fewer hardware failure reports.

Keywords

Reliability, audits, switching equipment, outages, maintenance, duplex.

1 INTRODUCTION The reliability of switching equipment is changing. Section 12, of the LATA Switching Systems Generic Requirements (LSSGR),[l] states that:

''A group of 24 or more trunks should be out-oJ-service Jor no more than 20 minutes per year"

A more recent supplement to this document[2], specifies downtime affecting 100 or more trunks states:

"Digital Trunk Multitermination Downtime shall be no more than 1.2 minutes per year"

Improved reliability and more stringent requirements result from improved hardware, software, redundancy, and telephone company procedures. Hardware reliability in particular has improved dramatically. Most personal computers users will agree that modern microprocessors and memory are far more reliable than they were 10 years ago. The same is true of switching equipment. More rigorous testing, structured and object-oriented programming, improved operating systems, and memory protection have all helped reduce software failure rates. Better understanding of user-friendly interfaces and human factors have also led to improved procedural failure rates. However these reductions do not fully characterize the change in reliability; the failure mix has changed as well. Although hardware is now extremely reliable and rarely fails, and software has improved, more is demanded of software, so it now accounts for a greater proportion of errors. Procedures also have improved, but larger, more complicated systems are being maintained by fewer people, so there are proportionately more procedural failures. Furthermore, the public perceives outages caused by procedural or software failures to be worse. Therefore if significant gains in reliability are to be made, software and procedural failure rates must be targeted.

Paradigm shift in reliability monitoring 5

To further reduce software failure rates, the types of the software failure must be understood. For this paper, the software failures we consider are those that are sufficiently severe to bring down a unit of duplex switching equipment.

At the risk of over-simplification, software failures fall into two categories: maintenance and call processing. Call processing software errors cause failures less often than maintenance errors because call processing code is more thoroughly tested through use of simulated traffic and in general is more visible[3]. Also, there are fewer exceptions in call processing software paths than in maintenance software. Maintenance software, being less visible with more exceptions, is less well tested. Our focus for software will be on reducing maintenance software errors.

There are many approaches to reducing procedural errors. Some major examples follow.

• Improve processes: Use two repair persons instead of one, even though this will increase costs.

• Make equipment easier to repair: Create better documentation and improve human factors design.

• Increase necessary maintenance actions: Ensure true failures are not ignored.

• Reduce unnecessary maintenance actions: Maintenance actions are inherently risky since repairs are intrusive and increase the chances of other failures. For instance, the wrong card might be replaced when a circuit pack is being changed.

Our focus for procedural problems will be on increasing necessary maintenance actions and reducing unnecessary maintenance actions.

Fortunately, both maintenance software failures and procedural problems can be addressed by a single operational decision to modify the continuous auditing of hardware.

Operational tests or audits form a large part of maintenance software. Used for testing switch equipment and taking corrective action, audits are scheduled by the unit's operating system, and run as maintenance processes which check the status of the communications equipment. In duplex configurations, both units are monitored and tested. When problems are found they are reported and corrective action is taken. Audits for checking hardware sanity are run frequently. For example, many hardware components in the trunk peripherals for Nortel' s DMS-100 switching equipment are checked every 10 to 400 seconds.

Audits bring the benefit of being able to make repairs before service is affected. If the inactive unit of a duplex peripheral has a detectable fault on a circuit pack, the audit will find it, report it to the operations personnel, and a repair will be made. Without the audit, the fault could remain undiscovered, so that when an error occurred on the sound unit, the backup (inactive) unit would be unable to assume duty; resulting in an outage.

Audits come at a price, however. Since they are tasks scheduled by the operating system, audits can "trap" (suffer a software failure); they can also report a problem where none exists (false positive); and they can also fail to report a

6 Part One ArM Switch Peiformance

problem when one exists (false negative). Software traps and false positive reports have similar results: the unit is taken out of service for repair. Unnecessary failures and repairs increase maintenance costs and decrease reliability. Furthermore, when the false positive rate is high, telephone personnel begin to mistrust the alarms, and may not respond to real problems. False negative reports decrease the benefit of testing, since audits need to find problems to provide value. They also lead to a faulty system state--which increases the chances of software failure.

The conclusion, therefore, is that audits should be run neither too frequently nor too infrequently.

It seems likely that the frequency of auditing has not kept pace with the changing failure rates. Formerly, under the paradigm that hardware was "unreliable", frequent hardware checks made sense--even at the expense of more procedural and maintenance software failures. But under the current paradigm that hardware is very reliable it would not make sense to risk the increase in software and procedural failure rates associated with frequent auditing.

In summary, the hypothesis is that running the audits less frequently will improve reliability and reduce maintenance costs. As a result, there will be fewer software failures in maintenance code, fewer procedural outages, and greater responsiveness to real problems because there will be fewer false positives.

The costs and benefits of auditing were weighed in a detailed analytic and simulation modeling exercise. This exercise not only provided a means of determining how much auditing should take place, but also gave further insight on whether audits were scheduled too frequently. Best estimates were then made for more appropriate audit schedules. These new schedules were tested in the field. The results, while not definitive, are encouraging.

2 MODELS The model for determining the correct audit schedule needed to be relatively complex. To understand the state of a duplex peripheral, the state of both active and inactive units must be known. This state depends on reality, perception, and failure-type.

Reality refers to whether the unit can perform service. Perception refers to whether the unit believes itself to be capable of performing service. Many states have a mismatch between the reality and perception which can cause inappropriately risky actions or lack of appropriate actions. If a unit is down, for example, but appears to be up, actions (such as repair, or switching activity to the inactive unit) will not take place. Conversely, if a unit appears to be down when it is up, expensive, risky, and unnecessary repairs will be performed. This mismatch between perception and reality is driven by the interaction between failures and audits. There are three types of failure. The first, Type 1, includes failures that are immediately obvious to the system. These cause events in the peripheral which are understood and reported by the software. For example, if a facility interface


card fails, frame synchronization is lost, the unit reporting the event runs tests to isolate the failure, and issues a report.

The second type of failure includes those where the system depends on the audit system to find them. The failure will not trigger operational events that would be understood by the system, since some errors are only visible when specific diagnostics are run. (Diagnostics are run periodically to check sanity in the units.) These are shown as Type 2 failures in the state table later in this document.

The third type of failure includes those the system does not find. They do not trigger events recognized by the software, nor are they detectable by the periodic audits, since diagnostic coverage is not 100 percent. Such failures are serviceaffecting, so complaining customers or observant telephone company personnel will eventually discover them. These are shown as Type 3 failures in the state table below.

2.1 State Descriptions Not all states generated by all combinations of the variables need be described because most states are not feasible. For instance, if both units are up and are perceived as being up, it makes no sense to categorize the failures since there are none (Not Applicable, NA, in the last two columns in Table 1). Similarly, when a unit is perceived as being down, it is unnecessary to describe the failure type, since the failure or perception of failure is already known, and is unimportant because a repair action will inevitably occur.

Table 1 contains the list of system states. State 1 is the typical healthy state--both units are up and perceived as up. State 5 is an outage--when both units are down and perceived as being down. States 7 and 8 are "unnecessary" outages where the active unit is down, but perceived as up, and the inactive unit is able to assume service if directed to do so.

T bl 1 S a e : System states State Perception Reality Perception Reality Type 2 or Type 2 or

Active Unit Active Unit Inactive Inactive Unit Type 3 Type 3 Unit Active InActive

1 up up up up NA NA 2 up up down NA NA NA 3 up up up down NA Type 2

4 up up up down NA Type 3

5 down NA down NA NA NA 6 up down down NA Type 2 NA 7 up down down NA Type 3 NA 8 up down up up Type 2 NA 9 up down up up Type 3 NA 10 up down up down Type 2 Type 2

11 up down up down Type 3 Type 2



8 Part One ATM Switch Peiformance

Using Markov modeling [4] [5] and numerical methods [6], the probabilities of being in state i--1ti (i=1,00,13) can be determined. The outage states are 5,6'00.13. The sum of these probabilities, multiplied by the number of minutes in a year, gives the expected number of downtime minutes per year--D.

13 D = 60 * 24 * 365.25* L1ti

i=5

3 MODELING RESULTS--ENGINEERING AUDIT FREQUENCY In this section the objective is to determine audit frequencies that result in nearoptimal reliability as measured by downtime and incidents. The analysis was done by independently considering the performance of individual hardware components in a duplex standby (inactive) peripheral. The failure rate, audit rate, false negative rate, false positive rate, and Type 3 failure discovery rate were estimated for the auditable hardware components. The best way to calculate the failure rates was to examine a large population of field data, software-generated LOGs, return rates, and fault-found rates on a per-circuit pack basis. Although this calculation was made for Nortel products in the US market, the results presented in this paper are based on failure rates in a generic duplex switching peripheral.

For a unit with 20 hardware components, using downtime reliability requirements as specified in [1], industry estimates on repair and dispatch times as in [1,2], breakdown of failures as in [1,2], and a procedure as in [7], failure rates ranging between 500 and 4000 FITs (failures in a billion hours) were found to be reasonable.

There were, however, certain limitations to the analytic modeling and engineering approach. The time between audits was closer to being fixed than to the classical exponential assumption. Also, a real-life unit consists of many hardware components with failure and audit rates of their own. Ideally, the analytical model should be composed of all the individual hardware components and their own failure and audit rates, but such a model would be too big to interpret and draw practical conclusions. Instead, the model used an aggregate of many hardware components and related failure and audit parameters. The method used to engineer the audit frequencies was to use the analytic model on individual hardware components one by one using relevant parameters. A simulation accounting for the fixed audit times and multiple hardware components is described in Section 4.0. It was used to understand the impact of these issues.

Other important parameters included false negative probability, Type 3 failure discovery time on the active unit, Type 3 failure discovery time on the inactive unit, mean time to repair, and probability of destructive repair (Pd). These parameters and their assumed values are discussed in Section 3.3, Assumptions.

The engineering methodology included determining the FIT rate, the probability of false positive, and the apparency level (this is the fraction of failures that are Type 1 failures) on a per hardware component basis. The time between audits on the inactive unit was varied discretely between 10 and 2880 seconds, and the time between audits on the active unit was varied discretely from 10 to 2880 seconds


for each fixed time between audits on the inactive unit. The FIT rate, false positive probability, and apparency level were then varied individually to yield other sets of results. The FIT rate was varied discretely from SOO to 4000. (As previously discussed, this should cover a wide range of FIT rates for both the hardware components and the generic peripheral.) The false positive probability took on two values, 10"-6 and 10"-7.The apparency level (see section 3.1) took on values of 0.0, O.S, and 1.0 for the active unit, with an apparency level of 0.0 assumed for the inactive unit in all cases. As a result, for each ordered triple of FIT rate, false positive probability, and apparency level, "good" audit frequencies were obtained for both the active and inactive units. A summary of the results is given below, together with an example of how to use the Table.

3.1 Audit Frequency Engineering Table The following table is indexed on hardware component FIT rate, false positive probability, and apparency level. An apparency level of O.S (Appar=O.S) means that SO% of the failures are of Type 1 and the other SO% is the total of Type 2 and Type 3. The false-negative probability is used to partition the Type 2 and Type 3 failures. For each ordered triple of these parameters, effective times between audits on both the active and inactive units are found in Table 2. The analytical results assume the capability of having distinct audit frequencies for both the active and inactive units.

T bl 2 Audit E ' a e npneenn2 Tbl ti T' Bt a eor nne e ween Audits FITS Active IActive Active IActive Active IActive

Appar=O ~ppar=O Appar=O.S ~ppar=O.5 Appar=O.5 ~ppar=O.S --6 0-7 --6

Pfp = 10-1 -6 Pfp = 10-7 Pfp = 10 Pfp =1 Pfp = 10 Pfp = 10

SOO (360,2880) (240,2880) (720,2880) (240,2880) 28802880 2880,2800 1000 (360,2880) (180,2880) (360,2880) I (180,2880) 2880,2880 2880,2880 2000 (240,2880) (90,2880) (360,2880) I (180,2880) 2880,2880 2880,2880 3000 (180,2880) (90,2880) (240,2880) 1(120,2880) 2880,2880 2880,2880 4000 (180,2880) (90,2880) (240,2880) 1(120,2880) 2880,2880 2880,2880

3.1 Using the Engineering Table The Engineering Table gives an effective audit frequency for a given peripheral hardware component. To use Table 2, the FIT rate, the probability of a false positive diagnostic, and the apparency level of failures for the hardware component must be known. For example, if a hardware component is known to have a FIT rate of approximately 1000 FITs, a diagnostic false positive probability of 10"-6, and an apparency level of approximately O.S, the Table shows the "best" time between audits to be 360 seconds on the active unit and 2880 seconds on the inactive unit.

An inter-audit time of 2880 seconds may not be truly "optimal", but rather the upper bound on the inter-audit time for the numerical results. Extending the audit times further may bring additional benefits, but of diminishing returns.

10 Part One ATM Switch Performance

3.2 Parameters and Assumptions Other parameters used in Table 2 are defined in the following list, which also includes assumed values for each parameter. False Negative Probability: This was assumed to be 0.1; and after discussions with maintenance personnel in central offices, and research into industry specifications, diagnostic coverage of 90 percent was assumed. Type 3 failure discovery times for the active and inactive units were assumed to be 0.25 and 2.0 hours respectively. These figures were arrived at after discussions with telephone personnel regarding various products in their networks. Mean Time to Repair was assumed to be one hour [1].

Probability of Destructive Repair: The probability that a procedural error will cause additional problems on an active unit while a problem is being investigated was assumed to be 0.01. This assumption was corroborated in conversations with workers at two major telephone operating companies. These assumed parameter values were "conservative"; that is, they favor more frequent auditing. For example, 90 percent coverage is quite high. If lower coverage were assumed, the optimal audit frequency would be less. 3.3 Engineering Graphs Some examples of how reliability responds to the model parameters are shown in the graphs that follow. Table 2 was developed from graphs like these.

Outages per Year per Peripheral

0.08---------------.. 0.08

0.06+---------------.. 0.06

0.04--=---------------+00.04

0.02 ~iiii;::::i==:::::;~=:J!!lmc::::;A~t 0.02

ol-.... - __ -r-_-...... .....,r--...... ---+ o

Active Inter Audit Time (seconds)

FITs=500, Incidents, Active Unit failures not apparent, False positive=10"-6 Outages per year per peripheral with inactive inter audit time as a parameter.

Paradigm shift in reliability monitoring

Downtime Hours per Year per Peripheral

0.04·,..--------------..... 0.04

..... --------------+0.03

10 secs

~~::;==::O:::====::::~Cl1 0.02

20secs

o·~~-~~~_r-~_.-~-r--+

= Active Inter Audit Time (seconds)

o

11

FITs=500, Downtime (hours), Active Unit failures not apparent, False positi ve= 1 0"-6 Hours of downtime per year per peripheral with inactive inter audit time as a parameter.

3.4 Modeling Conclusions Given that hardware reliability has improved vastly over the last 10 years, it is easy to schedule audits too frequently. The engineering approach allows more appropriate audit frequencies to be selected in a scientific manner.

4 SIMULATION MODELING A simulation model was developed for a duplex peripheral consisting of a number of hardware components, each with its own family of parameters including failure rates, audit rate, and repair rates as described in Section 3.0. The simulation could execute with either exponential or deterministic times between audits. Only a limited number of scenarios could be covered because there were so many parameters.

When the simulated system had a single hardware component and exponential service times, the simulation results and analytical results matched, as was to be expected. Moreover, when the simulated system had multiple hardware components and deterministic times between audits, the results for optimal audit rates were similar to those for the analytic model. Optimizing the audit rate for the individual components with exponential times seemed to match well with the best audit rates for the full system with multiple hardware components in the


simulation model. Nor did the determinist times impact optimum audit frequency (See [7] for a sensitivity of the fixed testing times as compared with the exponential.) This indicated that engineering the audit frequency as described in section 3.0 was appropriate. Results depended heavily on input data that had been carefully estimated through analyzing industry data and specifications. A field experiment was undertaken to further verify the approach and hypothesis.

5 EXPERIMENTAL VALIDATION An audit frequency experiment was conducted to validate (or invalidate) the analytic and simulation modeling results described previously. Actual field results were used to lend credence to the hypothesis that auditing is being carried out too frequently. An experiment was undertaken to reduce the audit frequency by a factor of 10, using a simple procedure that was easily applied to 13 peripherals in a large, feature-rich DMS switch in an urban area on the Ameritech network.

A special monitoring system installed in the office with the reduced audit frequencies collected details on the office performance. These details, which included system state tracking, audit reports, software failures, and hardware failures, were downloaded, aggregated, and reported on a daily basis.

To run a complete experiment it was necessary to estimate how much data should be collected. The data was measured in terms of peripheral in-service years, taking into account both the number of peripherals in the experiment and the length of time being monitored. For example, 10 peripherals monitored for one half-year would provide five years of in-service data. Applying a method for determining sample size for comparative experiments in [8] showed that it would take 100 in-service years to be 80 percent confident of detecting a 20 percent difference in outages between systems with the old and new audit frequencies. Less data would be needed to understand the differences in software errors and false positives, since these events are less rare.

So far 12 in-service years of data for the experimental group has been collected, results to date are promising. Eleven similar-sized switches with hardware and software similar to those of the experimental switches were also monitored over the same period of time. The measures were averaged and compared with the experimental group with the reduced audits. The results are summarized in Table 3.

T bl 3E a e ~xperlmen tal R nits P es ercen t R d f n in the Experimental Group e uc 10

Measure Percent Reduction

Outages 81% Software Traps 73%

Hardware Failure 39%

All measures are favorable. Not only was the experimental switch more reliable, it was also cheaper to maintain, since fewer maintenance actions were required.

It should be noted that slowing the audits does not affect the number of true hardware problems that are eventually found, the cost is that some failures are discovered later. However, the number of false positive hardware reports


decreases, and the data supports this. Software traps are also interesting; the data shows that running audits less frequently is helpful.

On the qualitative level, the site engineer monitoring the switch said ''We have not seen any problems with the reduced audit frequency. It has not contributed to any peripheral outages or any other problem."

Another operating company that has changed audit frequency in a test switch made similar qualitative observations, however no special monitoring was done. Plans are now in place to change the audit frequencies in four new switches.

Although there is insufficient data to make statistical statements at traditional levels of confidence, the data on running audits less frequently is very promising.

6 SUMMARY Changes in reliability and failures in switching equipment have been discussed. Hardware reliability has improved dramatically. Software and procedures have also improved also, but not as much as hardware. Analysis focused on maintenance software, since more problems occur there than in call processing software. For procedural problems, effort focused on minimizing unnecessary maintenance actions. Continuous auditing of the system was then considered, and the hypothesis made that the amount of auditing currently taking place was based on the outdated premise that hardware was unreliable and needed very frequent checking. We speculated that current auditing schedules did not adequately account for the improved hardware reliability. An analytic model was developed that accounted for both the costs and the benefits of auditing. This approach was partially validated in simulation, and then used to engineer the audit frequencies. A field experiment was conducted on a feature-rich OMS switch where the audit frequency on 13 peripherals had been reduced by a factor of 10. The results of that experiment, although not definitive, are promising.

7 REFERENCES [1] Bellcore, TR-TSY-000512, LSSGR: Reliability, Section 12, Issue 3, February 1990. [2] Bellcore, TR-TSY-000512, LSSGR: Reliability, Section 12, Issue 3, February 1990; Supplement 1, August 1993. [3] Houck, OJ., K.S. Meier-Hellstern, F. Saheban, and R.A. Skoog, Failure and Congestion Propagation Through Signaling Controls, ITC-14, Antibes Juan-IesPins France, June 1994. [4] Kleinrock, L., Queuing Systems Volume I: Theory, New York, 1975. [5] Bellcore, SR-TSY-OOl171, Methods and Procedures for System Reliability Analysis, Issue 1, May 1989. [6] Stark, P., Introduction to Numerical Methods, New York Macmillan Publishing Co., Inc., 1970. [7] Perry, M., O. Hickman and A. Nilsson, Optimal Execution Tests and System Reliability, Globecom, London, November 1996. [8] Snedecor G. and Cocharan G, Statistical Methods, Iowa State University Press, August 1989.

2 Performance analysis of multipath A TM switches under correlated and uncorrelated mp traffic patterns

A.-L. Beylot Laboratoire PRiSM, Universite de Versailles 45 Avenue des Etats-Unis, 78035 Versailles Cedex - FRANCE e-mail: [email protected]. Tel (+33) 1 39254059 M. Becker Institut National des Telecommunications, 9 rue Charles Fourier, 91011 Evry Cedex - FRANCE and Associate member of MASI Lab. 5 place lussieu, 75230 Paris Cedex, FRANCE e-mail: [email protected], Tel: (+33) 160764781

Abstract An A TM Clos switch under bursty Interrupted Bernoulli Processes is studied at the cell level. Different correlated and uncorrelated traffic patterns are considered : cells of a given burst mayor may not belong to the same VPNC and be directed to the same output port of the switch. Uniform traffic, SSSD (Single Source to Single Destination) and a SSSD high traffic embedded in a uniform traffic are considered. Cells of a given burst are routed independently. So a resequencing mechanism has to be implemented. Approximate analytical models of the switch are proposed, they are validated by discrete event simulations for the parameter values for which simulations can be run. It is shown that such interconnection networks lead to good performance results even with small buffers under those different traffic patterns.

Key-words A.T.M, switches, analytic models, bursty traffic, finite capacity queue.

Perfonnance of Information and Communication Systems U. Komer & A. Nilsson (Eds.) @ 1998 IFIP. Published by Chapman & Hail

Performance analysis oJmultipath ATM switches 15

1. INTRODUCTION

Performance of A TM networks will depend on transmission and switching performance. Many ATM switch designs have been proposed. There are monopath networks (Banyan, Delta, Omega networks) and multi-path networks (Clos, Benes networks). The first ones are easy to design; a self routing algorithm can be used to route cells in the switch. For multipath networks, several complex algorithms may be implemented (cell or call based). The main problem when dimensionning A TM networks is due to the fact that traffic is not well characterized and that input traffics into units of the network are mostly superposition of output traffics from other units.

Several models have been proposed for interconnection networks, especially for Banyan Networks. But, in most of these papers, the authors studied the influence of the burstiness of sources but did not take into account the correlation between the destinations chosen by consecutive cells of a given burst. Input traffic was modelled by ON/OFF Markov processes (Bassi 1992) (De Marco 1994) (Morris 1992) (Theimer 1994). The interstage traffic was modelled by a Markov chain with several states which captures the burstiness of this traffic. The parameters of those Markov chains are fitted to the actual output traffic (first moments of the distribution of the busy period, of the idle period and of the time between two consecutive cells). This method is valid if it is possible to characterize the input traffic into one output queue of the following stage. This is wrong when considering that cells belonging to the same burst are directed to the same output since consecutive cells will be correlated. In those models, the burstiness of sources will be mostly absorbed by the splitting effect. Consequently, results are not far from results obtained using Bernoulli input traffics and Bernoulli interstage approximations.

Studies concerning the dissymetry of the traffic were performed for bufferless switches especially for Single Source to Single Destination (SSSD) traffics or Hot Spot traffics (Kim 1988) (Kim 1991). It was shown that mono-path networks lead to bad performance results because it is difficult to find a path for each incoming cell. The examples of non-uniform traffic patterns can be classified as follows : • Non-uniform destination distribution

- SSSD type : each input port sends most or all of its cells to one output port (Chen 1992), (Kim 1988),

- Hot-Spot Traffic pattern: one (or several) output has a higher access load (Chen 1992), (Bassi 1992) . • Non-uniform input process: in (Kim 1988), one input port sends its cells to one output port and receives a heavier load. In (Morris 1992) input processes are IBP type; they differ by the squared coefficient of variation.

In this paper, we consider bursty input traffics (IBP type). Three traffic patterns are studied. The first one is the "classical" uniform traffic pattern case.


In the second one, cells of a given burst will be directed to the same output port. In this SSSD traffic case, at a given time t, an output port of the switch is chosen by, at most, one burst. Consequently, "new" bursts are directed to "idle" ports of the switch (i.e. no burst is directed to this output port). This traffic case has been studied in a previous work (Beylot 1996) with a monopath interconnection network. It was shown that such networks lead to bad performance results: as soon as two bursts compeat for a common link inside the switch, the corresponding queue increases and cells are lost.

In the last traffic pattern, a case of non-uniform destination distribution and nonuniform input process has been studied. One hot-spot output port is considered, it corresponds to one high load input port. It is an SSSD high traffic embedded in uniform low traffic.

In the present work, we consider a switch based on a multipath interconnection network. Cells of a given burst are assumed to be routed independently. Consequently, it is necessary to reorder cells of a given burst. The resequencing cost is estimated by discrete event simulations. Approximate analytical models are proposed for the switch itself for the different traffic cases to evaluate the cell delay and the cell loss probability. They are validated by simulations.

The paper is organized as follows. Section 2 will present the interconnection network and the different traffic cases. In section 3 analytical models in the different traffic conditions are described. Results for the whole switch are presented in section 4. Approximations used in the analytical method will be discussed. From this study a dimensionning of the multistage network might be derived. It will be possible to answer the questions: "Does this multistage switch have good performance? Is resequencing bad for the performance?". Finally, section 5 summarizes our results and outlines directions for future works.

2 SWITCH ARCHITECTURE AND OPERA nON

Let us consider a switch based on a three-stage Clos network (Clos 1953). The global number of input/output ports of the switch is N, the number of input ports of the first stage switching elements is a and the number of paths b (C{ N, a, b)

configuration). Let us sum up the main characteristics of the considered switch: • Switching elements of a given stage are identical • They include dedicated output FIFO queues with finite capacity • No backpressure signals are exchanged between adjacent stages • In each stage departure are taken into account before arrivals • Internal, input and output links are assumed to have the same throughput.

In the first traffic case, let us assume that each input link is offered the same traffic load, destination addresses of the cells are uniformly distributed over all the output links of the network. Clos networks are multi-path. We choose the random policy in the present work : the choice of the matrix of the second stage is uniformly (and randomly) done. A reordering mechanism should be implemented.

Performance analysis of multi path ArM switches 17

But, since the number of inputlouput ports of the switch is large, this cost is negligible (Kohlenberg 1996). It is not evaluated in this paper.

In the second traffic case, let us assume again that each input link is offered the same traffic load, cells of a given burst are assumed to be directed to the same output port of the switch. In this case a random routing policy has also been chosen. An algorithm based on burst routing may lead to well known results on non-blocking Clos switches, as far as the number of paths in the switch b is greater or equal to 2a - 1, the cell loss probability is 0 and the cell delay equal to 3 time slots. This is too optimistic because the input traffic will not be exactly SSSD. A resequencing mechanism has to be implemented to reorder cells of a given connection. This mechanism may be quite complicated. In the present work, since only one burst may be directed to a given output port, cells of this given burst may be numbered when they enter the switch. In the resequencing buffer, cells may be ordered according to this number. The resequencing queue has two parameters: its capacity Cw and its timeout Tw. Losses in the switch increase significantly the number of cells in the resequencer, since the resequencer will wait for lost cells and keep the following cells in order to resequence them afterwards. The present algorithm is not of general purpose. In a real switch implementation, a common buffer should be implemented and several bursts should be managed.

In the last traffic case, a SSSD IBP traffic (high traffic) is embedded in a uniform IBP traffic (low traffic). In our simulations, resequencing will be operated only for high traffic. The low load and the uniform distribution implies that low traffic generally, does not need to be resequenced. The cost is negligible. The previous algorithm has been adapted. The only difference corresponds to the low traffic cells directed to the hot spot output port. In the output queue designed for high traffic, if a cell of low traffic arrives, it will be transmitted on the output link.

3 ANALYTICAL MODEL OF THE SWITCH

3.1 Traffic hypotheses and characterization

IBP processes are discrete time "ON/OFF" processes. During the "ON" period, a packet is emitted according to a Bernoulli process (parameter a). "ON" and "OFF" periods are geometrically distributed with parameter p and q. The rate A, the mean burst length LB and of the mean silence length Ls of IBP sources are :

A = a Pr[" ON"] = a l-q 2-p-q

1 1 LB=-- Ls=--

1- P l-q

3.2 Model of the uniform traffic case

Let us first consider a first stage switching element. As the choice of the output is random and equidistributed, the splitted process produced by an IBP process on input link m is an IBP process with parameters (p,q, a/b) where b is the number


of output ports of the switching element. The output queue is then an n - IBP / D / 1 / M queue with departures before arrivals. The analysis of this queue has been presented in (Beylot 1998). The output traffic of such a queue is a D-MAP (Discrete Markov Arrival) process (Blondia 1992) but the number of states of this process is too large (equal to the number of states of the preceding Markov chain). Let us approximate the output process of such queues by an IBP process (Beylot 1998). The parameters are fitted to the actual interdeparture time of cells. From this approximation of the output process of the first stage switching element, a solution of the second stage will be derived. The solution is then iterated for the third stage. It leads to a model of the whole switch.

3.3 Model of the switch in the SSSD Traffic case

Cells within bursts are randomly directed over the output queues of the first stage switching elements. Consequently, an output queue of a first stage switching element can again be modelled by an n - IBP / D / 1 / M queue. The output traffic of a first stage switching element will be splitted and the input traffic into an output queue of the second stage cannot be derived from the previous study (it should be necessary to know to which output port, cells are directed, the choice is not random anymore). In fact, let us focus on an output queue of the second stage. It receives cells coming from all the input ports of the switch directed to a given switching element of the third stage that have chosen the output port of the first stage connected to the tagged switching element. In the SSSD traffic case, it receives at most cells belonging to a bursts directed to the corresponding output ports of the third stage. The input traffic offered to a given output port of a second stage switching element can consequently be modelled by the superposition of a IBP processes with parameters P, q, alb because of the

splitting effect of the first stage. Those input processes will be modified by the first stage queue. So let us consider an output traffic of the first stage switching element. It corresponds to the superposition of a input traffics. As in 3.2, it can be approximated by an IBP traffic with parameters Po"" q.." a.., and consequently an

input process modified by a first stage switching element can be modelled by an IBP process with parameters Pout,qout' aoutla.

An approximate model of the second stage will consequently be derived from the study of an a - IBP / D / 1 / M with such parameters. Let us note that in this approximate model we did not take into account the fact that several bursts from a given switching element of the first stage may be directed to the same output port of the second stage.

When considering an output queue of the third stage, it appears that it receives cells from one input port of the switch. Let us model the first two stages by a queue with b servers, each server corresponds to a path. The mean response time of this queue corresponds to the mean response time derived from the analytical models of the first two stages. This response time is mainly composed of two parts : the

Performance analysis of multi path ATM switches 19

service time equal to 2 time slots and the waiting time experienced in the first two stage queues. Let us approximate this response time by a Geo+D process. The deterministic part of this response time corresponds to the service time and the geometrical part to the waiting time. The third stage is modelled by a constant service time and finite capacity queue. Figure 1 shows the model used to study the performance of the third stage. The source is an IBP I Geo + D I bIb queue. It will be valid as long as the cell loss probability of the first two stages is negligible. Details of this study are presented in (Beylot 1998).

Geo+D M

Figure 1 Model of the third stage.

3.4 Model of the SSSD + uniform traffic case

In this traffic case, using IBP approximations for the interstage traffics, analysis of the different stages can be done by the study of n - IBP I DIll M and IBPI + n - IBP2 I DIll M queues. Details about different traffic types on different queues and the abalysis of the IBPI + n - IBP2 I DIll M queue are presented in

(Beylot 1998). On the last stage splitted processes corresponding to the same burst (high traffic) will go to the same output, so it would be very wrong to assume them to be independent. The solution that is proposed here is to consider that at one time there will be only one input link on which the burst will arrive.

For each low traffic cell the choice of the output by each cell from one burst is random. Consequently, the independence assumption is not bad for the low traffic. So, we approximate input processes on the different links by assuming that on one link, there is a superposition of high traffic and of one low load process. It is a DB MAP process. The performance criteria on the last stage will be derived from the solution of this DBMAP+n IBPID/1IM queue.

4 RESULTS

Several parameter values are chosen. The C(128,4,8) configuration has been chosen (Beylot 1995). The whole cell loss probability on the three stages and the cell delay across the whole switch are represented for the approximate analytical model and the simulation as a function of the memory size of the first stage. The memory size on the first stage varies and the best value for the memory sizes of the second and of the third stage, for a given global memory size, is derived from the analytical model (the best value is the one that leads to the lowest loss probability).


The points in the analytical model are validated by discrete event simulations. Confidence intervals are around 10-20%. For cell loss probability of 10-7 there are 20% confidence interval. For cell loss probability higher than 10-6 they are around 10%. Let us note A : the analytical model and S : the simulations.

4.1 Results· Uniform Traffic Case

The global memory size in the switch is 128x72. The input load is 0.8.

5 .. s,------------,

5.

/ . . . ~ . . . , .. _ .. _ ........ _ ..• rfII-!P"!·· .... ···_··_·· ..... •• ....

5.2+----r----r---...... ----\ o 10 15 20

Memory size of the lint stage

.. ........ Lb=loo.l.soll.7l.A

- Lb=loo.Ls=llll.S ........ l.bo6.61l;1.25.A _ l.bo6.61l;1.21$

Figure 2 Cell delay as a function of the memory size of the first stage, a=0.95-Uniform Traffic.

10 -

~ 10

10 -4 .. ... :: 10 -5 '" j

'ii 10 -6

U

10 -7

10 15

Memory size of the lint stage 20

... _.. Lb=l(lO).s=IS.7l.A _ Lb=IOO).s=IS.7l.S

......... Lb=6.61,i...s=1.25,A

.......... Lb=6.67,L.s=i.25,S

Figure 3 Cell loss Probability as a function of the memory size of the first stage, a=0.95 - Uniform Traffic.

Figure 2 presents the cell delay and the cell loss probability as a function of the memory size of the first stage. The switch is heavily loaded (load is 0.8). Approximate analytical solution results and simulation results are given for two traffic cases: Lb = 100, L, = 18.7, a = 0.95 and Lb = 6.67, L, = 1. 25, a = 0.95. For the same traffic parameters, the two simulation curves are nearly the same and the two analytical models are also very much the same. So it appears that the burstiness has not much influence on the delay (Figure 2). Each analytical curve is

Performance analysis oJmultipath ATM switches 21

not far from the simulation curve (1 %), this validates for the chosen values of the parameters the approximate analytical model. It appears that the cell loss probability does not depend on the burstiness nor on the peak rate for a given load, but depends much on the memory repartition (Figure 3). The best memory repartition is 9-10-34. For the chosen values of the parameters, the simulation results are not far from the analytical model ; so it appears that the approximate analytical model is validated. This traffic case is not the most realistic one.

4.2 Results· SSSD Traffic case

In this traffic case, the global memory size inside the swich is 128x36. The mean input rate is 0.72 and the mean burst length is 100. The peak rate is 0.9. Figure 4 shows the cell delay and the cell loss probability within the switched. The cell delay do not depend on the memory repartition. Cell delay is around 4 time slots and is well approximated by our analytical model. The best memory configuration is (8-7-6). In this case the cell loss probability within the switch is approximately 10-6• The cell loss probability is well approximated by our analytical model.

4.5

4 _------- ~"'.A -, "'" ---.. DeJay-S

3.5

8 10 12 14

1E+OO

1E·01

1E·02

1 E·03

1E·04

1E·OS

1 E·06

8 10 12 14

~ ~

Figure 4 Cell Delay and Cell Loss Probability as a function of the memory size on the first stage, Lb = 100, L, = 25, a = 0.9 - SSSD Traffic.

1E'()1

•• -02 10

•• -03

..... 1---· ...... ·1 1--RUeq-Delay-s I •• -oe

o J-;::;::;::::;::::::;:~ 2 4 6 8 10 12 14

Figure 5 Resequencing Cell loss probability and Resequencing Cell Loss Probability as a function of the memory size on the first stage - Cw = 10, Tw=10, L" = 1 00, L, = 25, a = 0.9 - SSSD Traffic.


Let us analyze now the performance of the resequencing unit. Figure 5 shows the resequencing delay and the resequencing cell loss probability obtained by simulations. The resequencing buffer size CO' is 10. The value of the time-out TO' is also equal to 10. With those parameter values, the cell loss probability inside the switch and within the resequencer buffer are of the same order of magnitude. It is shown that when the cell loss probability within the switch is high, the mean resequencing time and the resequencing cell loss probability are quite high because the resequencing unit waits for lost cells.

lE-Dl 1.2

lE-D2 ~\. 1 ./--lE-D3

.. 0.8 ..... " "" ~

,

~ lE-04 o.s --Tw ~Tw

lE-DS 0.4

lE-06 - ......... 0.2

lE-D7 0

2 4 6 8 10 2 4 6 8 10

Figure 6 Resequencing Cell loss probability and Delay as a function of CO' (Tw=lO) and of TO' (Cw=lO), L" = 100, L, = 25, a = 0.9 - SSSD Traffic.

Let us analyze now the influence of the parameters CO' and TO'. We only investigated the case when the memory in the different stages is (8-7-6) i.e. the case when the cell loss probability within the switch is quite low. It is shown (Figure 6) that the performance of the resequencer mainly depends on the resequencer buffer size. The cell loss probability decreases with CO' (in this case TO' = 10). The analysis of the influence of the time out parameter is quite different. In the case when CO' = 10, the cell loss probability is higher when TO'=2. It seems that when Tw = 4, the best performance of the resequencing algorithm is reached. It remains constant and does not improve when TO' is larger than 4.

4.3 Results· SSSD Traffic embedded in a uniform traffic

The global memory size in the switch is 128x48. Let us note High(Low)-A = the analytical results for high(low) traffic; High(Low)-S = the simulation results. Let index h (resp. I) respectively refer to high (resp. low) traffic. An output port will be heavily loaded, so it is necessary to choose parameters such than the load is not more than 1 on this output link. The following parameters are considered in Figures 7 and 8 (the output traffic rate will be quite high on the hot-spot):

• low traffic: A., = 0.1, p, = 0.99,q, = 0.99875, a, = 0.9

• hi~h traffic: A.~ = 0.54, Ph = 0.99, qh = O. 985, a~ = 0.9

Performance analysis of multi path ArM switches

Cell delay in the switch

7

6 -'-Low-A - - -~ 5 -r-High-A

~ ---.-- Low-S 'ii 4

U

3 ------ High-S

2

3 4 5 6 7 8

Memory size in the first stage

Cell los. probability in the switch

1E-03

g ---+-- Low-A

~ 1E-04

£ ---a....- High-A

1E-05 "' ---+-- Low-S j 'ii 1E-06

--0-- High-S U

1E-07 3 4 5 6 7 8

Memory size in the fin! stage

Figure 7 Cell delay and Cell Loss Probability in the switch, Ah = 0_ 54, A, = 0_1 Lb,h = Lb" = 100 - Low load SSSD Traffic embedded in a uniform traffic.

7

6 5 .. Tw=2

4 ----4---Tw=6 ~

~ 3

2 • Tw=1O

1

0

2 6 10 14

Cw

Figure 8 Cell Delay in Resequencer for high traffic - Low load mixed traffic.

23

24 Part One ArM Switch Perfonnance

Let us note that an estimation of the number of desequenced cells is 2%. Using the same burst length with traffic rates equal to 0.54 and 0.36, it is around 7 or 8%. So resequencing does not cost much and since it was shown that this switch is performant it appears to be good to choose this multipath switch.

5 CONCLUSION

A multi path A TM switch performance has been studied under non-uniform traffic patterns. These hypotheses for destinations are reasonable, because of reservations in VPs and VCs of A TM networks. Uniform traffic destination has first been considered to extend the known results to multi path switches. It was shown that the burstiness of the sources is mostly absorbed by the splitting effect. This traffic case is too optimistic and simple Bernoulli approximations would nearly lead to the same results.

Single Source to Single Destination (SSSD) and SSSD embedded in a uniform traffic were then considered. Analytical model were derived for the different traffic cases. The approximation of most of the interstage traffics by IBP fitting traffic seems to be working. The proposed solutions gave good performance results. The results show that buffer placement in the switch is very important. This stands at least for the parameter values for which simulations may be performed. Traffic assumptions are realistic in this case. Performance results are good in the SSSD case. For SSSD imbedded into a uniform traffic, performance is good as long as for the heavily loaded output link the load is not prohibitive.

The Clos switch is multipath. An independent routing for each cell of the same burst has been assumed. It is necessary to reorder incoming cells. A study of some performance results of a simple resequencing algorithm has been estimated. Our aim was not do design a resequencing algorithm ; it was to estimate the order of magnitude of the resequencing cost, in these traffic conditions. In any case, the performance is not bad, even with small resequencing buffers. It might be interesting to solve the resequencer model.

As a conclusion it appears that this multipath switch and the cell routing inside the switch avoid the congestion problems that appears in a monopath switch (Beylot 1996). A Clos network seems to be a proper choice for a switch.

6 REFERENCES

Bassi S., Decina M., Pattavina A. (1992) Performance analysis of the ATM shuffleout switching architecture under non-uniform traffic patterns, in Proceedings of IEEElnfocom'92.

Beylot A.-L., Becker M. (1995) Dimensioning an ATM switch based on a threestage Clos interconnection network, Annals of Telecom. , 50(7-8), 652-666.

Performance analysis of multi path ATM switches 25

Beylot A-L., Harfouche I., Becker M. (1996) Performance Analysis of monopath A TM switches under correlated and uncorrelated traffic patterns, in 5th Open Workshop on High Speed Networks ENSTIStuttgart Univ., Paris.

Beylot A-L., Becker M. (1998) Performance analysis of multipath A TM switches under correlated and uncorrelated IBP traffic patterns with independent routing and with resequencing, PRiSM research report 98-04.

Blondia C., Casals O. (1992) Statistical Multiplexing of VBR sources: A matrixanalytic Approach", Performance Evaluation, 16(1-3), 5-20.

Chen D., Mark J. (1992) A buffer management scheme for the SCOQ switch under non-uniform traffic loading", in Proceedings of IEEE Infocom '92, paper IDA.

Clos C. (1953) A study of non-blocking Switching Networks", Bell System Tech. 32, 406-424.

De Marco M., Pattavina A (1994) Performance Analysis of ATM multistage networks with shared queueing under correlated traffic, in Proceedings of ITC'J4, 601-610, Juan les Pins.

Kim H.S., Leon-Garcia A (1988) Performance of Buffered Banyan Networks under Non Uniform Traffic Patterns, in Proceedings of Infocom 88, 344-353

Kim H.S., Widjaja M.G., Leon-Garcia A (1991) Performance analysis of output buffered Banyan Networks with arbitrary buffer sizes, in Proc. of Infocom '91.

Kolhenberg I. (1996) Performances des commutateurs ATM dans des conditions non-uniformes de fonctionnement, Phd Report Thesis, University of Paris 6.

Morris T., Perros H. (1992) Performance Modelling of a multi-buffered Banyan Switch under Bursty Traffic, in Proceedings of IEEE Infocom'92, paper 3D.2.

Theimer T. (1994) A New Model for the Analysis of Multistage ATM Fabrics, in Proceedings of ITC'J4, Juan Les Pins.

7 BIOGRAPHY

Andre-Luc Beylot received the engineer degree from the Institut d'Informatique d'Entreprise in 1989 and the Ph.D. degree in computer science from the University of Paris VI in 1993. From 1993 to 1995, he worked at the Institut National des Telecommunications, and from 1995 to 1996 at CNET (France Telecom Research Laboratory) in Rennes. Since 1996, he is an associate professor at the University of Versailles. His interests are in the performance evaluation of communication networks, especially with regard to A TM networks.

Monique Becker graduated from Ecole Normale Superieure de Jeunes FiIles in 1968, passed the mathematics "agregation" and received the State Doctorate degree from the University of Paris VI in 1976. She joined the National Center of Scientific Research where she had the responsability for a group of researchers working on performance evaluation. In 1987, she joined France Telecom University where she got the position of Professor and Chairman of the Computer Science Department. She is managing a group of researchers of the Department (including professors and Phd students) working on performance evaluation of computer networks. Their main interest concerns A TM networks.

3 Performance of the Neural network controlled ATM switch

V.M Skulic, Z.R. Petrovic Faculty of Electrical Engineering, University of Belgrade Bulevar revolucije 73, 11000 Belgrade, Yugoslavia Phone:+38111 3370106,fax:+38111 3248681, e-mail: [email protected], [email protected]

Abstract In this paper a new NxN space division A TM switch architecture based on banyan and neural network is presented. The switching function is performed by extended banyan network and the neural network controller is introduced to allow the recirculation of the misrouted cells. The paper analyses the switching performances, especially cell loss probability, and shows the advantages of the proposed switch.

Keywords Banyan, HOL blocking, recirculation, neural network

INTRODUCTION

A number of switching architectures has been proposed to implement ATM standard. The solutions can be generally placed in three categories: sharedmemory, shared-medium (bus) and space-division type. In this paper a new space

Performance of Information and Communication Systems U. Komer & A. Nilsson (Eds.) © 1998 IFIP. Published by Chapman & Hall

Performance of the neural network controlled ArM switch 27

division switching architecture based on self-routing banyan network is analysed. The advantage of the banyan network is its capability to decentralise switching control. Hereby, big switches, with huge capacity, can be built. The deficiency of the banyan network is low throughput, due to the HOL blocking (Karol et aI, 1987), which further decreases when the size of the switch grows.

Many architectures, such as Tandem banyan (Tobagi et aI, 1991) and Rerouting network (Urushidani, 1991), which overrides HOL blocking by offering multiple paths from each input to each output and by replacing input with output buffering, have been proposed. In Section 2.1, we briefly describe the architecture and the performances of the Extended banyan network (Petrovic et aI, 1997), which we choose as the core of the switch proposed in this paper.

There are other solutions using the windowing technique to eliminate HOL blocking. In that case, the cells in the input buffers are analysed by the centralised control unit to resolve the conflicts between them. In order to satisfy high speed requirements, the control unit may be realised as a neural network (Brown et aI, 1990 and Park et aI, 1994). In our solution, recirculation of the misrouted cells is introduced, and the main task of the neural network is to maintain cell sequencing. The architecture of the whole switch is described in Section 2.2. The neural network is the modification of the well known Hopfield network (Hopfield et ai, 1985) and is given in Section 2.3.

The mathematical model of the switch is given in Section 3. According to this model, we calculate the throughput and the cell loss probability of the switch in Section 4. These results are compared with the results obtained by the computer simulation and good agreement is achieved.

2 ARCHITECTURE OF THE SWITCH

2.1 The extended banyan network

The switch is based on extended banyan network with m stages, m>n=log2N, shown in Figure I. The main feature of this arrangement is that any n consecutive stages build a banyan network. Therefore, a cell that fails to take its desired route due to cell contention at stage k can restart its routing from stage k+ I. The cell may start and likewise finish routing at any stage, when it is directed toward output buffer. Therefore, a cell routing tag should have an additional field indicating how many stages the cell should pass from the present stage to its destination called RNS. The routing algorithm in every cascade is as follows: in the case of conflict the cell with lower RNS will be passed to its desired output of the switching element, and its RNS is decremented; the RNS of the cell that is misrouted is reset to n; there is a logical filter at the output of the switching element directing cells with RNS=O towards output buffer, and cells with RNS>O to the next cascade.

An initial value ofRNS at the switch input may be lower than n. Namely, ifinput address S,..I ••• S ISO and desired output address d,..I ••• dIdo are the same in h


consecutive bits S". .• SzSl and d". .. d]dl then RNS is set to n-h. The routing at stage k is perfonned according to the cells RNS's and two bits of the destination addresses, do if RNS=l, or dn-I-((k-I)mod(n-I)) if RNS:;tl. The switching element perfonning the routing function is simple, as well as the logical filters at the output of the element.

0000 1111

Figure 1 An extended banyan network with N= 16 inputs and m=9 stages.

It is possible to calculate the cell loss probability as the function of the number of cascades in the banyan network (Petrovic et ai, 1997), for unifonn traffic (incoming traffic is Bernoulli process, independent for each input, with unifonn distribution of requested output ports), if we neglect correlation between the traffics at different links of the same cascade.

We introduce Po as the offered traffic per input line, poCr) as the offered traffic with RNS=r, and ptCr) output traffic intensity at stage k with RNS=r. So,

(1)

The relations between traffic intensities in the consecutive stages are derived in (Petrovic et ai, 1997). They are:

(2)

(3)

n n-l

Pk(n)= LPk-l(i)-LPk(i} (4) ;=1 ;=0

Performance of the neural network controlled ATM switch 29

The above equations can be recursively solved to get the probability of cell misrouting, Pm" as the function of the number of cascades m,

n

LPm(i) Pmr = .,!;i-::!.l __

Po (5)

The results are given in Figure 2 for different number of inputs and input traffic loads. These results are well proved by the computer simulation.

Pm~cf ~~~~=-i----=:t=~n 10"1

162

163

164

165

10-6

167

168

169

161°'-----'----'------'----'-----'----' o

2.2 Proposed architecture

It is obvious that traffic intensity decreases from cascade to cascade, since it is proportional to the cell loss probability. We can see that we need 54 cascades for the probability ofmisrouting 10-8, with input traffic load 0.9 and 1024 inputs. After 27 cascades, cell loss probability is already 0.1, which means that input traffic intensity decreases under 0.09. In the second half of the extended banyan traffic intensity is very low, and these cascades are not utilised well. So, we shorten banyan network and introduce recirculation of the misrouted cells (Figure 3).

The cells that didn't find the wanted output in banyan network, are sent in the recirculation buffers and they are waiting for the next time-slot (interval equal to the cell's duration) to enter banyan and try again. The cells that reached the desired outputs are directed towards concentrators at the inputs of the output buffers. Only mk cells can pass through the concentrator in one time slot. The output buffer speed has to be mk times the speed of the input buffer in order to avoid losses.

It is necessary to solve the possible congestion at the input of the banyan network, because it may happen that there are cells in the recirculation buffer and in the


input buffer at the same time. The answer is to give priority to the cell from the recirculation buffer in order to reduce the cell delay. The second problem is that there is possibility to loose cell sequence. The cells that enter on the same input and want to exit on the same output would be from the same connection, and so, they must be delivered in the same sequence they entered the switch. Neural network controller is used in order to accomplish cell sequence, because it is very fast.

extended banyan with N inputs

and m cascades

output buffers

Figure 3 Block diagram of the proposed switch with recirculation of the cells.

2.3 Neural network controller

The task of the neural network controller is to choose as many cells as possible from N recirculation and N input buffers, but less than mko satisfying certain constrains: 1. If there is a cell in the recirculation buffer i, it enters the banyan network. Ifthere is a cell in the input buffer i too, it has to wait for the next time slot. 2. If there is a cell in the recirculation buffer i/ with destinationj, and there is a cell on the head position of the input buffer i2 with the same destinationj, then the cell from recirculation buffer enters the switching network and the cell from input buffer waits for the next time slot, because the cell from recirculation buffer might be from the same input originally, and it must reach the output before the cell from the input buffer i2• If we pass them both, it is possible that the cell from the input buffer i2 exits the banyan network before the cell from recirculation buffer i/. 3. If there are more than mk cells, with the same destination j, that may enter the banyan network concerning 1. and 2., then only mk cells are passed, and others have to wait in order to avoid losses on the concentrators at the input of output buffers. The priority is given to the cells from the buffers that are more occupied at that moment optimising the length of the buffers.

The neural network designed to fulfil these requirements is a modification of the continuous Hopfield neural network. It consists of 2N neurones, which are

Peiformance o/the neural network controlled ATM switch 31

associated with N input and N recirculation buffers. The block diagram of the neural network is presented in Figure 4, and the scheme of the neurone is given in (Brown et aI, 1990).

a

Figure 4 Block diagram of the neural network. Odd neurones are for input buffers, and even neurones are for recirculation buffers.

The output V of the neurone is the function of its input U:

v- 1 -1+exp(- gU)

(6)

where g is the gain of the neurone. The neurone is said to be OFF if V=O, and ON if V=l. Neurones are amplifiers with positive and negative output. The behaviour of the neurone is described by differential equation

dUo N --' =a.[. -to - ~ a ·H· .y.

dt "'. ~ . J ',J J' J=I,J~'

(7)

The external neurone input 1/ is determined accordingly to the fact whether there is the cell in the head of the buffer i or not, that is whether its momentary length Li is greater than 0

{mk ,L; >0

[. = , 0 ,L; =0.

(8)

The neurone threshold is set to ti, which is calculated on the basis of buffer length L/, in the way priority is given to the cells from more occupied buffers:

L· t; =0.75-0.5-'-.

N;n (9)


The parameter HiJ shows whether the connection between the output of the jth neurone and the input of the ith neurone is set up or not

{I ,w(i)= w(j)

Hi,j = 1 ,i=j-1,oddi

o ,other

(10)

where w(i) stays for the wanted output of the cell from buffer i. The gain favouriting cells from the recirculation buffers is denoted by aj, and it is applied to the neurones in connection with the recirculation buffers, only. It has been found that good results are obtained with armk and g=2.

The neural network is very fast, because it works in parallel, and it is possible to reach steady state in the interval of the time slot. The states of the neural network controller neurones determine from which buffers the cells enter the banyan in this time slot; their neurones are ON. The design ofthe neural controller is verified by the extensive computer simulation.

3 MA THEMA TICAL MODEL

In order to analyse performances of the proposed switch architecture, the original mathematical model is established according to the role of the neural network controller described in the previous section. The throughput T as the function of the number of cascades m and the cell loss probability Ploss as the function of m and the length of the input buffers N in are found on the basis of this model.

The mathematical model is established for the Bernoulli traffic at the inputs of the switch, with the probability of the cell arrival in the time-slot Pin' Suppose that the intensity of the traffic at the input of the banyan is Po. This traffic is some kind of mixture of the traffic from the input and recirculation buffers and it is not of the Bernoulli type. Namely, the destinations are not uniformly distributed between the cells. But, we can see from Figure 2. that the probability of the misrouting isn't much sensitive if we change Po. It is expected that it's even less sensitive on small changes of the distribution of wanted destinations. In paper (Giacomazzi et aI, 1996) it is validated for the similar extended banyan network. Hereby, we use the result (5) from Section 2.1, the probability of the misrouting in the banyan network, as the function of the traffic intensity on its input and the number of the cascades to fmd the traffic intensity of misrouted cells

(11)

Now, it is possible to find the probability Pgo that a cell from the input buffer is not blocked due to the reasons given in Section 2.3. It is the probability that there is


no cell in the recirculation buffer at the same input of the banyan, and there is no cell in other N-l recirculation buffers that want the same output. These events are independent because the cells from the input and the recirculation buffers are from different time-slots. Accordingly,

{ )N-I P go = (1- fJ 11- ~ (12)

Let qL be the probability that there is L cells in the buffer at the end of the timeslot. The state of the buffer, the number of the cells in the buffer at the end of the time-slot, is modelled as the discrete birth and death process with the probability of birth Pin and the probability of death Pgo, From this model, if Pin<l, we get the probability that the buffer is empty

(13)

Now, we can fmd the traffic intensity on the input of the banyan network if we suppose the events that there is a cell in the recirculation buffer and in the same input buffer are mutually independent. It isn't possible that the cells from both buffers enter the banyan in the same slot, so

(14)

It is possible to solve the equations (l1)-{14) iteratively, starting with Po=l. Upon the completion of this iterative process, using the birth and death model mentioned above, we can calculate the probability that there is no place in the input buffer for the incoming cell,

[ ( )]

Nin

Pin 1- Pgo ~oss = qo (1- .) (1- Pin)

Pm Pgo (15)

The throughput of the switch T is found by using a similar method. Generally, if the input traffic intensity is Pin=l, the input buffer saturates and the probability that it is empty is equal to zero, qo=O, which simplifies (14). Equations (11)-(12) aren't changed. When we iteratively solve this changed set of equations, we gain

(16)


We assumed that the traffics in the inputs of the banyan are independent and with uniformly distributed destinations, that is not true because of the recirculation. But, if the number of the inputs N is not very small, and the intensity of the recirculated traffic is low, these assumptions are reasonable. The constrain 3, mentioned in Section 2.3 was not considered in the mathematical model. So, the model is valid if the probability of blocking the cell from the input buffer according to 3. is small compered to reasons named in 1. and 2. The fact that the cells from longer buffers have small priority is not examined in this model, too.

4 PERFORMANCES OF THE PROPOSED SOLUTION

Using the mathematical model derived in the previous section, we calculated the throughput of the switches of different sizes as the function of the number of cascades (Figure 5).

10 15 20 25 m 30

Figure 5 The throughput of the proposed ATM switch as the function of the number of cascades in the extended banyan network.

We can see that the switches have the throughput between 0.8 and 0.9 for m that is the half of the number of cascades needed for the probability of misrouting 10-8 in the extended banyan network (given in Figure 2). This is the benefit of the recirculation at the price of the slight throughput falling. But, the utilisation of the link at the output of an ATM multiplexer is hardly over 0.8--0.9 (Schwartz, 1996), and the throughput of 0.9 is sufficient. It is possible to fmd the cell loss probability using the mathematical model, and some of the results are presented in Figure 6. It could be pointed out that there is some value of m, the savings in the buffer length are not worth of further increasing, for the specified cell loss probability. We also analysed the behaviour of the switch with fixed number of cascades and different traffic intensities. As expected, one can fmd that the length of the input buffers increases rapidly as we approach the throughput of the switch.

Perfonnance of the neural network controlled ArM switch 35

01 "------'-_-'-_L------'-_--L--'-----"-------'-----'''-------'_--'

1 ° 2 4 6 8 10 12 14 16 18 Nin 20

Figure 6 The probability of the cell loss as the function of the size of input buffers, for the switch with N=64 and p=O.8. The curves are for different number of cascades in the banyan network at the core of the switch.

The calculation of the output buffer lengths is given in (Petrovic et aI, 1997). As we mentioned earlier, the results obtained using the mathematical model are verified using the computer simulations. The results are compered in Figure 7, and a good agreement is noticeable. The agreement is better if the ratio of the traffic intensity and the throughput is lower, and worse for smaller switch due to correlation between the processes in the links of the extended banyan network.

18~~--~--~--~~--~--~

2 3 4

e N=64, m=17, p=0,80 v N=64, m=17, p=0,95 III N=64, m=14, p=0,80 ~ N=16, m=9, p=0,80

5 6

Figure 7 The comparison of the results obtained using the mathematical model (thick lines) and computer simulation (lines with marks) for the switch with 64 and 16 inputs, different numbers of cascades and different traffic intensities.

The extended banyan network stands the unbalancing of the traffic very well (Giacomazzi et aI, 1996). We used the computer simulations to show that our


switch with recirculations keeps this property. The simulations were performed for unbalancing on the inputs and outputs. The input unbalancing means that the probability of cell arrival is not the same for all inputs. In the case of the output unbalancing the outputs that cell has to reach are not uniformly distributed. The detailed results of the simulations are in (Skulic et aI, 1997) and some of them in Figure 8. The output unbalancing has small influence on the needed input buffer lengths. The effect of the input unbalancing is bigger, but we can control it well, if we put one or two cascades more in the banyan.

It is well known that the number of cells designated to the specific output is almost independent of N, if ~16, and is the random variable with the Poisson distribution. The probability that 6 cells are designated to the same output is 3xlO-4, if the traffic intensity towards this output is 0.9. This probability is small enough to be neglected in (12). Hereby, we choose mk=6, and this is exactly the required speed up of output buffers.

o 10r-~--~~--~~--~~~--~-'

PIO!f 10

3 4 5

o IL o IH o OL ra OH • balanced

Figure 8 The results of the simulations for unbalanced traffic. The switch is with N=64, m=14, and the average traffic intensity 0.7. The'!' stands for input and '0' for output unbalancing. The linear decreasing of arrival rate, or the distribution of wanted outputs, over ports from 0.9 to 0.5 is denoted by 'L'. The 'H' stands if some inputs, or outputs, are wanted with probability 0.9 and others are empty.

5 CONCLUSION

In this paper the new A TM switch architecture based on extended banyan network was presented and its performances were analysed. The core of the switch is banyan network with simple switching elements. The number of cascades in the banyan is almost halved by introducing recirculation of misrouted cells and neural network controller to preserve cell sequencing. This controller is a modification of the continuous Hopfield network and is much simpler than neural networks used in (Brown et aI, 1990 and Park et aI, 1994) to implement windowing technique.


The mathematical model was established to detennine the performances of the switch. Computer simulations verified these results. It is shown that the proposed switch architecture with simple elements owns good perfonnances. The small drop of the switch throughput is a disadvantage but it causes only the need for the input buffers that aren't too long. The switch retains good perfonnances in the case of unbalanced traffic, especially output unbalanced.

6 REFERENCES

Brown T.X. and Liu K.H. (1990) Neural Network Design of a Banyan Network Controller. IEEE Journal on Selected Areas in Communications, vol. 8 no. 8, 1428-38.

Giacomazzi P. and Pattavina A. (1996) Perfonnance Analysis of the ATM Shuffieout Switch Under Arbitrary Nonunifonn Traffic Patterns, IEEE Transactions on Communications, vol. 44 no. 11.

Hopfield 1.1. and Tank D.W. (1985) Neural computation decisions in optimisation problems. Biological Cybern., vol. 52,141-52.

Karol M.J, Hluchuj M.G. and Morgan S.P. (1987) Input vs. output queueing on space-division packet switch. IEEE Transactions on Communications, vol. COM-35, 1347-56.

Tobagi F.A, Kwok T. and Chiussi F.M. (1991) Architecture, Perfonnance, and Implementation of the Tandem Banyan Fast Packet Switch. IEEE Journal on Selected Areas in Communications, vol. 9 no.8, 1173-93.

Urushidani S. (1991) Rerouting Network: A High-Perfonnance Self-Routing Switch for B-ISDN. IEEE Journal on Selected Areas in Communications, vol. 9 no. 8, 1194-204.

Park Y.K, Cherkassky V. and Lee G. (1994) Omega Network-Based ATM Switch with Neural Network-Controlled Bypass Queueing and Multiplexing. IEEE Journal on Sel. Areas in Communications, vol. 12 no. 9.

Petrovic Z.R, Skulic V.M. and Cvetinovic M. (1997) Perfonnance of the new ATM switch for B-ISDN. J.C.Baltzer Telecommunication Systems, voL7, 379-90.

Schwartz M. (1996) Broadband Integrated Networks. Prentice Hall, New Jersey. Skulic V.M. and Petrovic Z.R. (1997) Neural network controlled ATM switch,

different types of traffic. Proceedings ofTelsiks'97, Nis, Yugoslavia, 807-10

Skulk M. Vladimir received the B.S.E.E. degree from the Faculty of Electrical Engineering University of Belgrade, Yugoslavia in 1993. From 1994, he is with Department of Telecommunications. His research interests include switching systems and broadband networks. Petrovic R. Zoran received Ph.D. degree in electrical engineering from the University of Belgrade on 1984. He is with Department of Telecommunications, Faculty of EE Belgrade, from 1973, where he is presently an Associate Professor. His research interest is in B-ISDN.

4 A new method for assessing the performances in ATM networks

Hoon Lee Korea Telecom, Telecommunication Network Research Labs. Jeonmin-dong, Yusong-gu, Daejeon, Korea Tel:+82-2-526-6423; Fax:+82-2-526-6781 E-mail: [email protected]

Abstract

The authors present a new approach to evaluating the performances in ATM networks. First, we present a typical model for the ATM output multiplexer with a threshold in the queue and the priority in the bursty incoming cells. Secondly, we describe a basic concept for defining the penalty functions for the expected performance based on the status of the buffer occupancy. Finally, we present the results of numerical experiments for the proposed method, and discuss the implication.

Keywords

ATM networks, QoS, performance assessment, penalty function

1 INTRODUCTION

The real time services such as voice and video conferencing will occupy an important portion in future ATM networks. As a result, the problem of guaranteeing the time and loss related Quality of Service (QoS) to the real time services has been recognised to be significant.

One of the characteristics inherent in real time service is that it requires a finite cell delay and it can tolerate a very small portion of cell loss. Thus, the major QoS measures for it in high speed networks are the cell delay time and the cell loss rate [Ferrari(1990),Li(1989),Towsley(1993),Yuan(1989)]. If there exists a priority in a cell, the partial loss rate of high priority (HP) and low priority (LP) cell can be another QoS measure [Awater(1991)].

Perfonnance of Infonnation and Communication Systems U. Komer & A. Nilsson (Eds.) © 1998 IFIP. Published by Chapman & Hall

Assessing the perfonrumces inATM networks 39

The maximum cell delay can be guaranteed by providing a finite queue. In this case, the cell loss due to queue overflow follows inevitably. To guarantee the cell loss, in particular, for the HP cell of real time traffic, the partial buffer sharing (PBS) scheme has been recognised to be effective [Kroner(1993)].

In PBS scheme, it is assumed that there are two types of cell based on the loss tolerance: high-priority (HP) and low-priority (LP). A threshold is assumed in a queue. At the beginning of every time slot, the queue occupancy is observed, and if it is greater than the threshold, the LP cell is rejected to enter the queue, otherwise the LP cells can enter the queue so far as there is a vacant space in the queue. The HP cells can enter the queue so far as there is a vacant space in the queue irrespective of the state of the queue occupancy.

In this paper, we propose a new method for assessing the performance of the ATM switch which adopts the PBS scheme. The basic philosophy of the proposed method is as follows: We impose a penalty to the system based on the degree of heaviness of the buffer and the cell priority. The heavier the buffer, the more expensive the cost function, and the cost of penalty for HP cell is higher than that of the LP cell. The detailed discussion is given in section 3.

This paper is organised as follows: In section 2, we describe the system model and the queue behavior, and present a procedure for obtaining the steady state queue occupancy. In section 3, we present a method to assessing a penalty on the performance in the described system model considering the delay and loss related QoS measures. In section 4, we will present numerical results. Finally, in section 5, we summarise the paper.

2 MODEL AND ANALYSIS

2.1 System model

Consider an output multiplexer of ATM switch. ATM switch operates in discrete time basis called a time slot. A time slot is a duration to serve a fixed size cell. Assume that cells generated from multiple connections are routed uniformly to output multiplexer via a non-blocking hardware switch fabric. Since a number of cells can be routed to a specific queue in a time slot, the arrival process to a multiplexer is bursty and the cell arrival process in aggregation may be assumed to be independent on the time slot [Yegenoglu(1994)]. So, we can assume that the arrival process of to the queue has a general VBR (variable bit rate) "batch distribution [Marafih(1994)].

The queue capacity is finite with size B. A threshold T is assumed to a queue, and cell input regulation of PBS scheme is based on this threshold. At the beginning of every time slot, the queue state x is observed. H x > T, the LP cells are discarded and only the HP cells are admitted to the queue within the available space. H x~T, both HP and 1P cells are admitted to the queue within the available space.


2.2 System analysis

Consider an arbitrary time slot i, and assume that, during that time slot, cells arrive to a queue from N independent and identically distributed (i.i.d.) sources. The cell departure from the queue occurs just after the beginning of a time slot, and it is served during that time slot. Thus, the input-output principle seen from the queue is departure first.

Let Xi be the number of cells waiting in the queue just before the beginning of time slot i. Let ai be the number of aggregated HP and LP cells which arrive during time slot i, and let bi be the number of HP cells which arrive during time slot i. The service rule is FIFO (First-In-First-Out) and the service order for the simultaneously arrived cells in a batch is random. Since we assumed that a cell is served in a time slot, the state transition equation for the queue length between the consecutive time slots i and i+1 is given as follows:

X _{ min[max(Xi -1,0)+ai,Bj, O~Xi~T, it! - . mm[max(Xi -1,0)+.8i,Bj, T<Xi~B,

(1)

where ai and .8i are given as follows:

ai, 0~ai~B-Xi+1, B-Xi+1, ai>B-Xi+1,

(2)

and

(3)

The sequence (Xi)' i > 0, constitutes a Markov chain [Kemeny(1976)]' and its state transition probability is defined by

If we rewrite p(k,l), we have

p(k,l)=Pr{min[max(Xi -1,0)+')'i,Bj=ll Xi=k}

=Pr{min[max(k-1, 0)+1', Bj =l}

(4)

(5)

where I'i = ai when O~Xi~T and I'i = .8i when T<Xi~B, and I' is the time independent value for I'i since the cell arrival is Li.d .. Similarly, we can represent ai and .8i without the subscript i.

Then, we have, for k = 0,

(0 l) = {pr{a=l}=PI, 0~l~B-1, p , Pr{a~B}=PB' l=B,

(6)

Assessing the performances in ATM networks

and for 1~k~T,

{ PI-k+1,

p(k, l) = PB--kt-l, 0,

and for T+1~k~B,

k-1~l~B-1, l=B, otherwise,

{ Pr{,8 = l}=ih-k+1 ,

p(k, l) = Pr{,8 ~ B}=FB--kt-l, 0,

k-1~l~B-1,

l=B, otherwise.

The state transition matrix P= (p(k,l)), O~k~B and O~l~B, is given by

0 1 T T+1 B-1 B 0 Po Pl P2 PB-l PB 1 Po Pl P2 PB-l PB 2 0 Po Pl PB-2 PB-l

P= T 0 Po Pl PB-T PB-T+l T+1 0 0 Po Pl PB-T-l FB-T

B-1 0 0 Po Pl F2 B 0 0 Po A

41

(7)

(8)

(9)

Let 1r n be the probability that the queue length equals n in equilibrium and we denote the stationary probability vector of the Markov chain by 1r, 1r = (1ro, 1rl, ... , 1rB), then 1r is the solution of the matrix equation given by 1rP=1r, 1re=1, where e is the (B+1)x1 column matrix with all elements equal to one. The equilibrium probability 1r can be computed by employing the standard numerical method for the matrix equation [Neuts(1981)).

3 ASSESSING PENALTIES AND PERFORMANCE MEASURES

First, let us describe a method to assessing penalties to the possible performance degradation. Next, we will describe performance measures.

3.1 Assessment of penalty

First, let us define a basic philosophy for assessing a penalty to the arriving cells. The penalty is given to the system according to the class of the cell and the position of the cell in the queue. In particular, as to the queue position, let us impose penalty value differently for HP and LP cells. For HP cells,

42 Part One ArM Switch Performance

we assume three classes: fatal, h-dangerous, and h-cautious. We denote that the system is in fatal, h-dangerous or h-cautious state when the arriving HP cell finds the queue in overflow, in between [T+I,B-IJ or in between [O,T], respectively. For LP cells, we assume three classes: I-dangerous, I-cautious, and normal. We denote that the system is in I-dangerous, I-cautious, and normal state when the arriving LP cell finds the queue in overflow, in between [T+I,B-IJ or in between [O,TJ, respectively.

Note that we denoted x-dangerous and x-cautious (x=h or 1) for HP and LP cells, respectively, since the meanings for h-dangerous and h-cautious for HP cells are different from those of LP cells.

If we summarise the above definition, we obtain the following table.

Table 1 Classification of penalties

I x = [T + 1, B - IJ I x = [0, TJ Fatal(black) h-dangerous (red) h-cautious (yellow)

I-dangerous (red) I-cautious (yellow) normal (green)

Note that in Table 1 we described colors for each item for convenience of easy understanding and notation.

3.2 Penalty functions

In order to describe a penalty function to each class, let us denote as follows: ¢~ be the penalty function of the system when the cell arrives to the system given that the cell is in class x and it finds the queue in region z. x has an index H and L for HP and LP cell, respectively. On the other hand, z has an index b, r, y and 9 for black, red, yellow, and green, respectively.

Let us denote penalty function to each case. For HP cells, we have penalty functions given as follows:

¢f/ = a(x), x?B,

¢:f =.B(x),xE[T+I,B-IJ,

¢: = 'Y(x),XE[O,TJ.

For LP cells, we have penalty functions given as follows:

¢~ = c5(x),x?B, ¢~ = €(x), XE[T + 1, B-1],

¢; = ((x), xE[O, T].

(10)

(11)

(12)

(13)

(14) (15)

(16)

(17)

Assessing the performances in ATM networks 43

3.3 Measure of goodness

Let us define that the performance of the system is good if the following function is minimum.

'ljJ = aPzoss + bPdelay (18)

where a and b are weighting factors between cell loss and delay performance, and Pzoss and Pdelay are the penalties due to cell loss and delay, respectively. Note that a and b can be used as a design parameter which can be determined considering the priority between loss and delay depending on the application under consider. Pzoss is given as follows:

R { a(B)7r(B) for HP cell, loss = 8(B)7r(B) + L~:';'+1 t::(x)7r(x) for LP cell.

(19)

Pdelay is given as follows:

4 NUMERICAL RESULTS

In order to evaluate the goodness of the performance, we have to assume the source model as well as the penalty functions which are defined in the previous section.

4.1 Assumptions

Assume that N homogeneous and mutually independent Bernoulli like sources are superposed, and they form a bursty source which follows a binomial distribution. In each time slot a batch which is composed of HP and LP cells arrives with probability (J. The probability density function for the aggregated HP and LP cell arrivals from N sources is given by Pn= (~)(Jn(1_(J)N--n. Assume that the proportion of HP cells and LP cells in a batch is the same. Then, we can obtain the probability density functions for the HP and LP cell arrivals as qn =P2n and fin =P2n, respectively.

The number of source is assumed N =40, which corresponds to the offered load, p = N(J, ranging from 0.16 to 0.96 for (J = 0.004 to 0.024. The queue size is assumed to be B = 30 and the threshold is assumed to be T = 25. These assumptions on the parameters are effective unless they are specified explicitly.

As to the penalty functions, we can have a tremendous different kind of functions. The assessment of the system performance depends directly on the type of the penalty function. So, we have to be very cautious in assuming them. However, we do not know which type of function is best suited in


assessing the performance in ATM switching system. In reality, we have no alternatives except determining them intuitively. The only intuition we can have is as follows: A customer (cell in this case) will feel worriness as the resource (available buffer space in this case) becomes scarce. We also think that the degree of worriness will increase exponentially even though the resource dries up linearly. A more detailed discussion about this intuition is described in [Lee(1998)]. Thus, let us assume as described in Table 2:

Table 2 Penalty functions

I function II values

a(x) a = 10 f3(x) sigmoid function (defined in (21)) 'Y(x) 'Y=O 6(x) 6=1 f(X) f=1 ((x) sigmoid function (defined in (22))

Note that we assumed a ten-fold weight on a with respect to 6 since the overflow of HP cells is more serious than that of LP cells. The value of'Y is given zero since there is no trouble for HP cells to find the queue to be light. As to the functions f3(x) and ((x) we will use sigmoid functions, which are defined as follows:

f3(x) = 1 + e!(~-T-6)' 1

((x) = 1 + e-O.5(z-T/2)·

(21)

(22)

The curves f3(x) and ((x) are obtained by empirical manipulation. Figure 1 illustrates the curves for the f3(x) and ((x) for T = 25 and B = 30 .

Q) 0.8 ::I a; > 0.6 ~ ~ 0.4

~ 0.2

... : , , , I , I ,

~(x),' I I ~(x) ,

!) , . , , ,

... ' 5 10 15 20 25 30

x

Figure 1 Curves for penalty functions.

Assessing the performances in ArM networks 45

4.2 Results and discussion

Figure 2 illustrates the loss penalty functions for HP and LP cells. Note that

B 1e-5 a E .g 1e-10 8. ~ 1e-15

1e-20 "-------------....... 0.16 0.32 0.48 0.64 0.80 0.96 Offered load

Figure 2 Loss performance

the two curves cross at the point of offered load of 0.44. When the offered load is less than 0.44, the two curves almost coincides .. However, for the offered load greater than 0.44 the cost reverses. This trend illustrates that the offered load should be limited to a certain value if one wants to obtain a certain level of performance from the system.

Figure 3 illustrates the delay performance for HP and LP cells. There

i 1e-5

.g 1e-10 8. ~ CD 1e-15 o

1e-20!-. ---------------' 0.16 0.32 0.48 0.64 0.80 0.96

Offered load

Figure 3 Delay performance.

exists a great difference in the cost of two curves for the lightly loaded case. As the offered load increases, they approach each other, and when the offered load is 0.73 they reverses. So, for highily loaded system, the number of HP cells that imposed penalty to the system may be greater than that of LP cells. For lightly loaded system, the reverse holds.

Note that the loss performance for HP cell and the delay performance of HP cell has the same order. So, we can assume that the simplest selection is assignning the same value for the coefficients a and bj that is a = b = 1.


Figure 4 illustrates the overall penalty functions for HP and LP cells. From Figure 4 we can deduce that the cost imposed by the LP cells for

0.1

G) 0.01 u i 0.001 E .g

0.0001 G) 0-

j! 1e-05 G)

c3 1e-06

1e-0~.16 0.32 0.48 0.64 0.80 0.96

offered load

Figure 4 Overall performance

delaying in a buffer is dominant among other ones.

5 CONCLUSIONS

We presented a new approach to assessing the penalties and evaluating the performance of the ATM switch from the view point of the cell loss and delay of HP and LP cells, respectively. First, we presented a system model under PBS scheme using the finite capacity queue with a threshold. Next, we defined a new measure of system penalty function, and investigated the goodness of the system using the proposed method.

From the numerical experiments, we obtained the following results : The proposed method can clarify the weight of the system performance with respect to the position in a buffer as well as the class of ce1lloss priority. The proposed measure can measure the loss and delay performance of the system simultaneously and with different weight.

Therefore, we expect that the results can be applied to the design and control of the output buffer for the ATM switch.

6 REFERENCES

Awater, G.A. and Schoute, F.e. (1991) Optimal queueing policies for fast packet switching of mixed traffic. IEEE Journal on Selected Areas in Communications, vo1.9, no.3, pp.458-467.

Ferrari, D. (1990) Client requirements for real-time communication services. IEEE Communication Magazine, pp.65-72.

Assessing the performances in ATM networks 47

Kemeny, J.G. and Snell, J.L. (1976) Finite Markov Chains. Springer-Verlag, New York.

Kroner H., Hebuterne G., Boyer P. and Gravey A. (1993) Priority Management in ATM switching nodes. IEEE Journal on Selected Areas in Communications, Vol. 9, No.3, pp.418-427.

Lee Hoon (1998) A new performance assessment method in ATM networks. Proceedings of the international conference on probability and its applications, February 24-26, Korea.

Li, S.Q. (1989) Study of information loss in packet voice systems. IEEE Transactions on Communications, vol.37, no.ll, pp.1192-1202.

Marafih, N.M. and Zhang, Y-Q. (1994) Modeling and queueing analysis of variable-bit-rate coded video sources in ATM networks. IEEE Transactions on Circuits and Systems for Video Technology, vol.4, no.2, pp.121-128.

Neuts, M.F. (1981) Matrix-geometric solutions in stochastic models. The Johns Hopkins University Press, Baltimore and London.

Towsley, D. (1993) Providing quality of service in packet networks. Performance evaluation of computer and communication systems (ed. L. Donatiello, R. Nelson), pp.560-586, Springer Verlag.

Yegenoglu, F. (1994) Characterization and modeling of aggregate traffic for finite buffer statistical multiplexers. Computer Networks and ISDN Systems, 26, pp.1169-1185.

Yuan, C. and Silvester, J.A. (1989) Queueing analysis of delay constrained voice traffic in a packet switching system. IEEE Journal on Selected Areas in Communications, vol.7, no.5, pp.729-738.

7 BIOGRAPHY

Hoon Lee obtained B.E. and M.E. in electronics in 1984 and 1986, respectively, both at Kyoungpook National University, Daegu, Korea. He obtained Ph.D. in electrical and communication engineering in 1996 at Tohoku University, Sendai, Japan. Since 1986, he has worked on network planning, dimensioning, and teletraffic engineering, with a particular interest in the field of traffic modeling, traffic control, performance analysis, and QoS guarantee of ATM networks. Dr. Lee is a member of IEEE and lEEK of Korea.

PART TWO

ATM Network Performance

5 Overload generated by signalling message flows in ATM networks

S. Szekely, l Moldovan, Cs. Simon High Speed Networks Laboratory, Department o/Telecommunications and Telematics, Technical University 0/ Budapest Sztoczek u. 2, H-1111 Budapest, Hungary, Fax: +3614633107 {szekely, moldovan, simon}@ttt-atm.ttt.bme.hu

Abstract Although the importance of the signalling perfonnance of A TM networks has been recognized as a potential bottleneck (Gelenbe, 1997a), very few papers address the congestion situation in switches due to signalling message flow. In this paper the overload generated by signalling message flow in ATM networks is investigated by measurements and simulation. The results obtained by measurements ••• on a university campus network highlight the strong influence of call attempts arriving in a burst on setup time, and fonn a basis for the simulation model. We simulate the flow of call establishment messages to estimate the queue lengths of signalling messages at access and intennediate nodes, the call blocking probability of different traffic classes and the average round trip time delay (RIT) of connection establishment in two cases with or without wide-band Blocked Call Queueing (BCQ). In B-ISDN the call blocking probability (CBP) of wide-band (WB) calls is much higher than that of narrow-band (NB) calls'. The introduction of queueing the WB calls rather than reject is going to reduce the CBP of WB calls, at the expense of a small increase in setup time and an increase in CBP of NB calls. The signalling overload associated with WB BCQ and questions related to grade of service are also investigated. The main contribution of the second part of this paper is to show, that the WB BCQ mechanism does not cause congestion of signalling message flow at the network level, when it is applied for moderate overload conditions.

Keywords signalling protocol, round trip time delay, blocked call queueing, call retrial

... This work was supported by Ericsson Traffic Lab. and HSN Lab., Hungary

Perfonnance of Information and Communication Systems U. Komer & A. Nilsson (Eds.) @ 19981F1P. Published by Chapman & Hall

52 Part Two ATM Network Performance

1. INTRODUCTION Very few academic and industrial papers have appeared in the field of ATM signalling perfonnance evaluation until now. (Gelenbe, 1997a) and (Gelenbe, 1997b) argue that congestion can occur at the nodes due to request messages themselves, involving path selection, routing and call establishment. In addition, it offers a simplified analytical model to obtain the call blocking probabilities. Signalling perfonnance measurements on A TM switches are in focus in the A TM Forum. Automated test cases for perfonnance testing addressed the following aspects of UN! signalling layer: limits test, burst measurements, latency test and endurance test (AF-SIG, 1997). The proposed test suite is a full automated testing solution. The test suite will be responsible to test some performance aspect of UN! signalling (first UN! 3.0, UN! 3.1, Q.2931, then UN!4.0 and PNNI). In this paper the overload generated by signalling message flow in ATM networks is investigated by measurements and simulation. Our aim is to give an estimate of the RTf delay, and CBP and to determine the signalling CPU processing queue length at each node (access and backbone) as function of different signalling traffic load and network topology. For simulation we use some similar assumptions as (Gelenbe, 1997a). In addition to that, we have implemented the BCQ mechanism for wide-band calls and investigated the RTf delay, the CBP, not only the queue lengths, while using different topologies and signalling CPU speed. Section 2 presents signalling performance measurement results on some commercial A TM switches. The results obtained from measurements are incorporated into the simulation model. Section 3 motivates the introduction of queueing of blocked wide-band calls at the access nodes of the broadband network, rather than simply accept or reject them. The simulation model is given in Section 4, and comparative results are shown to highlight the difference between the two mechanisms, with or without wide-band BCQ in terms of RTf delay, CBP and queue lengths. It is shown that for moderate overload conditions, call queueing of wide-band blocked calls achieves a substantial reduction in the loss probability at the expense of a small call establishment delay. Section 5 draws some conclusions. Finally, the Appendix presents an extension of the UN! signalling protocol in order to support this new B-ISDN supplementary service at the usernetwork interface, called Blocked Call Queueing.

2. SIGNALLING PERFORMANCE MEASUREMENT TEST RESULTS The aim of this section is to show by measurements the overload generated by signalling messages on commercial ATM switches. The testing configuration is very simple, one isolated ATM switch connected to a tester (as calling user) and to an other terminal equipment (called party). To emphasise the signalling overload in the A TM switches, we have chosen a switch with a slow CPU service rate. The limits, latency and burst testing results are shown in Table 2.1 and Figure 2.1 a), b). Table 2.1 presents the RTf delay for the first and last successful connections establishment within a burst and the average RTf delay is also determined, for a burst containing subsequently 10, 20, ... , 100 SETUP messages. We have measured the total processing time, and monitored the number of successful and

Overload generated by signalling message flows 53

rejected calls. Because of T303 timer expiry, some SETUP messages have been retransmitted for a burst containing more than 30 SETUP messages. Except the last two columns, the results are obtained for the standard values specified in (AF-UNI, 1996). T303 and T310 are two timers at the UNI interface and are shown in detail in Figure A.l. in the Appendix. It is important to see that for the shortest path possible (only two links) the RTf delay is of the order of seconds when having bursty arrivals.

Table 2.1. Burst and limits measurement test results. Note: n.v. = not valid (because of the testing equipment limits we could not obtain valid results here)

#of RIT delay Ims] #of Total #of T303 increased initiated (between Setup and Connect) resent proc. reject from 4 sec to 100 Setup in First Last Average Setup time ed Total Reject a burst: conn conn. RIT msg Ims] msg. proc. t. msg.

10 405 2414 1705 0 3238 0 3271 0 20 596 4819 2998 0 4994 0 5003 0 30 425 4269 6418 5 6823 5 6850 5 40 822 10684 6364 13 11 341 11 8600 10 50 886 9840 4505 4 15330 9 11500 11 70 609 14912 7950 6 23250 33 16390 13 80 n.v. n.v. n.v. n.v. 50000 50 30000 30 100 n.v. n.v. n.v. n.v. 65000 70 30000 42

The line 50 shows some anomalies. Then line 80 and 100 face a huge number of refused connection, but we could not capture the detailed time stamps, because of the tester's buffer capacity limits. The total processing time is longer than T303 and T310 expiry time, that causes some of the retransmissions and rejected calls. For a burst of 100 initiated calls, the number of successful calls increase to 70 when we increase the values of timers T303 and T310 high above the standard values (not figured in Table 2.1). Even though we still have 30% rejected calls. This happens because of buffer overflow in the processing queue of the signalling CPU. Figure 2.1 a) shows that the RTf delay of a call establishment increases linearly with the number of open connections (the presented values are obtained for user-one switch--user configuration). Figure 2.1 b) shows that the influence of a bursty signalling arrival on the RTf delay is much stronger than that of the number of open connections. E.g., the lOth SETUP message within a burst suffers five times longer delay than the first one. We can easily calculate the average service time of the tested switch's CPU, being 1/1l = 100 ms. Some other commercial A TM switches showed lower signalling CPU service time (I/Il = 20,33 and 50 ms). These later three results are used in the simulation model in Section 4. The measurement results shown here highly motivated the investigation of signalling performance by simulation on the network level.

54

450

400

350

;;300 E - 250

Loo 5 150

100

50

Part Two ATM Network Performance

RITdday

......-

o 10 ~ ~ ~ ~ ~ ro ~ ~ 100

• of eclw connectton.

RITddays

~r---------------~

~~-------====-==--=.=4 1 2 3 .4 5 8 7 8 g 10

Specllc order of the meauge .... 1n • bur.t

Figure 2.1. (a) The average RTf delay of a new call establishment when we increase the number of active connections from 0 to 100; (b) The average RTf delays for each of the call establishment messages within a burst of 10, having different number of open connections

3. QUEUEING OF BLOCKED WB CALLS AT THE ACCESS NODE Since A TM is the switching and multiplexing technology of Broadband Integrated Services Digital Networks (B-ISDN's), it is essential for its signalling system that it supports the co-existence of narrow- and wide band services. B-ISDN's have been traditionally modelled on the call scale by the theory of multi-rate loss networks (Ross, 1995). A call request requiring a certain amount of bandwidth between a given originating - destination pair is blocked and disappears from the system if sufficient resources are not available at the time the call request arrives to the network, see e.g. (Ritter, 1994) and (Chung, 1993). Adopting this rule to a multi-rate environment with a large difference in bandwidth requirements between traffic classes implies that calls requiring a large amount of bandwidth will experience a much higher blocking probability than calls requiring only a small amount of bandwidth. By applying either trunk reservation or class limitation it is possible to level out the blocking probabilities. However, in most cases, the disadvantage put on the narrow-band traffic is much bigger than the advantage obtained for the wide-band traffic, because network utilisation is inherently low at multi-rate pure loss networks, when request sizes may differ with orders of magnitude, as it has been shown in e.g. (Sykas, 1991). The effect of repeated call attempts appears in telephony too, numerous traffic measurements and theoretical investigations were made, see (Elldin, 1967), (Le Gall, 1973), (Gosztony, 1975) and the bibliography attached to them. Measurements showed that several time periods related to the retFated call phenomenon are not exponentially distributed. On the 6th and 7 International Teletraffic Congresses several other papers were presented on this field. Finally, a quite recent paper opened the subject of call queueing in circuit switched network (Berezner, 1996). In this paper we are interested only on a part of the repeated calls, when rejection is caused by congestion in the network. In such a case, according to our proposal, there is no need of any action by the calling party.


Since with an advanced signalling protocol it may be possible to allow calls requiring a large amount of bandwidth to wait in a queue until resources become available, there is a hope to significantly reduce the blocking probabilities of these calls. These types of systems constitute an important generalisation of the pure loss systems and have already been studied in the literature as "mixed delay and loss" or "mixed queueing and loss" systems. In particular, numerical examples indicate that per-class blocking probabilities of wide band services decrease at the expense of a short delay during call set up and a slight increase of narrow band service class blocking. It is concluded that letting wide band calls to queue can decrease wide band blocking and increase network revenue and thus advantageous for both users and network operators (Szekely, 1996), (Fodor, 1999). In fact, these papers do not take into account the effect of signalling message flows and secondly, they look at a rather small network only (4 node fully connected network). The queueing of wide~band calls has been found as being efficient at the access node of the network, but it requires enhancement of the Call Admission Control (CAC) function to queue the unsuccessful wide-band calls. The Blocked Call Queueing mechanism holds some blocked calls by storing their signalling information in a buffer at the access ATM switch. These calls will be later connected when network resources become available.

Accessrme

~ ~ ~ UN~ NNI NNI I NNI I

r--:~S_~-P~ _____ ~~~PJI I

I(~~~) 1_ ~::= i ~_-----r R..C ! ,." I1nIc I

(~PJ") I .

UNI SAC .x. DEST

I ~pl

Figure 3.2 Successful call establishment with Blocked Call Queueing (simplified)

In case that a wide-band call attempt arrives to the access node of the network, the CAC function tests whether the network resources are available and proceeds either with resource allocation or the unsuccessful call joins the waiting queue. It is not trivial to determine which mechanism is better: to retry after "d" delay (according to the mean holding time of call type "t", MHT,.) or get feedback from the network first, then proceed again. We are mainly interested in the signalling overload it generates on intermediate and access nodes and particularly its effect on


the RTf delay. We assume here out-of-band signalling, and that signalling channel (VCI=5) is never congested (but it may create overload on the signalling CPU's and suffer long delays). As a solution for Blocked Call Queueing we have been using the existing UN! and public NNI protocols. A simplified example is given in Figure 3.2, when a call is blocked at the first attempt somewhere in the network because of unavailable resources on a link, rejected, then queued at the access node, waiting for a certain time and finally it succeeds at the second trial. The CALL QUEUED message and the T3xx timer are not part of the standard UN! specification (ITU-T, 1994), but an extension of that, which is described in the Appendix. To indicate the best algorithm for re-sending the SETUP message after the blocked call has been queued, is subject of further investigations. Hence, we assume that these messages are retransmitted within a 'd' delay as many times as necessary until success, i.e. a positive acknowledgement (CONNECT message) arrives back to the source. We assume here a preventive control at each node, by regUlating the admission of new calls into the network according to their required equivalent bandwidth. The difference between the total and used capacity on the outgoing link has to be compared to the capacity of the new call C( a). The new call is rejected if:

3Xk E lln(i, j): Cavailable(Xt) = Ctotal(X k) - Cu"iXk) < C(a), 'Vn = 1,2, ... ,N

where: X k = link k, 7rn (i, j) = nth path between source i and destination j

C(a) = capacity of call a, c .... ,Axk )= L""x. C(a)

Ctotal(X k) = total capacity of link k, N = number of retrials

According to our assumptions, if a narrow-band call is rejected, that is lost. In case of a rejected wide-band call, that is queued at the access node. At a possible next trial a new path is searched again for that call. The round trip time delay of this wide-band call (RTl) is bounded by:

N

Te";in(i, j) ~ RIT(i, j) ~ L(Te~t(i, j) + dalt,n) ~ T3xx + Te,,;in(i, j) n=1

where: dalt,n = time spent in the access queue at the ntll retrial, Ttst(i,j)= call establishment time on one specific path, T3xx= time-out value of the BCQ timer

The capacity check is inherently a sequential process. If we assume that all nodes have the same service rate (Jl) and we count each message transmission, reception and processing as a delay unit, it introduces a time delay which is linear with the length of the path (41rn(i,j)= number of nodes in the path "n"). In most practical network, this linear time cost is not critical since the diameter of the network is kept bounded by the topology design because of end-to-end considerations, However, in principle if the end-to-end paths are excessively long, this linear time cost may be a delay bottleneck in the process of the call setup, e.g.:

1) 20 nodes in the path, when l/Jl=5Oms for nodes, no queue -+ RTF=2 sec; 2) 20 nodes, lIJl=50ms, but avg. queue length=20 -+ RTF=40 sec> T3JfF30 sec!

Overload generated by signalling message flows

The expected value ofthe RTI for a wide-band call is given by,

R1T(i, j) = E(T..,(i, j» = T.';in(i, j). (1- Pmain (i, j» + dall,l +

+ 1'.~I,I(i, j). (1- Pall,l (i, j» +dall,2 + ...

57

where: Pmain (i,j) = probability of unsuccessful call establishment on the main path between nodes i and j

Palt,,(iJ) = probability of unsuccessful call establishment on the alternative path "r" between nodes i andj, if the main path is blocked. For simplification, let us consider:

1'.';in (i, j) = T:':I,r(i, j) = T(i, j) and P"",in (i, j) = Pall,r(i, j) = Po, r = 1,2, ... , N N

Then it results: R1T(i, j) = T(i, j). N . (1- Po) + Ldall,r r=1

The T( i,j) depends on the processing speed of signalling CPU on each switch, the signalling traffic load in the network, the number of switches in the path, the channel bit rate and the message format (e.g. the DTL information element in PNNI protocol is a source of overhead). While using 155Mbps optical interfaces we can neglect the dependency on the channel bit rate. Further on, if PkZ is defined as the call blocking probability on the link k directed from node Z,

PO=P""'in(i,j)=I- II (l-PkZ) X ,e ""'in _ palh (i ,j)

To find the probabilities PkZ for all nodes is a problem, If all links in the backbone have the same CBP, PBB as well as all links from the external network have P'XI' and E(L(7r,,(i,j))) is the average length of the path, moreover if PBB= PUI = p, then: Po = 1- (1- p)E(L(1f n (i,j)))

The average number of calls on the link k directed from node Z is: EkZ(m) = P/cZ(l- P/cZ), then

T(i, j) = 2· LE/cZ(m). Ek(T) =.!:. LE/cZ(m), while X,emain_patlJ(i,j) J1 X.emain_patlJ(i,j)

1 dall =d=-'p'(1-po)' r=1,2, ... ,N

,r J1

where p=A/Jl is the utilisation of one access node. The above formulas are even more complicated if we consider different CBP for different types of calls. Instead of considering the average RTI delay it may be more appropriate to consider the maximum delay, which is the delay experienced by an arrival to the queue that finds (m-I) queued calls in the node. The grade of service (GoS) requirement is stated in terms of both the loss probability and the call establishment delay, Queueing will therefore be beneficial if the maximum setup delay satisfies the GoS requirements, The distribution of the maximum delay at a node is a gamma distribution with parameters (1IJl, m-I). The expected value of the maximum delay (in a node) is (m-l)/Jl and the variance is (m-l)/Jl2 . The variance is thus very small for a range of parameters under consideration and the maximum delay is very close to its expectation. Call queueing will therefore be


beneficial if R1T < dGoS, the maximum delay for an acceptable service. So the timer T3x.t (see Appendix) has to be defined as being equal to dcos.

4. THE SIMULATION MODEL We simulate the call set-up phase of the ATM connection and the flow of call establishment messages in order to estimate the queue lengths of signalling messages at the ATM switches, the RTf delay and the CBP of different types of calls. In addition we simulate the WB BCQ mechanism (see Section 3) and compare the two methods (with and without WB BCQ).

4.1. Simulation overview Our evaluation is concerned with the load due to message processing by the nodes in the network. Therefore, we will focus on the number of messages which need to be processed for establishing and terminating a call, and the manner in which these messages are exchanged and routed is particularly relevant. The tested topology is a ring topology, with a core and an access network, where we can modify the number of nodes in the network. Despite of this, the topology used in (Gelenbe, 1997a) consisted of 100 nodes in a 10*10 mesh topology, where all link capacities were 45Mbps, and the call establishment message was processed in 30ms at each node. The processing of a call of type "t" from the source node "i" to destination node "j" with bandwidth requirement C,( a) is similar in both cases, but we focus on more parameters and in addition we have implemented the WB BCQ mechanism. Moreover, the measurement results presented in Section 2 are incorporated into our simulation model. Paths may have different lengths, and L( tr,,( iJ)) is the length of the nIh path between i andj. Because of the given ring topology (see Figure 4.1), the average length of the path is E(L(tr,,(i,j)))< 4 in the total network, while it is E(L(tr,,(iJ)))< 2 in the backbone network. A call establishment means a subsequent flow of SETUP and CONNECT messages travelling up and down the path. Hence, a new call attempt generates 2 * E(L(tr,,(iJ))) messages in the backbone network. For the sake of simplicity we use a very generic signalling protocol, generating only 4 types of basic messages: SETUP, CONNECT, RELEASE and RELEASE COMPLETE (RLC). If the call is successfully established, then the bandwidth is reserved for the holding time of the call. Upon termination, the bandwidth is released at each link by a message which travels up the path, from source to destination, and the network state table is then updated. We have "n" nodes fully interconnected in the backbone of the ATM network, and "n*m" switches on the external network, connected via double homing. We can specify the capacity of each link separately, and if one link does not exist, we can simply assume that the specified link's capacity is zero. In our case, we considered 4, 5, 6 or 8 switches in the backbone network fully interconnected by 310 Mbps links, and each switch-pair has 4 external nodes connected by 155 Mbps links to the backbone.


There are three types of traffic classes and two scenarios (see Table 4.1). The call arrivals are generated using Poisson distribution, and the source-destination pairs are selected by uniform distribution. The 'wait and retry' mechanism can be simply implemented in different ways, e.g. a separate queue for blocked calls, different priorities for different types of calls, etc. (Fodor, 1997). Our node model is very simple, it has only one queue and one processor per node. We assume static, alternate routing and there are no restrictions about the length of the processing call queues.

4.2. Simulation results The following figures highlight some of the simulation results. As a first result we obtained is as follows: the shorter the mean holding time of calls, the larger the bandwidth that is supported by the network. Secondly, the higher the signalling processor speed, the lower the RTT delay of connection setup and higher the bandwidth limit. The specific RTT delays obtained here confirmed the measurement results of Section 2. The minimum RTT delay is given by 2 * the average length of the path * the average service time of the nodes. Figure 4.1 (a) shows the average queue length of backbone nodes for 3 types of service rate, when increasing the number of call attempts in the network. The bandwidth requirements of connections are given very small to avoid link congestion. The higher the service rate, the smaller the buffer occupancy for the same load. In Figure 4.1 (b) the average backbone queue lengths are presented, when we have a given service rate (l/1l=30ms) and different number of backbone nodes. As we increase the network load above 25 callS/sec, in the configuration with 4 backbone nodes the service time of individual nodes is longer than the interarrival time of incoming calls, then their queues grows rapidly.

,. B~ que ... lencths

_~1:~ I-~---

t J, .L'

.;~

o '.33 1e.87 25 33.33 41.87 50 58.33 88.87 __ 1_1

12

10

Back ...... q ...... 'encths

--- I ,-- I --.~ ... -.---.... 11

~~ ~-

0.00 3.33 •. 87 10.00 13.33 16.87 20.00 No __ I_1

Figure 4.1 (a) Effect of the service time and (b) number of backbone nodes on the queue lenght

The backbone can not carry out the generated load, and congestion of signalling messages occurs. To avoid congestion for the same load, we can increase the number of backbone nodes, thus distributing the load to more switches and reducing the queue length. One solution for this problem is to increase the number


of the backbone switches. If we increase the number of backbone switches from 4 to 5, 6 or 8 (fully interconnected), the load will be distributed and the probability of the congestion decreases. The differences become important starting from medium signalling load (20 calls/sec), e.g. while the average queue length at the backbones is 10 having 4 nodes, it decreases to 1 for 8 nodes in the backbone. So a bottleneck having less speedy switches can be diluted by increasing their number in the backbone network. In the rest of the configurations we have mixed traffic. The network load is increased from low (O.lcallslsec) to high (33callS/sec). All nodes have the same service time (l/J,l=3Oms). The network topology is the same, using 6 nodes in the backbone. We can re-scale the x-axis (network load) to relative scales.

P = Pnode = Anode =_1_. ~elWOrk = 30. 10-3 sec' [0.OO ... 33.33~· 4~ = [0.00 ... 0.67] Pnode Pnode 6 6

Three traffic classes are specified: narrow-band class (lMbps), medium-band class (lOMbps) and wide-band class. Two scenarios are chosen (see Table 4.1).

Table 4.1. Traffic classes and their distribution

Call Mean Scenario 1 Scenario 2 Type Holding Call type Link occu- Call type Link occu-

[Mbps] Time [sec] distribution [%] pancy [%] distribution [%] pancy [%] 1 100 89 33 70 8 10 10 9 33 20 23 60 2 2 33 10 69

In scenario 1 the average link capacity is uniformly distributed between the three types of calls. As a result we have 89% narrow-band calls and only 2% wide-band calls. In scenario 2 the number of wide-band calls is increased, so it constitutes 10% of the total call attempt. The mean holding time for the WB calls is relatively short (2 sec). The maximum waiting time for a blocked wide-band call is set to T3xx=30 sec. Only WB call are queued, the other two classes are rejected immediately when network resources are not available for that specific call. The queue length of the access nodes has an average of less than 1 for both scenarios (see Figure 4.2 (a), (b».

Queue lengths, scenario 1

18

,. ~B8.q.wilb8CQ ,

.......l-AC-q.wiIlIBCQ , " -~BB.q.wiIhoutBCQ I '2

t '0 i • g

o 0.00

AC-q,willlDaBCQ

J I ~ ~

./' .......-!"':

8.33 16.67 25.00 33.33

Queue lengths, scenario 2

'0 ----+-lI8-q.wilhBCQ

~AC.q.wilbBCQ I _____ 88_q. .... BCQ I

6 •

r 5

j 4

AC·,,~BCQ , I

" g ",

./" '!'"

0.00 8.33 16.67 25.00 33.33

Figure 4.2 Access and backbone queue lengths for mixed traffic and two scenarios


The simulation results are obtained for 95% confidence intervals. The average queue length of the backbone nodes increases to order of 10th for p=0.67 (high load). Neither in scenario 1, nor in scenario 2 the WB BCQ mechanism does not have any impact on the queue length of access and backbone nodes. However the queue length is less than 20 for even a high signalling load, one can address schemes to trigger recovery actions (e.g. re-sending REL messages if the correspondent RLC message was not received, because of buffer overflow). Figures 4.3 (a)-(c) show that for the given scenarios the CBP of narrow-band calls (lMbps) is not deteriorated by applying the WB BCQ mechanism. The CBP of wide-band calls (60Mbps) drops from 0.8 to 0.5 %, respectively 5.5 to 1.9 % at the expense of a small increase in CBP of medium-band calls, that increases from 0.62 to 0.8 %, respectively from 1.7 to 3%.

· • 3

· ~ 2

" 1

D.'

1 Mbps call rejection

........... Wllhca~lCelllml.

........... W~ca .. ~ICe .... rkll. f

......... WJhc· ...... uilsoee ...... Z.

--Wilhoutc ....... umglCftllriol. I r ,

J .~

Iff .Lf

60 Mbps call rejection

........ Wilhcd-queuingsterllflOl

-60--WiIhoulcall-qumiaa;scllllrio I.

l ~3~----------~~-~ ~

8.33 16,67 25.00 33.33

10 Mbps call rejeetion 3 .• ,---------_---,

...........Wdhcall-~JCenanol

-....-Willloutcal-.... lIII8rceaariol.

--Wllhwtcill-quNpclel!MriP 2. l 2~ ___ ~~~~-t-i

~ fJ 1.St---------I-+i

o.,+ _______ ,..,...:........,,~

8.33 16.67 25.00

Ne'-il.Jo.d[clllllI.]

RTIdelay

2500 r;::::::::::;::::::;:::::==::;---, ........... WlIhnll.1pIIin&scmano I

2000 ~Mhoulcal.quNlliICIllBrio 1 i----fi ___ Wilhcall_quaaincICIIIIrioJ.

I 1500

! ~ 1000+-------~~

5OO+----=.,.r.I.-::;;.----I

0.00 8.33 16.67 25.00 33.33

LNd[oIIIIaJ

Figure 4.3 (a)-(c) Call blocking probability of narrow-band, medium-band and wide-band calls (d) The average RTf delay for all class of calls

When only 2% of the total calls requires wide-band capacity (scenario 1) the average RTf delay does not change significantly when using WB BCQ. When the WB calls form 10% of the total offered calls, the average RTf delay slightly increases. At a high traffic load (p=O.67) the RTf delay is still acceptable, however


the difference between the two curves (with and without BCQ) is equal to the value of RTf for a low traffic (400 ms). For a low traffic load, the RTf delay is 400ms for the given topology (the avg. length of the path = 4 nodes, and using switches with 1IJ..L=3Oms). That means the specific RTf delay/node = approx. lOOms. While at high load conditions RTf/node increases to 400ms with, respectively 300ms without WB BCQ. Hence, real size networks (less than 20 nodes in a path) will have approx. 6-8 sec RTf delay. That satisfies the grade of service requirements. We conclude that WB BCQ is most beneficial when p=[0.5 ... 0.67]. When p < 0.5, the BCQ mechanism is not needed, while for overload conditions (p > 0.67) this mechanism is not effective.

5. CONCLUSIONS In this paper the overload generated by signalling message flow in A TM networks was investigated by measurements and simulation. The results obtained by measurements for point-to-point connections showed the strong influence of call attempts arriving in a burst on setup time. By simulation we estimated the performance parameters on the network level, namely the queue lengths of signalling messages, the call blocking probability of different traffic classes and the average round trip time delay of connection establishment in both cases with or without wide-band Blocked Call Queueing. We have given an analytical method to compute the RTf delay. The signalling overload associated with WB BCQ and questions related to grade of service were also investigated. Finally we have shown, that the WB BCQ mechanism does not cause congestion of signalling message flow at the network level, when it is applied for moderate overload conditions. The implementation of WB BCQ was very simple, no complexity problems appeared (see Appendix). We plan to investigate in the future the implications of ABR connections setup and point-to-multipoint calls setup on the network level.

6. REFERENCES ATM Forum Technical Committee (1994) PNNI Draft Specification, Version 1.0,

ATM Foruml94-0471Rll ATM Forum Technical Committee (1996) ATM User-Network Interface (UN!)

Signalling Specification, Version 4.0, ATM Foruml95-1434R8 ATM Forum Technical Committee, Testing SWG (1997) UN! Signalling

Performance Test Suite, ATM Foruml97-0468 Berezner, S.A and Krzesinski, AE. (1996), Call queueing in circuit switched

networks, Telecommunication Systems, 6, 147-160 Chung, Cop. and Ross, K.W. (1993) Reduced Load Approximations for Multi

Rate Loss Networks, ACMIlEEE Trans. on Networking, 1222-1231 Elldin, A (1967) Approach to the theoretical description of repeated call attempts,

Ericsson Techn., 23,345-407 Fodor, G., Blaabjerg, S. and Andersen, AT. (1999) Modeling and Simulation of

Mixed Queueing and Loss Systems, Kluwer Acad. Publisher, Personal Wireless Communications, to appear


Gelenbe, E., Kotia, S. and Krauss, D. (1997a) Call Establishment Overload in Large ATM Networks, in Proc. ATM'97 Workshop, Lisbon, Portugal, 560-569

Gelenbe, E., Mang, X. and Onvural, R (1997b) Bandwidth Allocation and Call Admission Control in High-Speed Networks, IEEE Communications Magazine, Vol.35, No.5, 122-129

Gosztony, G. and Agostbazi, M. (1975) Characteristics of repeated telephone calls (in Hungarian), Hfradastechnika, 26, 109-119

ITU-T Recommendation Q.2931 (1994) B-ISDN. DSSS No.2 (DSS2). UNI Layer 3 Specification for Basic CalVConnection Control", COM JJ-R 78-E

Le Gall, P. (1973) Sur l'utilisation et l'observation du taux d'efficacite du trafic telephonique, 7th lTC, Stockholm, Prebook, 44311-8.

Ritter, M. and Tran-Gia, P. (1994) Multi-Rate Models for Dimensioning and Performance Evaluation of A TM Networks, COST 242 Interim Report

Ross, K.W. (1995) Multiservice Loss Models for Broadband Telecommunication Networks, Springer Verlag, ISBN 3-540-19918-7

Sykas, E.D., Vlakos, K.M., Venieris, 1.S. and Protonotarios, E.N. (1991) Simulative Analysis of Optimal Resource Allocation and Routing in IBCNs, IEEE Journal on Selected Areas in Communications, Vol. 9, No.3

Szekely, S., Fodor, G. and Blaabjerg, S. (1996) Call Queueing: The design and performance analysis of a new ATM signalling functionality, in Proc. B&MW'96 Workshop, Zagreb, Croatia, 99-113

Szekely, S. (1997) On Bandwidth Allocation Policies in ATM Network using Call Queueing, in Proc. 5th IFIP Workshop on Performance Modelling and Evaluation of ATM Networks, nkley, U.K., 46/1-10

Additional reading Onvural, RO. and Cherukuri, R (1997) Signaling in ATM Networks, Artech

House, ISBN 0-89006-871-2

APPENDIX. SIGNALLING CAPABILITIES NEEDED TO SUPPORT WIDEBAND BLOCKED CALL QUEUEING AT THE UNI This section extends the ITU-T Recommendation Q.2931 for point-ta-point signalling protocol to support blocked call queueing capability. As shown below, the first message sent by the user to the network for call establishment (SETUP message) needs an extension to support blocked call queueing service. This and some other extensions of the current signalling protocol Q.2931 necessary to support blocked call queueing are as follows: a new message (CALL QUEUED), a new timer (T3xx), a new information element (BCQ IE) and a new state (U*). Blocked call queueing service can be requested by the calling user's application process. In this case the signalling layer sends a SETUP message across the UNI, which contains the desired Blocked Call Queueing information element (BCQ IE). The network access node may ignore the BCQ IE if that information element is of no interest or that service is not implemented. When the service is implemented but there are not enough resources available in the network, the calling party is notified by a CALL QUEUED message that its call has been set in a waiting queue at the first node of the network. This CALL QUEUED message is sent to the caller only


in the case when he has asked previously for it by BCQ IE. This call is either served within a given time limit or removed from the queue by the calling party when Blocked Call Queueing timer T3xx expires. The Finite State Machine graph at the user side of the UNI in Figure A.l gives a detailed description about all the possible scenarios. The timer T3xx is used on the user side. The network side FSM graph is very similar and is not shown here because of lack of space.

~PllGI ... 'Q ... ""no,.

AlPIT ... . ~-e.oW'l -.DM,. _T'JD , DIit.-II ~...,.." .. ..

CIOMoI£CTt CDolItDti., ... blt. ,."

Figure A. I. Partial FSM graph of Q.2931 with the new BeQ state (user side)

7. BIOGRAPHY Sandor Szekely received the M.Sc. degree in communications engineering from the Technical University of Timisoara, Faculty of Electrical Engineering, Timisoara, Romania, in 1995. In 1994 he joined the High Speed Networks Laboratory at the Department of Telecommunications and Telematics, Technical University of Budapest, Hungary, where he is currently working towards the Ph.D degree. His research interests are related to optimisation of signalling protocols in A TM networks, and performance analysis of call establishment by measurements, simulation and analytical study. He is a student member of IEEE since 1997. Istvan Moldovan received the M.Sc. degree in computer engineering from the Technical University of Tirgu Mures, Faculty of Automation, Tirgu Mures, Romania, in 1996. Now he is a Ph.D student at the TU of Budapest. Csaba Simon received the M.Sc. degree in computer sciences from the Technical University of Tirnisoara, Faculty of Computer Science, Tirnisoara, Romania, in 1997. Now he is a Ph.D student at the TV of Budapest.

6 Quantitative Evaluation of Scalability in Broadband Intelligent Networks

G. Karagiannis, V.F. Nicola, /.G.M.M Niemegeers Centre/or Telematics and Information Technology (CTIT) University of Twente, P.O. Box 217, Enschede, the Netherlands Phone: +31 534893747; Fax: +31 534893247; Email: [email protected]

Abstract Scalability is the ability of a network to maintain the quality of service while increasing certain parameters relating to the size of the network, such as the number of users, the number of network nodes, the number of services provided, geographical spread, etc. In the design of a B-IN signalling systl>m, network scalability is an important issue that must be taken into account. In this paper we use simulation to investigate scalability issues related to a Broadband Intelligent Network (B-IN), such as that being considered in the ACTS project INSIGNIA. In particular, we study the impact of processor speed and configuration (in B-IN physical entities) on signalling performance. As signalling performance measures we consider the mean call setup delay of a B-IN service request and the network throughput. For Broadband Virtual Private Network (B-VPN) service, we perform scalability experiments by increasing some of the network parameters such as the number of users and the number of nodes.

Keywords Broadband Intelligent Networks, network scalability, performance analysis.

1 INTRODUCTION

Because of the expansive growth of the available capabilities in telecommunications it is expected that many services that today are provided by

Performance of Information and Communication Systems U. Komer & A. Nilsson (Eds.) © 19981FIP. Published by Chapman & Hall


other media, e.g., video films, will be taken over by telecommunication networks. This imposes many requirements that must be fulfilled by these networks. To achieve this, a new approach to building, maintaining, changing and providing services is needed. A solution to fulfil these requirements is intelligent networks (see (Thorner, 1994», a concept that was introduced in the 80's, mainly for fixed communication networks, and is now expected to be used in many other networks. The B-IN infrastructure allows the rapid and cost effective deployment of new services by separating the service control and service switching currently located in switches. Consequently, the main physical entities constituting a B-IN architecture (see Figure 1) are the Broadband Service Switching Point (B-SSP) and the Broadband Service Control Point (B-SCP). The Broadband Intelligent Peripheral (B-IP) provides the specialised resources that are required for the provision of IN broadband services, in particular multimedia user interaction. The Fixed Terminal (Ff) represents the end user. Each physical entity is composed of interactive functional entities. The Signalling System 7 (Modarressi, 1990) is used to control the flow of information between the interactive network functional entities to establish, maintain and release a B-IN service request.

Figure 1 B-IN architecture.

_ User part

-Slpll~

Scalability (see, e.g. , (Gauthier, 1996), (Lin, 1994), (Martini, 1996), (Saha, 1995» is one of the most important factors in the design of a distributed multimedia system, such as B-IN. The system must be able to sustain a large number of users and various types of services with different traffic characteristics and Quality of Service (QoS) requirements.

Network scalability can be defined (Karagiannis, 1997) as the ability to increase the "size" of the network, in some sense, while maintaining QoS and network performance criteria. The "size" of the network may relate to one of the following: • the number of users that must be supported by a network node: increasing the

number of users that must be supported by a certain physical entity can cause serious performance problems because of processing capacity and memory limitations.

• the number of network nodes and links: the growth of number of nodes and links may cause an increase on the offered load to a given physical entity,

Scalability in broadband intelligent networks 67

since the physical entity will have to manage the intercommunication with the additional nodes in a more complex topology.

• the geographical spread covered by the network: increasing the geographical area that is covered by a network while keeping the number of nodes constant will cause an increase of the message propagation delays since these delays are proportional to the length and number of the physical communication links.

• number of services provided by the network: increasing the number of services that a network provides will cause an increase in the offered load and its variability to a given physical entity, since the physical entity will have to support the additional services of different requirements.

• the size of the data objects: particularly in some cases like video and audio the size of transmitted files is too large, thus causing network scalability problems (e.g., I/O buffers and transmission bandwidth).

• the amount of accessible data: the increasing amount of accessible data makes data search, access, and management more difficult and therefore causes storage, retrieval and processing problems.

In this paper, unlike previous described work in literature, we investigate scalability issues related to the signalling system in a B-IN. Two sets of simulation experiments are performed. In the first set we investigate the ability of the B-IN to support an increasing number of users connected to the network. In the second set of experiments we investigate the network scalability when the number of B-IN nodes is increased. As test-bed we used typical network architectures specified in the ACTSIINSIGNIA (IN and B-ISDN Signalling Integration on ATM Platforms) project. The main objective of the INSIGNIA project is to define, to implement and to demonstrate an advanced architecture integrating IN and B-ISDN signalling (ACTS, 1995).

This paper is organised as follows. Section 2 describes the network architecture and topology for the performed scalability experiments. The performance models, i.e., user workload models and network models, used for the performance evaluation are described in Section 3. The experiments and performance results obtained from the first and second sets of experiments are described in Sections 4. Finally, Section 5 concludes.

2 NETWORKARCHTIECTURE

This section briefly describes the B-IN network physical entities, B-IN network topologies and signalling information flows used in the performed scalability studies. A network topology is composed of several interacting physical entities. The signalling information flows describe the interaction among the physical entities required to establish an IN service request.


2.1 Physical Entities and Topology

The physical entities used in this work are the B-SCP, B-SSP and FT. The B-SCP is a real time, high availability system that is able to interact with other B-IN nodes and contains the logic and processing capabilities required to handle enhanced network services, such as B-VPN. The B-SSP physical entity mainly provides BIN service switching. Additional to this functionality, the B-SSP handles the B-IN service call and connection control and it is able to modify processing functions that are required during service execution under control of the B-SCP. The B-IP physical entity provides specialised resources and functionality required for multimedia interaction between end users and B-SCP, e.g., a multimedia dialogue for selection of a Service Provider supported by interactive video. The FT physical entity is the interface of the B-IN network to the end user, e.g., a Personal Computer (PC) or a workstation.

The network topology used in the first set of experiments is depicted in Figure 2(a), and it consists of four B-SSP's and one B-SCP (B-IP is not included, since it is not required for the B-VPN service that is considered here). We call such configuration a B-IN island. In the second set of experiments we assume that there are more than one interconnected B-IN islands; this network topology is depicted in Figure 2(b). Each B-IN island is identical to the topology depicted in Figure 2(a). Note that two or more B-SSP's belonging to the same island or to different islands can intercommunicate.

One B-IN One B-IN One B-IN island island' ................... ... ..... island

2(a) One B-IN island 2(b) The total B-IN network

Figure 2 B-IN network topology.

2.2 Signalling Information Flows

The signalling information flows (message sequence charts) define the spanning and routing of signalling messages among the different entities in the network on behalf of a service request. For each service that is supported by a network


topology a specific signalling information flow scenario is required. The services considered in this paper are VOICE and B-VPN. The VOICE service is a normal plain telephony service, while the B-VPN service (INSIGNIA, 1996a) realises a logical sub-network of a B -ISDN which appears to a specific group of users as a private broadband network, for voice, video or data communication.

The VOICE message sequence charts (see (INSIGNIA, 1996b» are given in Figure 3(a) and Figure 3(b) for the cases where a called user is connected to the originating B-SSP and the terminating B-SSP, respectively. Note that the originating B-SSP is always able to communicate directly with the calling user, while the terminating B-SSP is always able to communicate directly with the called user. The used signalling messages are standardised Q.2931 (ITU-T Q.2931) and B-ISUP (ITU-T Q .276 1) messages.

1l~"11 n~ J I 1I~~wJn'l l Il~" tl I I~ U n~"11 n~~-" ~ VOICE ~ pO...

S/miP

- ' - vOICBSIffi1I..,-~ I~

S/miP

CAU..PROC CAU..PROC S/miP

CAU..PROC lAM

COllNOCr 1M

CO/lNOCrJ, :K S/miP

CONNECT CAU..PROC

OO/INOCr-"C CO/INOCr-"

CO/INECT

:K

VOICE B.i ...se.,- .v<M

RFllASE CO/IlIE.CT

RFllASE CO/INECT-"O IlEI.EASE..CI 'MP

IW..EASE...CO~ PI. VOD! RIlIJ!ASI!.- -

I I RFllASE - 1-

IW..EASE...cx!.u!

REI.

RFllASE

rue IW..EASE...CO' PI.

3(a) VOICE MSC 3(b) VOICE MSC (differenl originating and lerminaling SSPs)

Figure 3 VOICE message sequence chart (MSC).

The B-VPN (see (INSIGNIA, 1997b» message sequence charts are given in Figure 4(a) and Figure 4(b) for the cases where the called user is connected to the originating B-SSP and the terminating B-SSP, respectively. Note that the interface between users and a B-SSP is called User to Network Interface (UNI), the interface between different B-SSP's is called Node to Node Interface (NNI) and in this paper, the interface between a B-SSP and B-SCP is called Intelligent Network Interface (INI), whose signalling messages are described in (INSIGNIA, 1996b).


"- "" ... .... -. ..... . ...". Ej EJ - - ..... ...... ..,.,,- -..... " --, >0. ..

c_ ClOUJOoc ·

...... 1M

EI\1P

CAUJO~

""""'" ""''''CT ... ,,'"

COH'OItT ,,,, ..... , ... C<

...... ill ....... - - -I oaJ!AlIl

~L ....

l>UA'I! ........ -OLe

.EUAJi'.."'"

4(.) B· VPN MSC 4(b) B·VPN MSC (din ... n, oriainatina.rId Ie "",."., SSPs)

Figure 4 B-VPN message sequence chart (MSC).

3 PERFORMANCE MODELS

This section describes the performance models, i.e., user workload model and network model, used to accomplish the scalability experiments. The user workload model describes the user calling pattern and intensity that has to be supported by the B-IN network, while the network models represent the flow and processing of messages through the network on behalf of user requests. Two performance measures are used to assess the network scalability; namely the network throughput and the B-VPN mean setup delay. Network throughput is defined as the total number of calls (VOICE and B-VPN) per time unit that the network can support at a given utilisation. The B-VPN setup delay is defined as the time duration from the instant when the user starts the B-VPN call set-up procedure (i.e. , by sending a SETUP message to a B-SSP) until the call set-up procedure is completed (i.e., a CONNECT message is received by the initiating B-VPN user), excluding any user response times.

3.1 User Workload Model

In all experiments we have used a traffic mix of telephony (VOICE) and B-VPN. The inter-arrival time of all user call requests at each node (i.e., B-SSP) is modelled as a Poisson process. The percentage of VOICE calls is equal to 85% of


the total load, while the percentage of B-VPN calls is 15% of the total load. Therefore, a user call request is VOICE with a probability of 0.85 and B-VPN with probability of 0.15. It is assumed that the VOICE and B-VPN call duration distributions are identical and follow a mixture of two normal distributions as described below:

F(t) = aF; (t) + (1- a)F2(t) , t ~ O.

with,

1 (t-l1/

F(t) = e 2aj ,

I (Jj.J21t t~O, i = 1,2.

The values for the parameters of the above distribution are: a = 0.4, JlI = 0.655, crI = 0.165, J.12 = 1.055, cr2 = 0.25. It is assumed that the call rate per user is fixed, and that the called user is connected to any B-SSP in the B-IN network with equal probability. Note that the load per network node can be varied by varying the number of users per node.

3.2 Network Models

In order to perform the planned experiments, we must fully characterise the network model and its parameters. In this section we give the queuing models used for performance evaluation. The routing of messages through this queuing model is determined by message sequence charts of Section 2.2. The scheduling of user requests and signalling messages at the physical entities is also characterised. Finally, model parameters, such as message processing times are given.

3.2.1 Queuing models

Queuing network models are used to represent the processing and flow of signalling messages through the B-IN network. Each physical entity (Le., B-SSP, B-SCP) is modelled by a single server queue with an infinite buffer. As an example, Figure 5 depicts the queuing model used to represent the B-IN island viewed in Figure 2(a). The network topology viewed in Figure 2(b) could also be easily represented in a similar way by extending the queuing network model.


B-SSP B-SSP B-SCP

Users (FT's)

Figure 5 Queuing model for one B-IN island.

3.2.2 Message routing

B-SSP B-SSP

The spanning and routing through the queuing network model on behalf of a user request is defined by the signalling information flows. This means that the behaviour of the queuing models is different for each service that the network provides. When the VOICE service is used, then the message routing provided by the queuing models is defined by the signalling information flows depicted in Figure 3(a) and Figure 3(b). For the B-VPN service the routing is provided by the flows depicted in Figure 4(a) and Figure 4(b).

3.2.3 Priority scheduling of signalling messages

An important characteristic of the network model is the priority scheduling scheme used to serve the user requests and the subsequent signalling messages. In our performance experiments, the so called Time-Based priority scheduling discipline is used. By using this priority scheduling, new and cycled messages belonging to the same IN request get the same priority, which is assigned based on the arrival time of the IN request. Earlier IN requests and their messages are assigned higher priorities than those assigned to later IN requests and their messages. The priority assignment to a user request (and its messages) that arrives to the B-IN network can be described as follows. Let user requests be ordered according to their arrival times to the network. Then the m-th request and all its messages are assigned priority P(m) = P(m-I) - 1, if m > 0; P(m) = MAXIMUM, if m > 0, where


MAXIMUM is the highest possible priority. For example, suppose that a request message m1 arrives at the B-SSP at time step t1 and it gets a priority PI" This message will be served by the B-SSP and then sent to the B-SCP. Now suppose that a new request message m2 arrive at the B-SSP at time step t2 (t2 > t1). This request message will get the priority Pz (Pz < PJ The message m2 waits to be served by the B-SSP. Before this message is processed, message m1 comes back to the B-SSP. The message m1 will be queued before m2 at the B-SSP queue since it has a higher priority. After the m1 departs from the B-SSP, the message m2 will proceed with its requested service at the B- SSP. In (INSIGNIA, 1997a) it has been shown by performance evaluation experiments that the Time-Based scheduling performs better than other disciplines, such as FIFO. Therefore, this priority scheduling has been used in the performed studies.

3.2.4 Model parameters

Model parameters, such as message processing times at physical entities have been obtained experimentally from the prototype platform used in the INSIGNIA project. Due to confidentiality reasons, the absolute measured values can not be disclosed. Therefore, the processing time Service Request message (see Section 2.2) is used in the experimental studies as a "Time Unit" (TU). The measurements have been performed for a B-VPN and plain telephony (VOICE) services. The NNI (B-ISUP) message processing times (in TUs) are estimated from measurements on the UNI (Q.2931). The distribution of all message processing times is assumed to be deterministic. The ratios of the measured message processing times relative to the Service Request message processing time appearing in Table 1 to Table 3, have been used in the performed studies.

4 EXPERIMENTAL RESULTS

Once the network model has been constructed, and fully characterised, it can be used to evaluate performance measures of interest. In the experimental studies of the next sections the simulation technique is used to evaluate the queuing model of the B-IN network. To provide independent observations the method of batch means is used; thus making it possible to provide confidence intervals associated with estimates of the performance measures.

Two sets of experiments are performed. The ability of a B-IN to support an increasing number of users connected to the network is investigated in the first set of experiments. In the second set of experiments we investigate the network scalability when the number of B-IN nodes is increased.

For confidentiality reasons, the absolute estimated values of performance measures could not be disclosed. Instead, all processing times and estimated delays are normalised to the value of the Service Request message processing time, which we denote in this paper as TU (Time Unit).


Table 1 The service time ratios of the INI messages for a B-VPN service Entity Incoming Message Outgoing Message Service time (TU)

B-SSP 3*RequestReportSSMChange + ReportSSMChange 0.29381 JoinPartvToSession&LinkLeg Continue CALL]ROC 0.13745

Continue SETUP 0.22164

ReleaseSession OUT{end) 0.13745

B-SCP Service Request 3*RequestReportSSM 1

ReportSSMChange Continue 0.27319

ReportSSMChange ReleaseSession 0.39003

ReportSSMChange OUT{end) 0.27319

Table 2 The service time ratios of the UNI and NNI messases for a B-VPN service Entity Incoming Message Outgoing Message Service time (TU)

B-SSP SETUP ServiceRequest 0.40034

CONNECT ReportSSMChange 0.39690

CONNECT CONNECT_ACK 0.44158

CONNECT CONNECT 0.45704

CALL_PROC OUT(end) 0.04467

ANM CONNECT 0.31958

lAM IAA 0.20790

lAM lAM 0.29037

lAM SETUP 0.29037

CONNECT CONNECLACK (in this case 0.30584 ReportSSMChange is not created)

CONNECT CONNECT (in this case 0.31958 ReportSSMChange is not created)

IAA OUT(end) 0.07560

RELEASE RELEASE 0.02920

RELEASE ReportSSMChange 0.20790

RELEASE RELEASE_COMPL 0.30068

REL REL 0.02920

REL RELEASE 0.02920

REL RLC 0.30068

RELEASE_COMPL OUT(end) 0.02920

User SETUP CALL_PROC 0.11l68

SETUP CONNECT 0.89347




Table 3 The service time ratios of the UNI and NNI messaaes for a VOICE service Entity Incoming Message Outgoing Message Service time (TUs)

8-SSP SETUP CALL_PROC 0.20790

SETUP SETUP 0.29037


CONNECT CONNECT 0.31958

CALL_PROC OUT(end) 0.01374

lAM lAA 0.20790

lAM lAM 0.29037

lAM SETUP 0.29037

lAM ANM 0.29037

lAA OUT(end) 0.07560

RELEASE RELEASE 0.02920


REL REL 0.02920

REL RELEASE 0.02920

REL RLC 0.19759

RELEASE_COMPL OUT(end) 0.02920

User SETUP CALL_PROC 0.11340

SETUP CONNECT 0.92611



4.1 Increasing the Number of Users per Node

In this set of experiments the number of nodes is fixed while the number of users connected to a B-SSP node is increased. The B-IN network topology and network model used in this set of experiments are depicted in Figure 2(a) and Figure 5, respectively. It is assumed that the total load on the B-IN network is equally divided among the four B-SSP's. The experiments are accomplished in the following way: First the bottleneck of the network is found by increasing the load (e.g., increasing the number of users per B-SSP). In order to maximise the network throughput for a given utilisation, this bottleneck is removed by balancing the processing speed of all B-IN network physical entities, such that the utilisations Pscp, Pssp' of the B-SCP and each B-SSP, respectively, are approximately equal. The balanced network is then used to accomplish the actual scalability experiments. These experiments were performed in a number of steps, during which the processing speeds/capacities of all physical entities are multiplied by a factor a. The initial value of the factor a is set to 1, and the maximum value of a was set to 100. For each step the throughput for a network utilisation of 0.9 (i.e., throughput


for which one or more of the utilisations PSCP' Pssp reach the value 0.9) and the normalised B-VPN mean setup delay (i.e., in TUs) are estimated. Note that reaching full utilisation for one or more entities implies simulating unstable system, i.e., unbounded delays.).

The estimates (with their 95% confidence intervals) indicating the bottleneck of the B-IN network are listed in Table 4. Figure 6 depicts the normalised B-VPN mean setup delay (i.e., in TUs) when the total load is varied. It is found that (for the used performance and workload parameter values) initially the B-SSP is the bottleneck. To balance the network the processing speed of each B-SSP is multiplied by the factor 1.4684 such that the load on all B-IN network physical entities is balanced (the utilisations PSCP and Pssp' of the B-SCP and each B-SSP, respectively, are approximately equal).

Table 4 Utilisations and normalised B-VPN mean setuE dela~s Load (CallsfTU) 0.213768 0.427985 1.069948 1.713408 1.979207 2.139955 . ______ ~ __ ... ____________ ._._ .. M_. __ ._. ___ . __ .. _ ... _ .....• __ ._ .. __ ... __ .....

B-VPN mean setup delay (TU)

PSO'

PSSP

3.304123 ±O.01273

0.06

0.09

Q. 12

i c ~ 10 I~ E 5 8

~ I 6 lilt:. I.;" 4

~ ~ 2

3.458762 4.190721 ±O.O 1l 64 ±O.02776

0.12 0.32

0.18 0.45

........... Nonneliled B-VPN mean setup delay

5.922680 8.144329 ±O.09144 ±O.50584

0.51 0.59

0.73 0.84

~ o+-----~--~----_+----~--~ o 0,5 1,5 2 2,5

Total network Del [callllTlma Unit)

11.864261 ±O.680068

0.64

0.91

Figure 6 Normalised B-VPN mean setup delay as function of the total load.

After balancing the network we accomplished the actual scalability experiments. The obtained estimates (with their 95% confidence intervals) are listed in Table 5. In Figure 7 the results are illustrated in graphs having as X-axis the factor a and as Y-axis the corresponding throughput at the given network utilisation (i.e., 0.9). Figure 8 has as Y-axis the corresponding normalised B-VPN mean setup delay at the given network utilisation (i.e., 0.9). In order to estimate the normalised B-VPN


mean setup delay when the B-IN network load (Le., number of users per B-SSP) is varied, the speed factor (l is set to 10. These estimates (with their 95% confidence intervals) are listed in Table 6. Figure 9 depicts the normalised B-VPN mean setup delay as function of the total load.

From this evaluation we conclude that (see Figure 6 to Figure 9, and Table 4 to Table 6): For a load mix of 85% VOICE and 15% B-VPN, the bottleneck of an BIN island is initially (i.e., before balancing) the B-SSP. To balance the network the processing speed of each B-SSP is increased by a factor 1.4684. The total network throughput increases linearly with the processing speed. The normalised B-VPN mean setup delay decreases when the processing speed is increased. We have set (l = 10 in order to estimate the B-VPN mean setup delay when the B-IN network load (Le., number of users per B-SSP) is varied. From Figure 9 it can be seen that the B-VPN mean setup delay exhibits a typical delay vs. load characteristic, i.e., the mean delays increase sharply beyond a certain limit.

Table 5 Throughput and normalised B-VPN mean setup delays a 1 5 10 20 50 100 8-VPN mean 13.432989 2.737113 1.522852 0.739862 0.340378 0.215807 setup delay (TV) ±O.480068 ±O.125567 ±O.060137 ±O.037731 ±O.013934 ±O.015716

Throughput (callsrru)

3.101478 15.50448 31.01478 62.02956 154.32312 310.15944

350

~ 300 CL:;::o i;§ 250

~ ~ 200

~ ~ 150

fi 100 Z 50

-+-Network Throughput

O~~--~--~-----+----~--~

o 20 40 60 80 100

Pro_lng speed factor a

Figure 7 Total network throughput as function of the processing speed factor (l.


Q. i 100

: ~ 10 E:5 z .. Q. E

~E. .,,> :-i ~." 0.1 E ~ z 0.01 +-------+----------i

10 100

Processing speed factor a

Figure 8 Normalised B-VPN mean setup delay as function of a (log scale).

Q.

" 1,6 D ~ _ 1,4 co ., ~ 'i§ 1,2

z; 1 Q. E ~ E. 0,8

i ~ 0,6 ~ I 0,4

~ 0,2

-+- Normalised B-VPN mean setup delay

~ o+--+--~-~-~-~-~-~ o 10 15 20 25 30 35

TOiaI network load [callsfTime UnHsj

Figure 9 Normalised B-VPN mean setup delay as function of the total load.

Table 6 Normalised B-VPN mean setup delays Load (callsffU) 3.101478 B-VPN mean 0.341065 setup delay (TU) ±O.OOO568

13.55478 0.417353 ±O.OO2348

4.2 Increasing the Number of Nodes

20.16048 0.515292 ±O.006219

26.37624 0.730927 ±O.013 1 13

31.01478 1.522852 ±O.060154

In this set of experiments we consider a network with more than one interconnected B-IN islands. The used network topology is given in Figure 2(b). It is assumed that the processing speed factor a = 10, and that the total load on the BIN network is equally divided among all islands. The experiments were performed for an increasing number of islands N. Note that initially a fixed number of users is connected to each island. This number of users may change slightly in order to adjust the network utilisation to the chosen value of 0.9. The initial value of N is one and the maximum value of N is 10. For each value of N, the throughput for a given network utilisation (0.9) and the corresponding normalised B-VPN mean setup delay (i.e., in TUs) are estimated. The obtained estimates (with their 95% confidence intervals) are listed in Table 7. In Figure 10 the results are illustrated in


graphs having as X-axis the number of islands N and as Y-axis the corresponding throughput at the given network utilisation (i.e., 0.9). Figure 11 has as Y-axis the corresponding normalised B-VPN mean setup delay at the given network utilisation (i.e., 0.9).

Table 7 Throughput and normalised B-VPN mean setup delays, as functions of N N 1 2 5 7 IO ....... _ ..... _-_ ... -._---_ .. __ ._--_._ ... __ ._---------_¥_ ... _---_. __ . __ ._ ... _ .. _---_._._--_ .......... _ .. Load! island (callsrrU) 31.01478 29.46084 28.1688 27.7614 27.44712

Throughput (callsffU) 31.01478 58.9275 141.0768 194.3298 274.4886

B-VPN mean setup 1.522852 1.371993 1.209622 1.146219 1.113402 delay (TU) ±O.060154 ±O.072027 ±O.031597 ±O.054415 ±O.048178

o+---+---~--~--~--~ o 2 4 6 8 10

Number of islands N

Figure 10 Total network throughput as function of the number of islands N .

... i 1.6 • lA c";' Ii 1.2 z; 1 g; S 0.8 ad:. "i 1; 0.6

:! ~ 0.4

-+-Nonn.Used B-VPN maon setup dalay

§ 0.2

z o+---~--~----+---~--~ o 6

Number orlolancls N

10

Figure 11 Normalised B-VPN mean setup delay as function ofN.

For a fixed number of islands (N=10) the normalised B-VPN mean setup delay is estimated for a varying network load (i.e., a varying number of users per B-SSP). These estimates (with their 95% confidence intervals) are listed in Table 8. Figure 12 depicts the normalised B-VPN mean setup delay as a function of the load per island. From this evaluation we conclude that (see Figure 10 to Figure 12, and Table 7 and Table 8): The total network throughput increases linearly with the number of islands. The normalised B-VPN mean setup delay (i.e., in TUs) decreases by increasing the number of islands. The main reason for this is that (see Table 7) the input load on each island has to be slightly decreased (in order to


adjust the network utilisation to 0.9) when the number of islands N is increased, hence the slightly lower delays. For N = 10 we have performed experiments on the normalised B-VPN mean setup delay by varying the load per each B-IN island. From Figure 12 it can be seen that the normalised B-VPN mean setup delay increases by increasing the network load per island (or the total network load).

Table 8 Normalised B-VPN mean setup delays, for N = 10 Load/island (callsffU) 3.101478 13.55478 20.16048 26.37624 27.44712

B-VPN mean setup 0.350859 0.438144 0.556529 0.931958 1.113402 delay (TU) ±o.OO1654 ±o.OO2841 ±o.020859 ±o.048694 ±o.048178

D. 1,2 j c _ 1

:~ E:5 0,8 z • ~ ~ 0.6

i}' 0,4 :!-!I

-..- Normalised B-VPN maan setup delay (N = 10)

~ 0,2

z +---~--~---+--~----+-~

10 15 20 25 30

Network load per Island [callsfTime Unit]

Figure 12 Normalised B-VPN mean setup delay as function of the load per island.

5 CONCLUSIONS

This paper investigates some scalability issues related to a Broadband Intelligent Network (B-IN). In particular we have considered the B-IN signalling system being developed in the INSIGNIA project. The experiments are accomplished in several steps. First the bottleneck of the network is found by increasing the load (e.g., increasing the number of users per B-SSP). Then this bottleneck is removed by balancing the processing speed of all B-IN network physical entities (i.e., BSSP and B-SCP), such that their utilisations are approximately equal. The balanced network is then used to accomplish two sets of scalability experiments. In the first set we investigated the ability of a B-IN to support an increasing number of users connected to the network. From this set of experiments we conclude that the total network throughput increases linearly with the processing speed, and that the BVPN mean setup delay decreases by increasing the processing speed. In the second set of experiments we have investigated the scalability when the number of B-IN nodes is increased, and we concluded that the total network throughput increases linearly with the number of B-IN nodes, while the B-VPN mean setup delay remains almost unchanged. A future target for B-IN is to provide advanced services to fixed and mobile users; the scalability of such a network is an important issue which is currently being investigated.


6 ACKNOWLEDGEMENTS

This paper is based on work accomplished in the ACTS project INSIGNIA in which the authors participated. The authors would like to express their gratitude to the members of the project, and to the European Committee. The views expressed in this paper are those of the authors and not necessarily those of the project as a whole.

7 REFERENCES

ACTS (1995), ACTS'95, Project Summaries. INSIGNIA, (1996a), First Trial: Description of the Selected Services, project

document reference number AC068/CLT/IIIIDS/P/OOllcO. INSIGNIA (1996b), Node-based Signalling Traffic Models and Performance

Parameters, project document reference number AC0681U0TI114IDS/P/OO31b0.

INSIGNIA (1997a), Network-based Signalling Traffic Models and Performance Parameters, project document reference number AC0681U0T/114IDS/P/OO61bO.

INSIGNIA (1997b), First Trial: Protocol Specification, project document reference number AC068INTUI120IDS/L/OOllxl.

ITU-T Q.2761, ITU-T Recommendation Q.2761, Broadband Integrated Services Digital Network User Part.

ITU-T Q.2931, ITU-T Recommendation Q.2931, B-ISDN User-Network Interface Layer 3 Specification for Basic Call1Bearer Control.

Gauthier E., Le Boudec J.-Y., (1996) Scalability Enhancements on Connection Oriented Networks, in Lecture Notes in computer science, 1044,27-38.

Karagiannis G, van Beijnum B, Niemegeers I, (1997), On the Integration of the UMTS and B-ISDN System, in Proceedings of IFIP (HPN'97), Chapman & Hall, 39-56.

Lin X. M., Orlowska M. E., Zhang Y.-c. (1994), Database Placement in Communication Networks for Minimizing the Overall Transmission Cost, in Mathematical and Computer Modelling Magazine, 19, (1), 7-20.

Martini P., Ottensmeyer 1. (1996), On the Scalability of the Demand-Priority LAN - A Performance Comparison to FDDI for Multimedia Scenarios, in Lectures Notes in computer science, 1044, 146-60.

Modarressi A. R., Skoog R. A. (1990), Signalling System No.7: A tutorial, in IEEE Communications Magazine, 28, 44-56.

Saha D., Mukherjee A. (1995), Design of Hierarchical Communication Networks under Node Link Failure Constraints, in Computer Communications Magazine, 18, (5), 378-83.

Thorner 1., (1994), Intelligent Networks, Artech House Telecommunication Library.


8 BIOGRAPHY

G. Karagiannis received a bachelors degree in Electrical Engineering at the T.E.! Athens, Greece in 1987. In 1988 he joined the laboratory of Network Theory of the Electrical Engineering department at the University of Twente, the Netherlands, where he was involved in VLSI design projects. He received a MSc. degree in electrical engineering at the University of Twente in 1993. In 1995 he graduated for a post graduate designers course at the Tele Informatics and Open Systems (TIOS) group at the University of Twente. In 1995 he joined the CTIT at the University of Twente. His areas of interest include mobile communication systems, network control mechanisms, performance modelling and analysis. He has actively participated in the RACE-II project MONET and is presently actively involved in the ACTS project INSIGNIA.

V. F. Nicola holds the Ph.D. degree i!1 computer science from Duke University, North Carolina, the B.S. and the M.S. degrees in electrical engineering from Cairo University, Egypt, and Eindhoven University of Technology, The Netherlands, respectively. From 1979, he held faculty and research staff positions at Eindhoven University and at Duke University. In 1987, he joined IBM Thomas J. Watson Research Center, Yorktown Heights, New York, as a Research Staff Member. Since 1993, he has been an Associate Professor at the Department of Electrical Engineering, University of Twente, The Netherlands. His research interests include performance and reliability modeling, fault-tolerance, queueing theory, analysis and simulation methodologies, with applications to computer systems and telecommunication networks.

I.G.M.M. Niemegeers was born in Gent, Belgium in 1947. He received a degree in electrical engineering from the Rijksuniversiteit Gent in 1970. In 1972 he received a MSc. E. degree in computer engineering and in 1978 a Ph.D. degree from Purdue University in West Lafayette, Indiana, USA. From 1978 to 1981 he was a designer of packet switching networks at Bell Telephone Mfg. Cy., Antwerp, Belgium.Since 1981 he is a professor at the Computer Science Department of the University of Twente, Enschede, the Netherlands. He is presently Scientific Director of the Centre for Telematics and Information Technology of the University of Twente. His areas of interest are communication systems and performance analysis. He is active in research on integrated networking, highspeed networking, B-ISDN, optical networking, performance analysis and performability.

7 Hop-by-hop option based flowhandling compared to other IP over ATM protocols

Loukola, M. v. and Skyttii, J. O. Helsinki University of Technology Department of Electrical and Communications Engineering P.O. Box 3000,02015 HUT, Finland phone: +358-9-4512476,fax: +358-9-460224 e-mail: [email protected]

Abstract This paper introduces new ways to establish data link level forwarding for IPv6 packets on A TM links. The designed method is merged into to the core of IPv6 protocol. This improves the performance compared to the other traffic-based IP over ATM protocols. (RFC-1953) (RFC-2129)

Keywords Flow-handling, IP over ATM, IP switching

Perfonnance of Information and Communication Systems U. Komer & A. Nilsson (Eds.) e 1998 IFIP. Published by Chapman & Hall


1 INTRODUCTION

From Internet Protocol, Version 6, Specification (RFC-1883) page 28:

A flow is a sequence of packets sent from a particular source to a particular (unicast or multicast) destination for which the source desires special handling by the intervening routers. The nature of that special handling might be conveyed to the routers by a control protocol, such as a resource reservation protocol, or by information within the flow's packets themselves, e.g., in a hop-by-hop option.

From IPv6 The New Internet Protocol (Huitema, 1996) page 130:

Some researchers believe that they can define the quality of service requirements of a given flow in a hop by hop option. This option would be transmitted in some packets. The routers would remember the associated parameters and associate them with the flow.

The paper will study the implementation of the flow-handling based on the IPv6 Hop-by-Hop Options extension header.

2 LAYER 2 VERSUS LAYER 3 FORWARDING

Layer 2 forwarding provides simple and fast packet forwarding capability. One primary reason for the simplicity of layer 2 forwarding comes from its short, fixed length labels. A node forwarding at layer 3 must parse a relatively large header, and perform a longest-prefix match to determine a forwarding path. (Doolan, 1996) (RFC-1987)

When a node performs layer 2 forwarding it can do direct index lookup into its forwarding table with the short header. It is arguably simpler to build layer 2 forwarding hardware that it is to build layer 3 forwarding hardware because the layer 2 forwarding function is less complex. (CalIon, 1997) (RFC-1954)

By bypassing the conventional IP forwarding (the packet assembly/reassembly) process using cell-relaying, we could dramatically reduce both the IP packet processing delay and the queuing delay at the router. (Esaki, 1997) Pushing traffic to layer 3 may cause congestion. If data is discarded (Hop Limit = 0) or lost (buffer full) TCP will backoff. (RFC-1885)

Hop-by-hop option based flow-handling 85

3 LABEL ALLOCATION

Label allocation can be made both by the downstream node and the upstream node. Downstream allocation is similar to the other designs in the way that the upstream node asks the downstream node to allocate a label for a specific flow. Only in this design no extra request packets are sent. The request for label is carried within every IPv6 packet that belongs to the specified flow. The request for label resides in packet's Hop-by-Hop Option header. Only the label itself needs to be transferred in its own IPv6 packet from the downstream node to the upstream node.

The label resides in the Destination Options header of the IPv6 packet with zero length payload.

The upstream label allocation is very simple. The upstream node can pick up a label and start to send packets belonging to the specific flow using the label. The downstream neighbor needs to reassemble the IPv6 packet in order to make the label bindings to its Label Base (LB). In an ATM switch, the VPIIVCI bindings are link specific so both the upstream and the downstream node know what labels are used and what are unused. The VPI/PCI values are only unique in the physical interface as illustrated in Figure 1. (Esaki , 1997)

Figure 1. A TM cell multiplexing and relaying


The upstream label allocation requires some specific features from the A TM switch. It is contingent on A TM switches to keep the cells of a PDU contiguous and in sequence. That is why there is a need for a specific solution in case of upstream label allocation.

3.1 Downstream label allocation method

Trigger IP packet starts the cut-through operation (1), Figure 2. The trigger packet has a Hop-by-Hop Options header in its header chain with the Option Type 00110110 (bin). This Option Type is used for all Augmented IP Router Protocol (AIRP) messages. This is just some unique Option Type to be used. This protocol is part of the design and is needed to carry messages between the upstream and downstream node. The trigger packet carries a request for layer 2 forwarding label or layer 3 IPv6 Flow Label for accelerated layer 3 forwarding. Once the 2nd router receives such a request it sends the label to its upstream neighbor in a IPv6 packet (2), Figure 2. This packet has also a Options header with the Option Type 00110110 (bin). This Option header resides in Destination Options header and contains the label to be used for the specific flow. Once the upstream router has received this packet it can start to send packets belonging to that flow labelled with the specific label (3), Figure 3.

When the 3rd router receives the trigger IP packet (4), it sends the label to its upstream neighbor router (5), Figure 3. The 2nd Router can now start to send packets belonging to that flow on the dedicated-VC (6). The label allocation process is illustrated in Figures 2-4.

Tril!!!l'r IP I'a 'kct

t :lht' rnl'I • 1 Router

\ '1 \I 2" Router

\ '1'" ... Ethernet 3 Router

Figure 2. Downstream label allocation #1


LahcllCl Ih(' up.,lrram lIuM Triggl·r II' P"d.l·1 -------

Llcdil'alcd- \ T .'l'u labc l

~ El hrrnrt 3 Router Ethernet •

1 Router ATJ\I

2"' Router


lI l-ThrUIIllh


3.2 Upstream label allocation method

Another way to achieve cut-through operation is to use upstream label allocation. This means that the upstream node chooses the label (=VCI) to be used. In this case the node choosing the label and the node which needs to interpret packets using that label are not the same node.

When the 1st Router receives trigger IP packet belonging to a new flow, it allocates a label i.e. VCI to it. After that the upstream node is free to send the packets belonging to that flow on the dedicated-VC (I). When the downstream node receives cells on the new VCI that it has no entry in its LB, it has to reassemble the IPv6 packet is order to determine where the packet is going (2). After the packet is reassembled, a next link label is allocated and a entry is entered to the LB. After that the 2nd router begins to send cells to the next router on this new dedicated-VC (3). After the cells belonging to the flow arrive at the border node of the ATM domain (3rd router), the packet is once again reassembled and sent on the non-ATM link (4). The cut-through establishment is illustrated in


Figure 5. The following IP packets receive the cut-through treatment at the 2nd router (5) as shown in Figure 6.

Figure 5. Upstream label allocation #1

2" Router

Figure 6. Upstream label allocation #2

4. LABEL DISTRIBUTION

Label distribution occurs between A TM switches which have been augmented with standard IP routing support. The IP routers must be able to recognize the IPv6 Option type (00110110 bin) used in this design. Such IP routers are referred as Augmented IP Routers (AIRs). The word augmented here refers to the AIRs ability to recognize the needed IPv6 Option type.

In the downstream label allocation mode the request for label is passed in the IPv6 Hop-by-Hop Options header and the label is passed to the upstream node in the IPv6 Destination Options header. Both the Destination Options and the Hop-byHop Options headers can contain Options in the same format. (RFC-1883)


Labels expire when there has not been any packet carrying that specific label for 180 seconds.

4.1 Traffic Based Soft-State Label Base Bindings

The AIRP protocol exchanges layer 2 labels based on traffic like IP switching. (RFC-1953) This reduces the overhead of exchanging labels between all peers in a routing domain and reduces the size of the label binding information bases in routers.

Topology based methods have the ability of forwarding all the packets on layer 2 including the first packets of each flow, while in traffic based methods the first packet has to be reassembled in all the routers along the packets delivery path. But this was not a sufficient argument to make AIRP a topology based protocol. Simplicity is beautiful.

The nature of the bindings in the LB is soft-state because the connection is established due to the request in the first IPv6 packet. But on the other hand there is no refreshment procedure or keep-alive messages between the neighboring Augmented IP Router (AIRs).

5. AUGMENTED IP ROUTER PROTOCOL

The AIRs need to exchange information with each other. That is why a simple Augmented IP Router Protocol (AIRP) is needed. The messages are transferred within the IPv6 packet's Hop-by-Hop Options header or the Destination Options header. (RFC-1883, RFC-1884)

5.1 Message Types

Three kind of message types are defined: 1) request for label message, 2) label transfer message, and 3) label removal message.

Request For Label Message This message must be within all the IPv6 packets belonging to the same flow that want special AIRP treatment. The first packet triggers the downstream label allocation procedure. Table 1 shows the format of the Hop-by-Hop Options header.


Table 1 Format of the Request For Label message

octet field data

1" Next Header 2nd Hdr Ext Len 00000000 3rd Option Type 00110110 4th Opt Data Len 00000100 5th Action 00000001 6th Reserved 00000000 7th Reserved 00000000 Sth Reserved 00000000

After a downstream AIR receives this message it allocates a 24-bit label to be used for the flow, and enters that label to its LB. After the label is entered to LB, the downstream AIR sends a label transfer message to the upstream AIR.

Label Transfer Message This message is a response to the label request message. Table 2 shows the format of the Destination Options header.

Table 2 Format of the Label Transfer Message

octet

1st 2nd 3rd 4th

5th 6th_Sth 9th _24th 25th_40th 41st_43rd 44th_4Sth

field data

Next Header Hdr Ext Len = 0000 0101 Option Type = 0011 0110 Opt Data Len = 0010 1100 Action = 0000 0010 Label Source Address of the IP packet that triggered downstream a. Destination Address of the IP packet that triggered downstream a. Flow Label of the IP packet that triggered downstream a. Reserved

As the upstream AIR receives this message, it is ready to use the VCI for the specified flow.


Label Removal Message If the upstream node wants the downstream node to delete a LB binding it can send a label removal message instead of waiting the 180 seconds. This is desired if the number of ongoing flows is near to the maximum, but otherwise it is a waste of bandwidth. The format of this message is shown in Table 3.

Table 3 Format of the Label Removal Message

octet field data

I" Next Header 211d Hdr Ext Len = 0000 0000 3'd Option Type = 0011 OlIO 4111 Opt Data Len = ()()()() 0 I 00 Sill Action = ()()()() 00 II 6111_8111 Label

This message is sent on default vel. After this the downstream node deletes the binding from its LB and can make use of the same label immediately after the deletion.

6. SIMULATIONS

ATM 625

Figure 7. The simulation platform


The IP over A TM protocols were simulated in a fixed platform illustrated in Figure 7. The simulator is based on the performance of real A TM switches available from Cisco Systems. The throughput oflayer 2 forwarding (1.357 Gbps) is taken from the LightStream 2020 Multiservice ATM Switch specifications (Cisco, 1995). The throughput of layer 3 forwarding is taken from the TCPIIP Router Tests, v2.5 (Digital, 1997). The throughput depends on the packet size. The average layer 3 forwarding speed is 7.25 Mbps when packet sizes of 64, 128,256, 512, 1024, 1518 bytes are used randomly. (Loukola, 1997)

In the simulation each host has ten ongoing flows to other hosts. The destination of each flow is chosen randomly. The average flow lengths can be configured. When one flow is ended another is established. At all times each host has ten ongoing flows. Each individual packet of each flow is randomly picked from the six possible packet sizes listed above. This simulation platform gives the possibility to find the maximum forwarding speed of Router6 that is the bottleneck of the network. When the number of IP packets in the layer 3 queue of a router exceeds the buffer size the load has been too heavy. The maximum forwarding speed of the Router6 can be found by adjusting to transmitting speeds of the hosts. When the peak layer 3 queue size of the Router6 is between 90% and 100%, the forwarding speed can be considered the maximum one.

The optimistic estimation of the effect of cached flow-handling (CFH) in layer 3 performance is used. An existing CFH entry in a router is estimated to decrease the layer 3 processing delay to 5 percent of the normal processing time.

III 1400 c:a. ~ 1200 ....

11000 III 800 01 C 600 :a .. ! 400 0 - 200 >C as E 0

0 II) C') (\J ~ 8 8

... 0 0 (\J

flow length I packets

Figure 8. Simulation Results

--Topology-based protocols

_AIRP Upstream

---.-AIRP Downstream

~Updated IFMP

-e-CSR - traffic-based

_ Normal L3 Forwarding WithCFH

Topology-based protocols like Tag Switching, Aggregate Route-Based IP Switching (ARIS), and Switching IP Through ATM (SITA) have the maximum

Hop-by-hop option basedflow-handling 93

forwarding speed in spite of flow length because the ATM switch is configured prior to the IP packet transmissions. AIRP with its upstream label allocation proves its power. AIRP is merged to the core of IPv6. This reduces processing overhead in the routers. (Feldman, 1997) (Viswanathan, 1997) (Cisco, 1997) (Heinanen, 1996) (Davie, 1997)

7. REFERENCES

Feldman, N. and Viswanathan, A. (1997) ARIS Specification, Internet Draft <draft-feldman-aris-spec-OO.txt>, IBM Corporation, March 1997

Viswanathan, A., et. al. (1997) ARIS: Aggregate Route-Based IP Switching, work in progress, Internet Draft <draft-viswanathan-aris-overview-OO.txt>, IBM Corporation, March 1997

Loukola, M. (1997) Data Link Level Forwarding for IPv6 Packets On ATM Links, Licentiate's Thesis, TKK, November 1997

CalIon, R., et. al. (1997) A Framework for Multiprotocol Label Switching, Network Working Group, Internet Draft <draft-ietf-mpls-framework-OO.txt>, May 1997

Conta, A. and Deering, S. (1995) Internet Control Message Protocol (ICMPv6) for the Internet Protocol Version 6 (lPv6) Specification, RFC 1885, Digital Equipment Corporation, Xerox PARC, December 1995

Deering, S. and Hinden, R. (1995) Internet Protocol, Version 6, Specification, RFC 1883, Xerox PARC, Ipsilon Networks Inc., December 1995

Hinden, R. and Deering, S. (1995) IP Version 6 Addressing Architecture, RFC 1884, Ipsilon Networks Inc., Xerox PARC, December 1995

Newman, P., et. al. (1996) Ipsilon Flow Management Protocol Specification for IPv4 Version 1.0, Ipsilon Networks Inc., RFC 1953, May 1996

Newman, P., et. al. (1996) Ipsilon's General Switch Management Protocol Specification Version 1.1, Ipsilon Networks Inc., RFC 1987, August 1996

Huitema, C. (1996) IPv6 The New Internet Protocol, Prentice Hall PTR, 1996 Cisco Systems (1997) LightStream 2020 Multiservice ATM Switch", Cisco

Brochure, Cisco Systems Inc., September 1995 Cisco Systems (1997) Scaling the Internet With Tag Switching, White Paper, urI:

http://www.cisco.comlwarp/publicn321tag/pjtag_wp.htm. urI valid: october 20, 1997, Cisco Systems Inc., April 1997

Doolan, P., et. al. (1996) Tag Distribution Protocol, work in progress, Internet Draft <draft-doolan-tdp-spec-OO.txt>, Cisco Systems, Inc., September 1996

Digital Equipment Corporation (1997) TCPIIP Router Tests, v2.5, Digital Equipment Corporation, July 1997

Nagami, K., et. al. (1997) Toshiba's Flow Attribute Notification Protocol (FANP) Specification, RFC 2129, Toshiba Corporation, April 1997


Newman, P., et. al. (1996) Transmission of Flow Labelled IPv4 on ATM Data Links Ipsilon Version 1.0, Ipsilon Networks Inc., RFC 1954, May 1996

Heinanen,1. (1996) Updated SITA Proposal, Telecom Finland, November 1996 Davie, B., et. al. (1997) Use of Tag Switching With ATM, Internet Draft <draft

davie-tag-switching-atm-01.txt>, Cisco Systems, Inc., January 1997 Esaki, H., et. al. (1997) White Paper on CSR (Cell Switch Router) Provided by

Toshiba Corporation, Toshiba Corporation, April 1997

8. BIOGRAPHY

Mika Loukola works currently at Helsinki University of Technology as a research engineer in the Laboratory of Signal Processing and Computer Technology. Loukola has recently graduated as a Licentiate of Technology. His Licentiate's Thesis Data Link Level Forwarding for IPv6 Packets On ATM Links studied the wide spectrum of IP over ATM protocols. His previous Master's Thesis ATM Network Emulator for Private Network-to-Network Interface studied the A TM Forum specifications for high speed data communication. Loukola is currently involved with priority based IP networking.

Jorma Skytta is associate professor of signal processing and computer technology at Helsinki University of Technology. He holds Doctor of Technology from the same university at the area of digital signal processing implementations. His current research interests include high speed data communications.

PART THREE

Traffic Characteristics

8 Peakedness Characterization Teletraffic S. Molnar, Gy. Miklos

• In

High Speed Networks Laboratory, Dept. of Telecommunications and Telematics, Technical University of Budapest H-1111, Sztoczek u. 2, Budapest, Hungary Tel: +36 1 4633889, Fax: +36 1 4633107, Email: {molnar,miklos}@ttt-atm.ttt.bme.hu

Abstract The bursty nature of traffic over many time scales is one of the most challenging characteristics of high speed networks. In this paper we deal with the generalized peakedness as a promising candidate measure of this poorly understood phenomenon. An extension of the framework of the theory of generalized peakedness in discrete time with the applications for the most important traffic models are developed and the results are demonstrated in the paper. A new model fitting technique is also given in this framework with examples. Finally, the engineering aspects of the measurement of peakedness and applications for various real traffic (MPEG video, aggregated ATM, Ethernet) are presented.

1 INTRODUCTION

An important experience from recent measurement studies (including Ethernet, ATM LAN/WAN networks [7,14,16]) regarding the nature of broadband traffic is that traffic exhibits bursty properties over many time scales.

One of the key concepts for capturing the bursty character of traffic is selfsimilarity which resulted in active research on fractal characterization [7,14]. So far it is not clear how successfully we can utilise self-similarity from a practical traffic engineering point of view but one thing is for sure: burstiness seems to be the most important yet poorly understood characteristic of traffic in high-speed networks. Our work is motivated by this need. In this paper we focus on peakedness as one of the most promising candidate measures of traffic burstiness.

The simplest burstiness measures take only the first-order properties of the traffic into account. A set of candidates are the moments of the interarrival time distribution. In practice the peak to mean ratio and the squared coefficient of variation are the most frequently used first-order measures [13, 15J.

Measures expressing second-order properties of the traffic are more complex. The autocorrelation function, the indices of dispersion [4,18] and the generalized peakedness [2,3] are the most well known measures from this class.


98 Part Three Traffic Characteristics

Moreover, there are a number of burstiness measures based on different concepts, e.g. we can use burst length measures [15,19] or parameters of a leaky bucket for burstiness characterization [12]. By the concept of self-similarity the Hurst parameter and other fractal parameters are also candidates for burstiness measures [7,14].

In this paper we review the theory of generalized peakedness and further develop the basic concept by introducing the generalized peakedness in discrete time. The advantage of this approach is that it allows us to apply the general framework of peakedness for traffic engineering. We provide the computation of peakedness for a number of important discrete time models including the Markov modulated batch Bernoulli process and the batch renewal process. The relationship between IDC and peakedness is also presented. We discuss the challenges of measuring peakedness in practice. Moreover, we show a technique how Markov modulated traffic models can be fitted to a measured peakedness curve. Finally, the practical applicability of peakedness and our modeling technique are demonstrated by examples based on measured MPEG video, aggregated ATM and Ethernet traffic.

2 PEAKEDNESS MEASURES

Peakedness of a traffic stream has been found a useful characterization tool in blocking approximations and in trunking theory [5]. It has been defined as the variance to mean ratio of the number of busy servers in an infinite hypothetical group of servers to which the traffic is offered, where the service times of the servers are independent and exponentially distributed with a common parameter.

2.1 Generalized peakedness

Eckberg [2] extended this definition by allowing arbitrary service time distribution and defined genemlized peakedness as a functional which maps holding time distributions into peakedness values. For a given complementary holding time distribution FC (x) = P {holding time> x}, Eckberg defines the peakedness functional z{FC} as the variance to mean ratio of the number of busy servers in a hypothetical infinite group of servers with independent holding times distributed according to Fe. The general definition provides a way to characterize the variability of an arrival stream with respect to a given service system.

Let us have a stationary arrival process S in continuous time with counting function N(t) = the number of arrivals in (0, t] for t ~ o. The mean arrival intensity is denoted by m = E {N(t)} It, which is independent of t due to the stationarity of S.

Arrivals are allowed to come in batches of random size B. We define the

Peakedness characterization in teletraffic 99

batchiness parameter as b = E { B2} /E {B} which can be shown to be the mean size of a batch that an arbitrary arrival finds itself in. The differential process [1] LlN(t) is defined for a fixed Llt as the number of arrivals in (t, t + Llt], that is, N(t + Llt) - N(t). We define the covariance density of the arrival process k(s) for s > 0 as the covariance of the differential process as Llt goes

to zero: k(s) = lim~t-+o COV{~~~h~N(t+8)} which is independent of t due to

the stationarity of S. For s < 0 we let k(s) = k( -s). We offer the arrival process S to an infinite server group where the service

times are independent and have a complementary holding time distribution of FC(x) (x ~ 0; for x < 0, we define FC(x) = 0), mean holding time of 1/ J-L = J~oo FC(x)dx where J-L is the service rate, and finally the autocorrelation of FC is PFc (x) = J~oo FC(s)FC(s + x)ds.

Denoting the number of busy servers at time t by L(t), the generalized peakedness functional is defined as

{FC} = Var {L(t)} Z E{L(t)} . (1)

If the arrival stream is defined for the whole time axis (-00,00), it is independent of t due to the stationarity of S. In practice, we never have an arrival process for an infinitely long time; in this case, we have to define the peakedness for a t which is large enough for the initial transient period in the service system to be negligible. (More precisely, z{FC} = limt-+oo Var {L(t)}/E {L(t)}.)

With the notation introduced above, the peakedness of the arrival stream can be expressed in terms of the covariance density function as [2]

J-L roo z{FC} = 1 + m Loo (k(s) - mc5(s))PFc(s)ds (2)

where c5(s) is the Dirac delta function. The important case of exponential service time simplifies to

(3)

where k*(J-L) = Joo::. k(s)e-/l8 ds, the Laplace transform of the covariance density function. Here we have the peakedness of a given arrival stream as a function of the service rate J-L.

It is shown [2] (and is suggested by eq. (3)) that the peakedness function zexp(J-L) together with m determines k(s) and therefore the pair (zexp(J-L),m) is a complete second order characterization of the arrival process.

The peakedness function zexp(J-L) can be used to compute the peakedness functional for a large class of holding time distributions as shown in [2]. The method is elaborated in [11] to give the peakedness functional for Coxian


holding time distributions. The importance of Coxian holding times lies in the fact that any holding time distribution can be approximated with arbitrary accuracy by Coxian distributions. Eckberg also investigated the application of generalized peakedness in delay systems [3]. Eckberg's definition of generalized peakedness for point processes has been extended in [8,9] to allow fluid flow models given by a rate function.

2.2 Peakedness in discrete time

In order to use the peakedness measures in a B-ISDN framework, we now extend the peakedness concept for discrete time arrival streams.

We use the following notation: w[i] is the number of arrivals at epoch i, where i = ... -1,0,1, .... We assume the stationarity of w[i]. The first and second moments of w[t] (independent of t) are denoted by ml and m2. The covariance density of continuous time is replaced here by the autocovariance function k[s] = Cov {w[i], w[i + s]} = k[ -s]. (It is seen that k[O] = m2 - mi-)

The service time random variable T is also discrete and has the distribution t[l], t[2], ... on positive integers. (It cannot take on zero value.) f.L = liE {T} is again the service rate, and it is easily shown that II f.L = E {T} = 2::-00 FC[s] where FC[x] is the complementary holding time distribution function: FC[x] = 2:~=x+l t[u] = P {T > x} if x ~ 0 and FC[x] = 0 if x < o. The autocorrelation function is now PFc[X] = 2::-00 FC[s]FC[s + x]. It is seen that PFc[O] = 2::-00 (FC)2[S].

The traffic is offered to an infinite group of servers with independent identically distributed service times determined by FC[x]. Each arrival takes a separate server. The peakedness of the arrival stream is defined as the variance to mean ratio of the number of busy servers in the infinite server group:

{FC} = Var {L[t]} Z E {L[t]} (4)

where L[t] is the number of busy servers at time epoch t. An important modification of the definition is to let the service time depend

on the arrival epoch only (have a common service time for all w[t] arrivals at epoch t). We call (in accordance with [9]) the peakedness value defined in this way the modified peakedness z{FC}. As we have shown [10],

(5)

that is, their difference is constant (cf. (35) in [9]). The first factor in the difference is zero if and only if the arrival stream has no simultaneous ar-


rivals, the second factor is zero if and only if the holding time distribution is deterministic.

The importance of this modified definition lies in the fact that it gives a way to handle a whole batch of arrivals together, which can save a lot of computational effort in the case of measuring the peakedness for a general holding time distribution. However, in the case of geometric service times, the original definition of peakedness is easier to measure as shown in section 3.1. We will use the original definition of peakedness (eq. (4)) below.

We can express peakedness in terms of the auto covariance function k[s] similarly to eq. (2) as

00

z{FC} = 1 + ~ L PFe[s](k[s] - m1c5[s)). ml B=-OO

(6)

The most important case in discrete time is the case of geometrically distributed holding times: t[i] = JL(I- JL)i-l, 0 < JL < 1 (with E {T} = 1/ JL which justifies the notation).

In order to simplify the formulas, let us introduce the notation

{ ~ k[s] K[s] = n!: k[O]

if s > 0 if s = 0

and let its z-transform be K*(w) = E:'oK[s]wB •

The peakedness function of the arrival stream with respect to geometric holding time distribution, as we derived in [10], is given by

K*(I- JL) -1 Zgeo(JL) = 1 + --'-2--'-'-

-JL

2.3 Peakedness and IDC

(7)

The widely used measure to characterize the variability of an arrival stream on different time scales is the index of dispersion for counts (IDC). It is defined as I[t] = ~ = ¥!N where E[t] and V[t] are the mean and variance of the number of arrivals in t consecutive epochs (t = 1,2, ... ).

The connection of IDC and peakedness for geometric holding times is, as we have shown [10]

( ) _ 1 + JL2fwI*(w)lw=1-I' - 1 Zgeo JL - 2 -JL

(8)

where I*(w) is the z-transform of I[t].


We can use eq. (8) to get asymptotic results which connect them [IOJ:

(0) _ lims-too I[sJ + 1 Zgeo - 2 ' (1) = I[lJ = Var {w[i]}

Zgeo E {w[i]} (9)

2.4 Peakedness of traffic models

Next, we present the peakedness results for important traffic models. We consider discrete time models for the number of arrivals in consecutive epochs.

( a) Batch Bernoulli process A very simple type of arrival stream model is the model with the number of arrivals in a time epoch be independent identically and generally distributed with mean ml and second moment m2.

In this case, k[iJ = 0 for all i > O. Thus, K*(l - p,) = K[OJ = VE~~~\i} and Var{w[i]} 1

Zgeo(P,) = 1 + E{;~~ For the special case of Poisson batch arrivals, the

distribution of arrivals in an epoch is Poissonian, thus VE~~~\i} = 1 which

gives Zgeo(P,) = l. The Poisson process can be considered as a reference process with respect

to peakedness characterization. Batch arrival processes that are more bursty than the Poisson process have higher peakedness values, smoother processes have lower peakedness. (In the case of deterministic traffic, Zgeo(P,) = 1- 2~JL')

(b) Markov modulated batch Bernoulli process A very general Markovian process is the Markov modulated batch Bernoulli process (MMBBP). In this model, we have a discrete time Markov process as a modulating process. In each state of the modulating Markov-process, batch arrivals are generated according to a general distribution corresponding to the state.

Let P and D denote the transition probability matrix and the steady-state distribution vector of the modulating Markov process, respectively (DP=D). Let Ml and M2 be diagonal matrices corresponding to the first and second moments of the number of arrivals in the corresponding states. Let e be a vector of all ones and let I be the identity matrix.

We can express the mean number of arrivals as ml = DM1e and the second moment as m2 = DM2e. The auto covariance function of the arrival process is given by k(i) = DM1piM1e - mi.

Using eq. (7) we have derived the peakedness function as [IOJ

Zgeo(p.) = 1 + _1_ (2(1 - p.)DMIP(I - (1 - p.)p)-lMle + m2 _ 1) _ ml (10) 2 - P. ml p.


A very important case of MMBBP is the Markov modulated Bernoulli process (MMBP); its peakedness curve is the special case of eq. (10).

( c) Switched batch Bernoulli process Another important special case of MMBBP is the 2-state MMBBP (SBBP, switched batch Bernoulli process). Let us use the following notation: the tran-

sition matrix is P = [ 1 - 01 1 01 ] and the steady state distribution is 02 -02

thus D = Ql!Q2 (02 od· Denote 'Y = 1 - 01 - 02. In state 1, the first and second moments of the

number of arrivals are m1,(1) and m1,(2), respectively; in state 2, the moments are m2,(1) and m2,(2)'

The first and second moments of the number of arrivals are given by m1 = Ql!Q2 (02m 1,(1) + 01m 2,(1)), m2 = Ql!Q2 (02m 1,(2) + 01m 2,(2))' Let us also introduce the notation m. = Ql!Q2 (02m~,(1) + olm~,(l))' Note that if the distribution of the batch size in a given state is deterministic, or if it is geometric or Bernoulli, we have m~,(l) = mi,(2) (i = 1,2) and thus m. = m2.

If the batch distribution is Poisson, we have m. + m1 = m2.

Using eq. (10) and the possibility to explicitly compute the inverse of 1-(1 -IL)P in the 2-state case, we get

Zgeo(lJ) = 1 + _1_ (~(I-IJ) [m. _ (m. -mn(l- ')')] + m2 _ 1) _ ml (11) 2 -IJ ml IJ 1 - ')'(1 -IJ) ml IJ

and byeq. (7) we get the peakedness curve. It is interesting and important to note that the peakedness curve depends

on the SBBP parameters only through m1, m2, m., 'Y. Therefore, we can get identical peakedness values for different SBBPs if these four parameters coincide.

(d) Batch renewal process The batch renewal process is important to consider because of its ability to model the correlation structure of traffic [6]. The discrete time batch renewal process is made up of batches of arrivals, where the intervals between batches are independent and identically distributed random numbers, and the batch sizes are also independent and identically distributed, furthermore, the batch sizes are independent from the intervals between batches.

We use the following notation for the discrete time batch renewal process: a and b are the mean length of intervals between batches and the mean batch size, respectively. The first and second moments of the number of arrivals in an epoch is given by m1 = bfa, and m2 = m1b(Cl+l) where Cl is the squared coefficient of variation (variance to mean square ratio) of the batch size. The probability generating function of the distribution of time between batches is


denoted by A*(w). (A*(w) = E:1 a[s]w8 where a[s] is the probability that the time between two consecutive batches is s.)

We have derived the peakedness for geometric holding times which is given by [10]

( )-1 1 (I+A*(I-JL) b m2 1) m1 Zgeo JL - + -- - + - - - -

2-JL I-A*(I-JL) m1 JL (12)

If the distribution of time between batches follows a shifted generalized geometric distribution [6], that is, art] = 1 - CT if t = 1 and art] = CTT(I -

T)t-2 if t = 2,3, ... , then its probability generating function is: A*(w) = w (1 - CT + l_&T_wT)w) which makes the peakedness values easily computable.

2.5 Fitting traffic models to peakedness curves

The peakedness shows the variability of the arrival stream with respect to different service holding times. It is of interest to investigate whether we can fit traffic models to peakedness curves based on measurements.

We outline here a fitting procedure based on the mean rate m1 of the arrival traffic, the peakedness value at JL = 1 and at three other points, JL1, JL2, JL3. The model we fit to the peakedness curve is an interrupted batch Bernoulli process (IBBP): in one state of the modulating Markov process, the arrival number has a general distribution, in the other state, there are no arrivals.

First, by z(I) = m2/m1 - m1, we get m2. Introducing w = 1 - JL, Wi = 1 - JLi and using the notations of section c, we can compute (using the values K*(Wi) = (Zgeo(JLi) - I)(Wi + 1) + 1)

Using eq. (11), Y(w) = m* _ (m.-;.~~~l--r)

Let us denote Y = Yy:1 - Y:y:2 which evaluates to Y = 2- 3

(13)

y"'3-"'2 -1 we get 'Y = Y ~I Once we have 'Y, we can obtain an estimation for m*

W2- Wl WI-W3

",~(1-.,.) 3 y,.-

as m* = ~ Ei =l '1-~ where we have on the right hand size an average

for the known values Wi, Vi. Then it is possible to fit an IBBP (no arrivals in state 2) as follows: m1,(1) =

'!!!""m ,a2 = m,:p--r) , a1 = 1 - 'Y - a2, m1 (2) = m2 olio2 • Given the first and 1 1,(1) , ~2

second moments of the number of arrivals in state 1, we can use for example a generalized geometric distribution for modeling the batch size distribution.


In this case, there are no arrivals with probability 1 - cp, and there is a batch of arrivals with geometrically distributed size of parameter 'Ij;. The moments are given by m1,(1) = cp/'Ij;, m1,(2) = cp/'Ij;2 by which we can get cp, 'Ij; for the model.

If it is possible to exactly fit an IBBP to the JLi, Zgeo(JLi) pairs, the values that are summed in the equation for m. are identical. If there is no IBBP that exactly fits the given peakedness values, m. gives an estimation and the peakedness curve of the fitted IBBP model approximates the JLi, Zgeo(JLi) pairs.

3 GENERALIZED PEAKEDNESS OF REAL TRAFFIC

3.1 Measuring peakedness

To measure the generalized peakedness of a traffic with a given holding time distribution, one can simulate the infinite server group. In discrete time, one can keep track of the first and second moment of the number of busy servers and compute the variance to mean ratio from them. The following points should be made about the estimation.

• We should take care of the initial phase of the simulation. If we have no prior knowledge about the traffic, we do not know what the mean number of busy servers will be. In this case, we can start from an empty system. The initial transient in the number of busy servers should be excluded from measurements.

• According to the definition, we should assign a server to each arrival, that is, assign a random holding time variable to every arrival in an epoch, which could involve a huge amount of computational effort. However, using the modified definition of peakedness and eq. (5), we can reduce the computational effort by assigning only one random service time variable to all arrivals in an epoch.

• When the service time is geometric, we can minimize the computational effort by making use of the memory less property. If at epoch t we have L[t] busy servers, then at the next epoch we have L[t+ 1] = L[t] +w[t+ l]-D[t] where D[t] is the number of departures from the service system at epoch t. The distribution of D[t] is known to be binomial with parameters L[t] and JL because each of the L[t] servers finish service with probability JL. Therefore, in the measurement, it is enough to keep track of L[t] together with the first and second moments of the previous L[i), i ~ t values. This gives us the following procedure for computing the peakedness value for geometric holding time distribution with parameter JL:

1. Reset L1 = 0, L2 = 0, Laid =initial value (see comments below);

106 Pan Three Traffic Characteristics

2. Set Lnew = Lold+Wnew-d where d is a random number with distribution binom(Lold,J.L) and Wnew is the number of new arrivals in the next epoch;

3. Set L1 = L1 + Lnew , L2 = L2 + L~ew; 4. Set Lold = Lnew and loop back to 2. unless the measurement is over; 5. Compute 11 = LdT,12 = L2/T, z = 12/11 -it where T is the length of

the total measurement time.

The setting of the initial value of LOld depends on the amount of a priori information that we have about the traffic. If we know the mean rate, we can set the initial Lold to its mean value determined by Little formula as m1 / J.L. If we do not know the mean rate, we have to start from an empty system (initial LOld = 0) and simulate the service system without actually measuring (executing step 3.) until the initial transient is over.

• An important advantage of using peakedness characterization is that we can measure peakedness by going through the traffic trace in only one sequence. This gives us the possibility of measuring peakedness for real-time traffic on the fly. Computing peakedness for one value of J.L involves N cycles of the above procedure (where N is the total length of the measured traffic); if we want to measure peakedness at several J.L values, we can easily implement the parallel execution of the procedure. In each cycle, we only have to compute a small number of additions and multiplications, and generate one binomially distributed random variable. Therefore, the complexity of the measurement is O(N). The most time-consuming step in the measurement is the generation of the binomially distributed random number. We can reduce the computational cost of the measurement tremendously by approximating it with a normally distributed random number, for which pre-computed look-up tables can be used.

• The advantage of our approach compared to Eckberg's method for estimating peakedness for exponential holding times (cf. [3,9]) is that our method does not neglect a lot of arrivals in the computation due to the selection of an arbitrary arrival.

3.2 Peakedness of video traffic

Video traffic is a very important example of variable rate traffic. We investigated the application of peakedness measure for the characterization of variability of MPEG video traces [17]. The MPEG sequences that we considered had a GOP (Group of Pictures) length of 12 frames, a GOP pattern of IBBPBBPBBPBB, and frames capture frequency of 25 frames per second.

Figure 1 shows the peakedness curve of an an MPEG video trace of a movie (MrBean) as a function of the service rate J.L. The mean service time of a server is therefore 1/ J.L time epochs, where one time epoch is now 40ms. The solid


curve is the peakedness function for the frame sequence (one frame corresponds to one epoch), whereas the dashed curve is the peakedness function for the GOP sequence (one GOP corresponds to 12 epoch so that is has the same time-length as the frame sequence) The scaling in the vertical axis is such that one arrival corresponds to one bit.

By decreasing the service rate, the service times become longer, and the number of busy servers in the infinite server group depends on the traffic properties on longer time scales. In this way, the peakedness curves show the variability of the traffic on different time scales, i.e. on the time scale of 1/ J.L.

Figure 1 shows that on short time scales, the variability of the frame sequence is much greater compared to the GOP sequence. But as we go to longer and longer time scales, the variability of the two sequences converge. What we can learn from this is that on longer time scales (for example, when dimensioning larger buffers), the statistical characteristics of GOP structure is less significant, and it is enough to consider the GOP sequence.

Figure 2 shows the peakedness curves for geometric service time distributions for five MPEG video GOP size traces. It gives us a relative comparison of the variability of different kinds of video sequences. (In this figure, one time epoch is set to one GOP which introduces a scaling compared to Figure 1.) The highest values of peakedness are exhibited by the MTV sequence, which is known to have lots of scene changes. Movie sequences show lower peakedness compared to the MTV sequence. The peakedness of a video conference sequence is found to be the smallest by orders of magnitude.

Figure 3 shows an IBBP fitted to an MPEG movie trace (MrBean, [17]). The solid line is the peakedness curve of the GOP sequence, the dashed line shows the peakedness curve of the fitted model. The circles show the peakedness values where the fitting was made. The points were chosen to represent the variability of the traffic on a long time scale (corresponding to the time scale of 1/0.01=100 epoch, here one epoch corresponds to 0.48 sec). As we can see, the model is able to capture the variability of the arrival stream on the investigated time scales.

3.3 Peakedness of aggregated ATM traffic

We analysed the peakedness curve of an aggregated ATM traffic trace taken from the Finnish University and Research ATM WAN network (FUNET) [14]. The trace was approximately one hour long and consisted of the number of cell arrivals in each second. Figure 4 shows the peakedness curve of the measurement and two IBBPs fitted to it. The IBBP that was fitted at short time scale fits the measured peakedness curve well for shorter time scales, but it gives lower peakedness values for time scales longer than 1/0.05 = 20sec. The other IBBP was fitted at a longer time scale; this model gives lower peakedness values for time scales shorter than 20sec.


3.4 Peakedness of Ethernet traffic

Figure 5 and Figure 6 show the peakedness curve of an Ethernet traffic taken from the Bellcore measurements [7]. The measurement covers 1 million arrivals (approx. one hour). Figure 5 depicts peakedness on a lin-lin plot, Figure 6 is a log-log plot. We can investigate 5 different time scales in Figure 6. The interesting finding is that the peakedness increases linearly on the log-log plot as we decrease the rate (go to long time scales). Due to eq. (9) and knowing that lims-+oo I[s] = 00 if there is long range dependence (LRD) in the traffic, the peakedness diverges as the rate goes to zero. This observation of monotonicity in Figure 6 supports the presence of LRD assuming that the traffic stationarity assumption holds. It is important to note that the peakedness cUnJe can be used as an indicator of LRD.

At different time scales we fitted simple Markovian models (IBBPs) to capture the peakedness curves in Figure 6. We can see that the burstiness scaling property of these models are not appropriate i.e. these models can cover a shorter range of time scales in burstiness than it would be necessary to follow the burstiness of the real traffic over all the investigated time scales.

Our investigations of the aggregated ATM and Ethernet traffic indicate that simple Markovian models are not able to capture the burstiness characteristic of traffic over many time scales. For this case fractal traffic models seem to be more appropriate [7,14]. However, for several practical cases we do not need to focus on all time scales but only on our working time scales (e.g. time scales of queueing) which can be efficiently modeled by Markovian models, too.

4 CONCLUSION

We have shown that peakedness can be used to characterize the bursty nature of traffic. Peakedness curves show the variability of traffic on different time scales and can be efficiently computed for real time traffic. We have extended the peakedness theory to discrete time and applied the peakedness characterization to variable rate video traffic, Ethernet traffic and aggregated ATM traffic as well as to the most important traffic models. We have shown that generalized peakedness can also be used for detecting long range dependence. We have also presented a new model fitting technique based on the concept of peakedness.

The basic idea of peakedness characterization is that we characterize traffic by its interactions with the service system. Its generality is shown by the observation that peakedness gives a complete second order characterization, i.e. it contains all information about the correlation structure of the traffic.

The further development of peakedness theory including its extension to characterize non-stationary traffic are the topics of our future research.


REFERENCES

[1] D. R. Cox and P. A. W. Lewis. The Statistical Analysis of Series of Events. Methuen & Co Ltd, 1966.

[2] A. E. Eckberg, Jr. Generalized peakedness of teletraffic processes. In ITC-10, Montreal, 1983.

[3] A. E. Eckberg, Jr. Approximations for bursty (and smoothed) arrival queueing delays based on generalized peakedness. In ITC-11, Kyoto, Japan, 1985.

[4] R. Gusella. Characterizing the variability of arrival processes with indexes of dispersion. IEEE Journal on Selected Areas in Communications, 9(2), February 1991.

[5] H. Heffes and J. M. Holtzman. Peakedness of traffic carried by a finite trunk group with renewal input. The Bell System Technical Journal, 52(9):1617-1642, November 1973.

[6] D. Kouvatsos and R. Fretwell. Batch renewal process: Exact model of traffic correlation. In High Speed Networking for Multimedia Application, pages 285-304. Kluwer Academic Press, 1996.

[7] W. E. Leland, M. S. Taqqu, W. Willinger, and D. Wilson. On the self-similar nature of Ethernet traffic (extended version). IEEE/ACM Transactions on Networking, 2(1), February 1994.

[8] B. L. Mark, D. L. Jagerman, and G. Ramamurthy. Application of peakedness measures to resource allocation in high-speed networks. In Proceedings of ITC-1S, Washington D.C., USA, June 1997.

[9] B. L. Mark, D. L. Jagerman, and G. Ramamurthy. Peakedness measures for traffic characterization in high-speed networks. In Proceedings of IEEE INFOCOM'97, 1997.

[10] Gy. Miklos. Peakedness measures. Technical report, High Speed Networks Lab, Department of Telecommunications and Telematics, Technical University of Budapest, 1997.

[11] S. Molnar. Evaluation of Quality of Service and Network Performance in ATM Networks. PhD thesis, Technical University of Budapest, Department of Telecommunications and Telematics, 1995.

[12] S. Molnar, I. Cselenyi, and N. Bjorkman. ATM traffic characterization and modeling based on the leaky bucket algorithm. In IEEE Singapore International Conference on Communication Systems, Singapore, November 1996.

[13] S. Molnar and Gy. Miklos. On burst and correlation structure of teletraffic models. In D. D. Kouvatsos, editor, Sth IFIP Workshop on Performance Modelling and Evalution of ATM Networks, Ilkley, U.K., July 1997.

[14] S. Molnar and A. Vidcics. On modeling and shaping self-similar ATM traffic. In Proceedings of ITC-1S, Washington D.C., USA, June 1997.

[15] R. O. Onvural. Asynchronous Transfer Mode Networks, Performance Issues. Artech House, Boston, London, 1994.

[16] V. Paxson and S. Floyd. Wide area traffic: The failure of Poisson modeling. IEEE/ACM Transactions on Networking, 3(3):226-244, 1995.

[17] O. Rose. Statistical properties of MPEG video traffic and their impact on traffic modeling in ATM systems. In Proceedings of the 20th Annual Conference on Local Computer Networks, pages 397-406, Minneapolis, MN, 1995. ftp://ftpinfo3.informatik.uni-wuerzburg.de/pub/MPEG/.

[18] K. Sriram and W. Whitt. Characterizing superposition arrival processes in packet multiplexers fo voice and data. IEEE Journal on Selected Areas in Communications, 4(6), September 1986.

[19] G. D. Stamoulis, M. E. Anagnostou, and A. D. Georgantas. Traffic source models for ATM networks: a survey. Computer Communications, 17(6), 1994.


18 x 10~ mrbean frame seq. and scaled GOP seq.

,.

---------0~0~0~.1~0~.2--0~.3~0~.4~~0 .• ~7.0 .• ~7.0.7~~0 .• ~~0.~.~ service rate

Figure 1: Peakedness of the frame (solid) and GOP (dashed) sequence of MPEG video trace (MrBean).

mrbean GOP sequence

0.'

~~~om=-~0.~M~0~.~~0~~~0~.1~0~.12~0~.14~0~.1~.-0~.1~.~02 selVicerate

Figure 3: Peakedness curves of MPEG GOP movie trace (MrBean, solid) and its IBBP model (dashed).

BCtraca

5000

............ -1000

$lINicarate

Figure 5: Peakedness of Ethernet trace (solid) and IBBP models (dotted) fitted to it. The two IBBPs are fitted at short (stars) and long (circles) time scales.

mtv_2, mrbean, news_1, starwars, videoconf GOP seqs

o,~====~~--~----~~--~~--~ o ~ U U U M M U U U

aervicerate

Figure 2: Peakedness of MPEG GOP video sequences. From the uppermost downwards, the sequences are from: TV (MTV), movie (MrBean), TV (News), movie (StarWars), video conference.

FUNET 6000~,--~~--~~--~~--~~--~~ , , 5000

~~~0~.1~0~.2~0~3--0~.4--0~.'--0~~~~OJ~~Q8~~0 .• ~~ service rate

Figure 4: Peakedness of aggregated ATM traffic (solid) and IBBP models (dotted) fitted to it. The two IBBPs are fitted at short (stars) and long (circles) time scales.

Figure 6: Peakedness of Ethernet trace (solid) in log-log plot. On five time scales (separated by vertical lines) IBBP models are fitted (dashed).

9 On the combined effect of self-similarity and flow control in quality of service for transactional Internet services.

Javier Aracil, Daniel Morato and Mikel Izal Dpto. A utomatica y Computacion Universidad Publica de Navarra Campus Arrosadia sin 31006 Pamplona, Spain Tel: +34 48 16 97 33 Fax: +34 48 16 92 81 email: {javier.aracil.daniel.morato.mikel.izal}@upna.es

Abstract In this paper we show that the combined effect of heavy-tailedness and flow control leads to considerable transaction delays. Neither heavy-tailedness nor flow control separately imply a significant degradation in quality of service. We consider transactional Internet services such as WWW and relate user perceived quality of service to total transaction delay instead of packet or cell instantaneous delay [2]. We evaluate transaction delay by simulation of an IP over ATM link in which a large number of users are multiplexed and we compare to M/G /1 analysis. Our traffic model assumes heavy-tailed features in file sizes and a constant rate for packet interarrival times within transactions. We show that an in increase in bandwidth assignment, i.e. a decrease in link utilization factor, does not translate into a significant performance improvement. However, an increase in window size proves more effective.

Keywords Internet service provisioning, self-similarity, TCP

1 INTRODUCTION AND PROBLEM STATEMENT

Nowadays, we are witnessing a huge demand of Internet services like the World Wide Web. Internet traffic self-similarity poses new challenges regarding bandwidth allocation, billing and pricing for Internet services. Traffic burstiness is preserved at any time scale, in contrast to short-range dependent models such as the Poisson process. Queueing analysis with self-similar input is an active

Performance of Information and Communication Systems U. Kilmer & A. Nilsson (Eds.) @ 1998 IFIP. Published by Chapman & Hall


research area since network dimensioning for Internet services has became a very important issue. However, performance metrics are obtained at the cell or packet level : buffer overflow probability and delay estimates under selfsimilar input [4, 7,9, 10]. Buffer overflow probability and delay at the packet or cell level may not be an adequate QOS metric for service provisioning. Little literature exists on QOS metrics that relate Internet user satisfaction and network parameters such as end-to-end delay and bandwidth. David Clark addresses this issue in [2], arguing that user satisfaction grows with transaction throughput. Namely, a large instantaneous bit rate is useless unless such bit rate is mantained during the whole transaction. Since it is possible to know the file sizes before the transaction takes place bandwidth allocation can be done beforehand. If we consider transaction duration as the valid QOS metric a detailed analysis at the transaction level is needed.

Transactional services (FTP-data and WWW) represent the most important part of Internet traffic [8, 1, 3]. Pareto distributions prove accurate to model file size and transmission duration for FTP-data and WWW [8, 1, 3]. Inactivity periods of a single user turn out to be heavy-tailed as well [11]. This approach leads to an on-off model with heavy-tailed distribution to model individual users. The multiplex of a large number of users shows exponential behavior in the transaction interarrival times [1, 6]. The transaction arrival process in the busy hours can be modeled approximately as a Poisson process. Nabe et al. [6] show that Poisson arriving heavy-tailed bursts constitute an accurate traffic model for busy hours of WWW service.

Tsybakov and Georganas show in [10] that Poisson arriving heavy-tailed batches with constant cell rate within the batch lead to an asymptotically second order self-similar process. If we consider Tsybakov and Georganas model, a transaction level analysis of a multiplex of a large number of users in a single virtual circuit can be undertaken using the well-known M/G/1 or M/G/1/PS model [6]. Furthermore, the M/G/1 model provides a simple framework to explain how self-similarity affects user perceived QOS. Since file sizes are heavy-tailed the service time squared coefficient of variation (namely, variance normalized by the squared mean [5, page 187]) is large and degrades performance. Other factors such as TCP flow control also make such squared coefficient of variation increase since transaction duration increases due to source active waiting periods.

In this paper we show that the joint effect of a simple window flow control mechanism and heavy-tailed file sizes causes a significant performance drop, even in a small roundtrip delay environment. However, neither the former nor the latter separately degrade QOS in a so significant manner. Our methodology consists of simulations using a single virtual circuit model and comparison to M/G/! analysis. We evaluate network contribution to QOS perceived in contrast to other factors such as heavy-tailed file sizes. Our findings suggest that network parameters such as window sizes may be tuned to provide a better QOS.

Quality of Service for transactional internet services 113

The rest of this paper is structured in three parts: section 2 explains our traffic model and simulation setup, section 3 presents the results and discussion and section 4 presents the conclusions that can be drawn from this study.

2 USER TRAFFIC MODEL AND SIMULATION SETUP

Our simulation setup is shown in figure 1. We consider a large population of users whose traffic is being multiplexed over the same link with a unique queue. That is the common situation for Internet Service Providers (ISPs) and corporation and academic networks: the edge router is configured with a unique constant bandwidth VP IVC to the ATM cloud and a unique inbound queue to the users. We will assumme that both queues have infinite capacity. IP packets are segmented into ATM cells but there is no cell interleaving from different IP packets.

Server

Server

Server

Figure 1 Simulation setup

We evaluate the input queue to the router from the ATM cloud because Internet traffic is highly asymmetric. We assumme that file transfer queries (GET commands) are issued from the users population. In response to such queries the bulk traffic stream comes in the inbound direction. Transaction duration and size (bytes) are both heavy-tailed [1, 3, 6].

Our sliding window flow control mechanism resembles TCP behavior: Each ACK packet acknowledges all transmitted packets whose sequence numbers are smaller than or equal to the sequence number announced by the ACK packet. The traffic source stops transmission whenever the negotiated window is full of unacknowledged packets. Such behavior is typical of transport layer

114 Pan Three Traffic Characteristics

protocols such as TCP. TCP also incorporates a congestion control algorithm known by Slow Start. At any given transmission time the minimum between the flow control window and the congestion control window is selected by the TCP protocol agent as the actual transmission window. The value of the flow control window is negotiated at the connection establishment phase (SYN PDUs). Note that the negotiated flow control window determines the maximum size of the transmission window. Even if the congestion control window eventually allows for a larger transmission window size the negotiated flow control window imposes a limit. We will show later that small window sizes imply performance penalties. Slow start makes transmission window decrease if congestion is detected.

We will assume no packet loss in the transmission link, i. e. no retransmissions. We aim at showing the influence in network performance of a simple, yet explanatory, sliding window flow control algorithm in presence of heavytailedness in file sizes. Our simple model represents a best-case model in comparison to TCP since for the latter the transmission window can take values smaller than the negotiated flow control window due to the congestion control algorithm, as explained before. Note that unacknowledged packets may suffer considerable queueing delays in high load situations. If the flow control window is full of unacknowledged packets such queueing delays are particularly harmful because the source gets stopped until new acknowledgments are received. Note that even though flow control is performed on an end-toend basis a unique queue is shared by all sources. We observe two different contributions to transaction duration: queueing delay, that depends on the utilization factor and service time squared coefficient of variation (M/G/I) and flow control delay, which increases transaction delay each time an ACK is needed from the destination in order to alleviate the flow control window of unacknowledged packets.

We will assume a roundtrip delay of 0.01 s., which is a reasonable empirical value for TCP connections within a statewide network. Larger RTDs, such as the ones for overseas connections would make transaction duration increase.

Once the simulation scenario is defined we are faced with the selection of a traffic model that accurately portrays user behavior. Several studies show that an on-off model with heavy-tailed on-off periods is accurate to model a single user behavior for Internet bulk data transfer services (i.e. WWW and FTP-data) [11]. The heavy-tailed nature of the on period is mainly due to the Internet file sizes distribution while off periods are related to user think time. File sizes variance and mean depend on the media: text, images, sound or video files [6]. Considering the mUltiplex of different types of files in a real trace a mean value in the range of 50 KB can be adopted for WWW services [3].

Fluid-flow on-off models assumme that the time to transfer a file equals file size divided by link capacity, namely no time gaps between packet transmissions. However we do not use a fluid-flow model for activity periods since


transmission time is larger than file size divided by link capacity. The operating systems and network interface cards impose limitations in the packet interarrival times so that a larger service time for a transaction is observed. In order to evaluate interpacket spacing, we perform a number of WWW transactions between a client and server stations in two different situations: dedicated LAN and departmental network. The client WWW cache is set to zero bytes so that we always enforce transmission.

We perform two different measurement experiments: the first one in a dedicated Ethernet of a SUN workstation and a PC, the second one is taken with both client and server in the departmental network in the busy hour. We perform a total of 600 transactions with file sizes ranging from 10 KB to 3 MB with a 100 KB step size. Our departmental network is not isolated by a router to the campus backbone so that we receive the traffic multiplex of approximately 900 hosts. The results show packet interarrival times in the vicinity of 1.5 ms (P(interarrivaltime < 1.5ms) = 0.85) so that a significant deviation from a fluid-flow behavior is not observed. A 1500 bytes (Ethernet MTU) packet transmission time is 1.2 ms for a 10 Mbps Ethernet. However, the cumulative effect for large file transmissions can be significant. In order to have a better picture of packet-level transmission we plot in figure 2 the measured transaction duration and the same transaction duration assuming a fluid-flow model and a constant rate packet transmission (1500 bytes) with interarrival times equal to 1.5 ms and 5 ms. Note that significant deviations can be observed specially with large file sizes. Therefore, we adopt the discrete model (constant packet rate within the bursts) in contrast to the fluid-flow model.

,. I· I· f. .§

--

---:=~~ ..................... . ------------

~~~ •.• ~-7--~,~ .• --~--7.2 .• ~~ Resize (MByIu)

,.,----------~--~--......--,

14 -SmucslntlrantvellirM

r -'. ~ r

..1.5 maecainierarrivalkM -.Ruidlow

---, ..

Fl. tile (M8yte.) 2.'

Figure 2 Transaction duration: real trace, fluid-flow model and constant packet rate model (1.5 ms and 5 ms). Right: dedicated network, left: departmental Ethernet

As far as the transaction arrival process is concerned, we assume that the multiplex of a large number number of independent arrivals converges to a


Poissonian model. However, such connection arrival process has little influence in our analysis.

As stated before, Tsybakov and Georganas show in [10] that a Poisson batch arrivals process with heavy-tailed batches and constant cell rate is an asymptotically second order self-similar process. Therefore, we are considering a self-similar model in our simulation setup.

One important factor in our analysis is the flow control window size value (Kbytes). We collect a traffic trace to determine what is the typical window size value in the TCP flow control algorithm for transactional Internet services such as FTP-data and WWW.

The trace is obtained from Public University of Navarra campus network, that consists of a high-speed backbone (FDDI) and approximately 30 departmental Ethernets. The estimated number of hosts connected is 900. The analyzed trace comprises 244,568 FTP-data and WWW connections recorded during 12 hours. Interestingly, the probability mass function shows two outcomes that dominate the sample: 8760 bytes and 31744 bytes with a probability of 0.61 and 0.33 respectively. Thus, we consider window sizes of 8 KB, 16 KB and 32 KB for our simulation experiments.

Our conclusions about the traffic model can be summarized as follows. Since we consider a large population of users we choose a Poisson transaction arrivals model in which file sizes are heavy-tailed. Furthermore, we consider that file sizes follow the Pareto law since such distribution models accurately transaction sizes (bytes) for FTP-data and WWW services [1, 3]:

Ix (x) = akOtx-0t - 1 (1)

where k represents the minimum batch size, which we adjust to a value of 1000 bytes. The parameter a relates to the batch size heavy-tailedness and, ultimately, to the service time variability. A value of a in the range 1 < a < 2 would produce self-similarity features in the packet counting process [10]. We truncate the file size distribution in equation 1 to a maximum value of 10 MB. The probability of such maximum file size in a WWW or FTP transaction is around 10-7 [1, 3]. Such truncation permits the calculation of the variance and coefficient of variation. On the other hand, the truncated distribution resembles accurately the file sizes distribution in the Internet. Crovella et al. report a value of a for WWW transactions approximately around 1.1 [3]. In previous studies we report a value of a = 1.28 for FTP-data transfers, considering a sample size of four days worth of IP traffic from the U C Berkeley campus network (439 Mpackets, 69 Gbytes) [1]. Finally, we assumme Ethernet rates (10 Mbps) for the capacity assigned in the inbound queue and constant size packets of 1500 bytes (MTU size).


3 RESULTS AND DISCUSSION

In this section we present simulation results and discussion. We perform three different simulation experiments with a finite horizon simulation (24 hours simulated time):

• Experiment one: we analyze the effect of flow control with fixed size batch. A fixed size batch is the best case regarding service time (M/D/I) so that it should provide the best performance figures as far as transaction delay is concerned. Our aim is to show that the influence of flow control in QOS is not significant if file sizes are deterministic.

• Experiment two: we replace the fixed-size batch by a heavy-tailed batch with no flow control. We show that the effect of heavy-tailed file sizes is not so significant for QOS if flow control is not activated.

• Experiment three: we assume heavy-tailed file sizes and 8 KB, 16 KB and 32 KB flow control window sizes. We show that the effect of flow control in presence of infinite variance of file sizes is dramatic. Our findings show that an increase in window size translates into a very significant performance improvement.

3.1 Fixed size file sizes and flow control

Figure 3 shows transaction delay for fixed size (50 KB) files and different values for the flow control window size (4, 16 and 32 KB). Furthermore the M/D /1 results are also shown for comparison purposes .

ltoM[YlWln4088 +Win8l5l2-+··

WIn 16384 -&WIn327I11_··

f ,I i ... ~

~ .. '.!-: .':-:, .. ':-:.':-: ... ':-: ... ':-:,.':-: .. ':-: ... ':-: .. '=""', , _ .... .

• "011-W1n4Ol8-+·W1nBl92-+··

Win 18384-eWin32788*-·

f'·' J

• .!-:.':-:, .'="=".'="= ... '="= •. '="= .. '="= .. '="='",,="=, •. :-', , -_. Figure 3 Fixed-size file sizes. Right: 5 ms packet interarrival times, left: 1.5 ms packet interarrival times

Let p be the utilization factor, B the file size in bits and C the link capacity in bps. Let A be the joint arrival rate of the multiplex of users and let the utilization factor be p = AB / C.

It is important to note that the time to transfer a file is not equal to file


size divided by link capacity. Such time can be computed as the total time to transfer a file taking into account real packet interarrival time (see figure 2). Let tp be the packet interarrival time (1.5 ms or 5 ms in figure 3) and M the MTU size in bytes (1500 bytes) then the time to transfer a file x equals x = (B/M) * tp. The average transaction duration, considering a fluid-flow model in which service time equals time to transfer a file (x) is given by:

(2)

Interestingly, curves differ considering 1.5 and 5 ms packet interarrival times. As far as the latter is concerned some statistical multiplexing gain can be observed at the packet level in comparison to the fluid-flow model. Such gain is neglectable at 1.5 ms packet interarrival time since this time is too close to the packet transmission time (1.2 ms). User perceived quality of service can be estimated with the simple M/D/l model at the expense of an estimation error in the range of 10-1 seconds.

Furthermore, we observe that no significant differences in comparison to the M/D /1 case are observed if packet interarrival time is close to packet transmission time (1.5 ms in comparison to 1.2 ms.) and window sizes are large. Intuitively, the performance drop due to flow control depends on the ratio (file size)/(window size). A combination of large file sizes and small flow control windows makes the probability of source active waiting increase. The worst ratio shown in figure 3 is around 10 (4 KB window size and 50 KB file size). Same results can be observed if window size and file size are increased mantaining the same ratio.

3.2 Heavy-tailed file sizes and no flow control

In this section we evaluate the effect of heavy-tailed file sizes with no flow control. Figure 4 shows the average transaction duration with a heavy-tailed file size (Q = 1.05, 1.2, 1.6) and no flow control. Probability of transaction delay beyond 10 seconds and measured utilization factor versus the transaction arrival rate are also presented. The results match our intuition: the smaller the value of Q the larger the squared coefficient of variation and, therefore, smaller values of Q imply performance degradation.

The results shown in figure 4 are rather striking: the performance drop caused by file sizes variability is not so significant as far as QOS perceived by user is concerned. Values of Q equal to 1.05, 1.2 and 1.6 give approximately the same performance figures (compare with figures 5 and 6). In the next subsection we evaluate the effect of flow control in a heavy-tailed file sizes scenario.


I 0.' ..• 0." j/ ;: ...

a1phal.05_ §

i R ... IIIphal.2-... - I ." a1phal.05_

..... <~~~ ! .,IIaU -g ..

J f ." alphal.2-+-'-

t alphaU-a··

I O. j ! ~/ M

,.- alpha 1.6 .g .. j 0.' " .- ~ ",.TiI :aF.r:-':':.e···rJ

0 0 0 0 , .. " 20 " 0 0.' 0.4 0.6 .. . 0 0.' 0.4 0.8 .. .

r,.,uclonarTlYalrall Ullllzalionlaemr UtilizalionlaclDr

O. 1/ i ... a1phal.05_ i

IIIfphal.2-+-- i alphaU15_

O. ! .,""1.6-0·· alphal.2-+-'-/ ...•... • li lIphal.8-D···

L 0.' J li IJI/ .. rl·1iI

··lIphal.06_ I

i ~ 0.'

" alptlal.2-+-·· i< 0." !!l •• t/til 1IIp/la1.6 -g ••

0 0 0 0 , .. " 20 25 0 ., 0.4 O.S 0.' . 0 ., 0.' 0.'

TranllllCllonarrival rl» UtilzallonlaclDr UlllizationfaclDr

Figure 4 Utilization factor (left), mean transaction duration (center) and probability of transaction duration beyond 10 s. (right). Heavy-tailed file sizes and no flow control. Top: 1.5 ms packet interarrival times, bottom: 5 ms packet interarrival times

3.3 Heavy-tailed file sizes and flow control

Figures 5 and 6 (1.5 and 5ms respectively) show the performance degradation suffered by introducing flow control in a heavy-tailed file sizes scenario. Utilization factor, mean delay and probability of transaction delay beyond a 10 seconds threshold are shown. Note that the typical value reported for a is in the range 1.0 ::; a ::; 1.2 with an estimate of a = 1.1 for the most popular service in the Internet: the WWW [1, 3J. Utilization factors in the range of 0.4 give unacceptable QOS to users for window sizes of 8 KB. Recall from section 2 that a window size of 8KB dominates in our sample with a probability of 61 %. The queue seems to be saturated as far as user QOS perception is concerned even for small utilization factors. However, note that the performance degradation is due to the combined effect of flow control and heavy-tailed file sizes. Neither the latter nor the former would produce such performance drop separately as seen in previous sections.

The mean file size for a value of a = 1.2 is 50 KB, that gives a ratio of (file size)j(window size) equal to 6.2 for an 8 KB window size and equal to 3.1 for a 16 KB window size. Even in the last case we observe a significant degradation compared to the deterministic file size scenario with a ratio (file size)j{window size) in the vicinity of 10. The heavy-tailed features of file sizes increase the probability of large files present in queue. The performance penalty implications are twofold: first, large files make the service time squared coefficient of variation increase, secondly, since the ratio (file size)j{window size) is larger the traffic source performs active waiting more often.

Considering a 5 ms packet interarrival time (figure 6) we observe a similar behavior. Note that the measured performance is slightly worse. Larger packet


WlndClWlIDIKB W1ncbr8IDaICB

1 j 0.6

I

,. II ...... . 0.8 I A.JS

~ ..•.. 0.4 ,,_

,- a/pIWIl.05_

0.2 l ..• ··• ==:~;:: .... °0 5 10 IS 20 25

T..,-=tIonanlvlll ....

1.8 ~'i~ / f 1.6 .pt\II1.8 ... !

I,. .. / .. / I :~ .::::. ........ .

o o 0.2 0.4 0.8 0.1 1

u __

o o 0.2 0.4 0.8 0.8 1 --W1nctowllH32K8

1.8 fJpllal.05_ ~ 1.8 alpI\I.l.2_

L~ O~ 1!' ..... -Et ............ 1I'"

o 0.2 0.4 0., 0.8 1 UllllzatianlalDr

~

0.' .--'-=;:=';':=-..-, 0."

o

aIpI\IIl.05_ alphal.a ...... -alpt..1.fI-g···

.--::::::: ~~.~:

o 0.2 0.4 0.8 0.8 1 UIIIIudIontw::1or

" 1IIpIM,1.C15_

f =~~:;.::

1 O.OI~ o

o 0.2 0.4 0.8 0.8 1 ......... ,.,..

Figure 5 Utilization factor (left), mean transaction duration (center) and probability of transaction duration beyond 10 s. (right). Heavy-tailed file sizes and flow control (top 8 KB window size, center 16 KB window size, bottom 32KB window size, 1.5 ms packet interarrival time). .

interarrival times produce an increase in statistical multiplexing gain at the packet level for small values of utilization factor. However, they also make time to transfer a file increase and thus the probability of active waiting for larger values of utilization factor.

4 CONCLUSIONS

Implications for self-similarity. An important conclusion of this paper is that the high variability of file sizes, which generates self-similarity, does not degrade QOS significantly in presence of infinite buffers and large flow control window sizes. In the finite buffer scenario, the joint effect of high variability in file sizes and window flow control supposes a significant performance drop since retransmissions are more likely to occur due to buffer overflow. Such retransmissions make transaction duration grow larger and window size decrease due to the congestion control algorithm.

Implications for billing and pricing TCP services. If we assume that user perceived QOS is determined by transaction duration, an increase in network bandwidth is not translated directly into user satisfaction. Such increase

Quality of Service for transactional internet services

o o'--,~,~o -,~, _"''----.J" Tran&aCbOn~.lrale

:: t/·/<~·········· 04 :'.J!J /' ... Ilr a1phaIO!i_

'. ,,)01 a1pna12 ...... _. 02 :' jI alpha 1.B·il

~.D

'0 L ---:-, ---'-:" ---::"---::",:----:',, Tran....:lIQnamvalral8

" ~ ~

i , i<

0 0

!l

i ~ , i<

0 0

§

f I , i<

0 0

alphal05_ alphaI2-+--alpha!S

A ...... - ... - [l " __ ....... .11 ail

" 04 0.6 " UtoiltallOOh.c:lor

a1phaI05_ IlIphaI2 ...... · IlIphll16 .

~ " 04 06 " UI~12aloo facIO.

alpha1.05_ a1phaI2-+-alpha 16 .

~ " 04 06 0.'

UI,ioZlihonlactn

121

,

,

,

Figure 6 Utilization factor (left), mean transaction duration (center) and probability of transaction duration beyond 10 s. (right). Heavy-tailed file sizes and flow control (top 8 KB window size, center 16 KB window size, bottom 32KB window size, 5 ms packet interarrival time)

would make utilization factor decrease, but note from figures 5 and 6 that an increase in window size would significantly contribute to a better QOS at a lower cost. Therefore, billing for bandwidth may not be an adequate scheme as far as user perceived QOS.

Finally, the use of window flow control protocols with relatively small window size may not be justified in an Internet in which workstations and PCs have a growing capacity of CPU and I/O. New mechanisms for flow control and selective retransmission have to be investigated in order to meet the increasing demand for quality of service in the Internet.

REFERENCES

[1] J. Aracil, R. Edell, and P. Varaiya. An empirical Internet traffic study. In 35th Annual Allerton Conference on Communications, Control and Computing, Urbana-Champaign, Illinois, October 1997.

[2] David D. Clark. Adding service discrimination to the internet. Technical report, MIT LCS, September 1992.

[3] M. E. Crovella and A. Bestavros. Self-similarity in world wide web traf-


fie: Evidence and possible causes. In ACM SIGMETRICS Annual Conference on Measurement and Modeling of Computer Systems, May 1996.

[4J A. Erramili, O. Narayan, and W. Willinger. Experimental queueing analysis with long-range dependent packet traffic. IEEE/ACM Transactions on Networking, 4(2):209-223, April 1996.

[5J L. Kleinrock. Queueing Systems, volume 1. John Wiley and Sons, 1975. [6] M. Nabe, M. Murata, and H. Miyahara. Analysis and modeling of World

Wide Web traffic for capacity dimensioning for Internet access lines. In SPIE Video, Voice and Data Communications Conference, Dallas, TX, November 1997.

[7] M. Parulekar and A. Makowski. Tail probabilities of a multiplexer with self-similar traffic. In IEEE INFO COM '96, volume 3, pages 1452-1459,1996.

[8] V. Paxson and S. Floyd. Wide area traffic: The failure of Poisson modeling. IEEE/ACM Transactions on Networking, 4(2):226-244, April 1996.

[9J B. K. Ryu and S. B. Lowen. Point process approaches to the modeling and analysis of self-similar traffic - part I: Model construction. In IEEE INFOCOM '96, volume 3, pages 1468-1475, March 1996.

[10] B. Tsybakov and N. D. Georganas. On self-similar traffic in ATM queues: Definitions, overflow probability bound and cell delay distribution. IEEE/ACM Transactions on Networking, 5(3):397-409, June 1997.

[11] W. Willinger, M. S. Tacqu, R. Sherman, and D. V. Wilson. Self-similarity through high-variability: Statistical analysis of Ethernet LAN traffic at the source level. In ACM SIGCOMM 95, pages 100-113, Cambridge, MA,1995.

5 BIOGRAPHY

Javier Aracil received the Ph. D. in Telecommunications Engineering from Technical University of Madrid in 1995. In 1996 he was a Fulbright scholar and Postdoctoral researcher of the Dpt. of Electrical Engineering and Computer Sciences of University of California, Berkeley. Nowadays, he is an associate professor of Public University of Navarra, Spain.

Daniel Morat6 received the MSc in Telecommunications Engineering in 1997. He is a research and teaching assistant of Public University of Navarra.

Mikel Izal received the MSc in Telecommunications Engineering in 1997. He is a research and teaching assistant of Public University of Navarra.

PART FOUR

Multicast

10 An analysis of retransmission strategies for reliable multicast protocols

M. Schuba, P. Reichl Informatik 4, Aachen University of Technology 52056 Aachen, Germany email: [email protected]

Abstract In this paper we present an analytical comparison of retransmission strategies for three types of reliable multicast protocols. In the first protocol (called sender-originated) it is the task of the source to guarantee reliable delivery of data to all receivers. The other two approaches additionally allow either receivers or routers to retransmit packets (these protocols are termed receiver-originated and router-originated, resp.). Thus the load on the sender is relieved while at the same time transmission cost decreases since packets can be retransmitted with a limited scope. We determine the retransmission cost of all three protocol types based on discrete-time Markov chains. In contrast to other analytical models this approach does not require loss events to be independent for different receivers. Numerical results show that the cost for sender-originated protocols may become unacceptable even if loss probabilities within the network are small. In larger networks with widely spread groups the performance of receiver-originated protocols is also very limited. In such scenarios only router-originated protocols yield acceptable cost.

Keywords Reliable multicast, performance analysis, Markov chain


126 Part Four Multicast

INTRODUCTION

The widely spread introduction of multicast protocols (e.g. IP multicast (Deering, 1988), (Hermanns and Schuba, 1996» has led to an increasing interest in groupware applications. An important feature required by such applications is the support of reliable data transfer to a group of receivers, for instance for realizing distributed simulation, updating software on a large number of computers, pushing web pages, distributing learning materials in a distance learning environment or news in a news group. To achieve reliability some error recovery mechanism for lost packets has to be implemented. In protocols designed for small (local area) multicast groups these mechanisms are usually realized at the sender, which is responsible for processing positive or negative acknowledgements (ACKsINAKs) and for retransmitting packets. Examples for such "sender-originated" reliable multicast protocols are MTP (Armstrong et aI., 1992) or AMTP (Heinrichs, 1994). However, with increasing size or geographic spread of the multicast group the performance of these protocols gets worse, and more scalable protocols are required. Only recently some reliable multicast protocols have been developed for that purpose. Besides the sender these protocols allow either dedicated receivers (e.g. in RMTP (Paul et aI., 1997) or TMTP Yavatkar et aI., 1995) or routers (e.g. in SRMT (Schuba, 1998» to handle ACKs/ NAKs and to retransmit packets for members in their local environment (we will call these protocols "receiver-originated" and "router-originated", respectively). Thus the cost for retransmissions can be decreased and the ACK processing load on the sender is relieved. Moreover, by a hierarchical ordering of retransmitting nodes the work can be homogeneously distributed in the network.

In the past performance evaluations of reliable multicast protocols were usually based on measurements or simulations of a single protocol. There are only some exceptions to this rule, e.g. the analytical investigations in (Pingali et aI., 1994) (which are restricted to different types of sender-originated strategies) or (Schuba, 1998). However, these analyses make simplifying assumptions, e.g. they assume loss probabilities to be identical and loss events to be mutually independent for all receivers. Our approach differs from previous work in several ways. First, we compare generic protocols with respect to their retransmission strategy, i.e. sender-originated, receiver-originated and router-originated protocols. Second, our analysis is based on homogeneous discrete-time Markov chains. Hence, loss events are allowed to be dependent for different receivers, and loss probabilities can be defined separately in the multicast tree and thus may be different for all destinations.

The remainder of the paper is structured as follows. In chapter 2 we motivate the demand for new analytical models by demonstrating in a simple example that the independence assumption of loss events may lead to significant errors in analytical results. Next we describe how Markov chains can be used for a more realistic modelling of retransmission strategies (chapter 3). We then apply this model for an example multicast tree and different retransmission strategies in chapter 4, 5 and 6, respectively. The numerical results of our analysis are presented in chapter 7. Finally, concluding remarks are given in chapter 8.

Retransmission strategies for reliable multicast protocols 127

2 DEPENDENT VS. INDEPENDENT LOSS EVENTS

First, we want to demonstrate that investigations of reliable multicast protocols which are based on the simplifying assumption of independent loss events for all receivers in a multicast group, may lead to a significant overestimation of the expected number of retransmissions. This error is due to the tree-based transmission of multicast data, where packets are duplicated only at branching points of the delivery tree (see fig. 1). If a link in the tree has a positive packet loss probability and this link leads to more than one receiver, the packet loss events that happen on this link are obviously dependent for its receivers. Because a large number of links in a multicast tree transport packets to several receivers (bold links in fig. 1 left), the independence assumption may lead to serious errors in analytical results.

Figure 1 Real multicast tree vs. "tree" with independent loss events.

For a comparison of dependent and independent loss events let the random variable X denote the number of retransmissions until all receivers in a multicast tree have obtained a packet. Assuming independent loss events (cf. fig. 1 right) and a loss probability p for each of the D destinations the expected number of retransmissions E[X] (see (Pingali et aI., 1994) for details) is given by

E[X] = l~(p) (_I)i+l_l_. ]-1. t I (1- p') (1)

We will use this formula to calculate E[X] for multicast groups with 5, 10 and 20 destinations.

Now imagine a multicast tree with only one unreliable link. If this link happens to be located between the source and the first branching of the tree (e.g. the first link in fig. 1 left), all receivers (independently of their number) will be affected by a lost packet on this link. Thus the packet loss events for all receivers are strongly dependent. The number of retransmissions in such a multicast tree is geometrically distributed with mean E[X] = P / (1- p) (what may also be computed using (1) with D = 1).

Fig. 2 compares the expected number of retransmissions for the four different scenarios. Note that the loss probability for each receiver is always the same.


P (loss probabilily)

Figure 2 Independent vs. strongly dependent loss probabilities.

As can be seen clearly, the overestimation increases with the number of receivers, for which independent loss events are assumed. If we consider the worst (real) case, i.e. all loss events are dependent (dotted line), the values ofE[X] may be overestimated by more than factor 2 even for only 5 receivers. Thus, when assuming independent loss events, all results should be interpreted very carefully.

To overcome the overestimation of retransmissions in our analyses we will use a Markov chain model with only the following assumptions:

• All retransmissions are sent as multicast to the receivers.

• ACKs or NAKs are never lost.

3 MODELLING OF MULTICAST RETRANSMISSION STRATEGIES

We first need an appropriate cost metric for the comparison of sender-originated, receiver-originated and router-originated protocols. From our point of view a reliable multicast protocol should minimize transmission time as well as the required network resources. Since the time until all receivers successfully have received a data packet is closely related to the number of retransmissions we use retransmission cost as measure for our investigations. Let the random variable Xk denote the number of retransmissions of a node k. Then we define the retransmission cost produced by this node as

• the average number of times E[Xk] a packet is retransmitted by node k until all its receivers have obtained the packet

multiplied by

• the number of multicast tree links Ck (cost parameter) involved in a retransmission of node k.


The overall retransmission cost R for a packet can be written as

R:= LE[Xt]·Ct. (2) all k

For example consider the multicast tree in fig 3. Obviously a retransmission from a node near the receivers yields less cost than a retransmission from a node farther away. For instance each retransmission multicasted by sender S to 0, and O2 results in additional retransmission cost of C = 3 (cost per link = I) while a retransmission multicasted from router MR to 0, and O2 only leads to retransmission cost of C = 2.

s

Figure 3 A simple multicast tree.

Now look once more at the multicast tree given in fig 3. Let the variables p; (i E

{ I, 2, 3}) denote the packet loss probabilities of the respective links. We first examine a sender-originated protocol. The probability distribution function of X (number of retransmissions) can be determined based on a homogeneous discrete-time Markov chain (OTMC) shown in fig. 4.

Figure 4 OTMC for the simple multicast tree.

The OTMC consists of four two-bit states dJdz, d; E {O, I}, i E {I, 2}. d; = I means that the transmission for destination 0; has been a success while d; = 0 indicates a failure. The corresponding transition probabilities * can be written as matrix

[

PI + (I - PI )PZPl

p= 0 o o

(1- PI)(I- pz)P1

PI + (1- PI )Pl o o

(1- PI)PZ(l- P3) (1- PI)(I- pz)(I- P3)] o (1- PI )(1 - P3 )

PI+(I-PI)PZ (I-PI)(I-PZ) • o I

* We will also use the binary notation for transition probabilities, e.g. Po 1.11' The state order is given by the decimal value of the binary state number, e.g. the binary state 11 equals state number 3 (decimal),


The initial state distribution of the DTMC is given by 1t(0) = (1too(0), 1~1l(0),

1t1O(0), 1t11 (0» = (Poo.oo, Poo.OI> POO.IO, POO.II), since one transmission is already finished before retransmissions begin, i.e. we just have to consider the transition probabilities originating from state 00. The probability to be in a certain state of the DTMC after n steps 1t(n) can be determined simply by calculation of the nth power of P (see e.g. (Stewart, 1994». We are only interested in being in state 11, which indicates that all receivers have obtained the packet. Hence, we get

(3)

where we take the n-step transition probabilities p~n~ II from matrix pn. The probability In that exactly n retransmissions are required 'is given by In = 1t ll (n) -1tll(n-l) for n > 0 and/" = 1tll (O) for n = O. The expected retransmission cost for a sender-originated protocol now can be written as

00

E[R] = E[X]·c = c· Lin ·n. (4) n=O

4 ANALYSIS OF SENDER-ORIGINATED RETRANSMISSIONS

For the comparison of the three retransmission strategies we use the multicast tree with five receivers shown in fig. 5.

s~

Figure 5 Multicast scenario to be analyzed.

We limit the group size to five because an analysis with i receivers results in 2i states in the DTMC and 22i transition probabilities, i.e. 32 states and 1024 probabilities in our example. This multicast tree is simple but very useful for analyzing many different multicast scenarios, e.g. by changing the loss probabilities of the links. Thus local groups (small p;) can be examined as well as groups with large geographic spread, i.e. large Pi values. Moreover, the example tree corresponds to typical structures of real multicast groups.


For example look at the map of the German MBONE (Multicast Backbone, fig. 6) in which all german IP multicast routers together with their logical connections are shown. The logical interconnection of our example tree (fig. 5) can be found very often in this map, e.g. if the sender is located in Aachen, two receivers are listening in Berlin, another receiver is located in Stuttgart and two more receivers are connected to the multicast router in Niimberg.

Figure 6 German MBONE (December 1997).

The analysis of the sender-originated strategy can be performed in the same way as in the example for two receivers, now numbering the states with bits djdzd,¥14ds, d; E {O, I}, i E {I, ... , 5} where d; = 0(1) corresponds to the success (failure) of D;. Because the corresponding matrix P is too large to be printed here we just give the following transition probabilities as example. All other probabilities look similarly.

POOOXJ,OOOXJ = PI + (1- PI) . [P2 + (1- P2 )P3P4 Hps + (1 - Ps )P6 (P7 + (1- P7 )PSP9 r POOIIO.IOIIO = (1 - PI )(1- P2 )(1- Pl )P4[PS + (1- Ps )(P7 + (1- P7 )P9)].

The expected overall retransmission cost can be directly derived from (4) with parameter c set to 9 because there are 9 links in the multicast tree originated at the source.


5 ANALYSIS OF RECEIVER-ORIGINATED RETRANSMISSIONS

For the receiver-originated approach we first have to divide the multicast group into subgroups. Let us assume that a receiver-originated protocol would use three (local) subgroups in our example (see fig . 7):

• GroUPl consisting of S, D2 and D3 (the source being responsible for retransmissions),

• GrouP2 with Dl and D2 (D2 being the dedicated receiver) and

• GroUP3 consisting of D3, D4 and Ds (D3 being the dedicated receiver).

Figure 7 Local groups for receiver-originated retransmissions.

While source S globally multicasts packets to all receivers (but listens only to ACKs from D2 and D3), we assume that retransmissions in GrouPl and GrouP2 are multicasted only to the members of the respective subgroup (local multicast).

To analyze this scenario let us first look at GroUPl . The sender S retransmits a packet until D2 and D3 have correctly received it. This is just like a sender-originated protocol with two receivers. Thus the number of retransmissions can be computed according to (3). For the expected cost E[~roupd (defined in (4» we have to set the cost parameter c to 9 because each retransmission is sent as global multicast.

For Group2 the situation is different. Obviously there exist three different retransmission situations in which Dl might receive a packet for the first time:

1. The packet is retransmitted by S only, i.e. D2 (the dedicated receiver for Dl) has not yet received the packet.

2. Sand D2 retransmit the packet, i.e. D2 has received the packet but D3 has not.

3. Only D2 retransmits this packet, i.e. both, D2 and D3, have received the packet.

Since all retransmissions of S (case I and 2) have already been taken into account for the cost of GrouPl we only have to consider the retransmissions from D2 (case 2 and 3). Once more we can use a Markov chain (we call it DTMCl) to determine the number of retransmissions from D2 (see fig. 8 left). As before the bits in the states


indicate the reception status ofthe receivers Dl> Dz and D3, state 010 corresponding to case 2 and 011 to case 3, resp. State lxx is the success state, i.e. there is no more retransmission required for D I , independently ofDz and D3.

Figure 8 DTMC I (left) and DTMCz (right) for Groupz.

The (non-null) transition probabilities for DTMC I are given by

POIO.OIO = (PI + (1- PI)' [P2 + (1- P2) · P3]) ' (P5 + (1- P5) ' P6 ) · (P4 + (1- P4) ' pJ, POIO.011 = (1- PI) ' (P2 +(1- P2)' P3) ' (1- Ps) · (1- P6) ' (P4 +(1- P4) ' P3)'

P OIO.ln = (1- P I)' (1- P2)' (1- P3)+ (PI +(1- PI) ' [P2 +(1- P2)P3]) ' (1- P4) ' (1- P3)'

P011.Oll = P4 + (1- P4) ' P3'

P011.ln = (I - P 4) . (I - P3)'

Note that POIO.OIO' POIO.OII and POIO.lxx include retransmissions from Sand DI. DTMC I might start in each of the states depending on the success/failures of the transmissions initiated by the sender before. In order to get the initial state distribution 1t(O) = (1tOIO(O), 1toll(O), 1t lxx(O) we need Markov chain DTMCz, (see fig. 8 right), modelling the possible transitions from the very start to the states ofDTMC I .

The limiting distribution of DTMCz determines for each of the three states 1 xx, 010 and 011 the probability that it is reached first, i.e. the initial state for DTMC I .

Given the initial state distribution we can determine 1tlxx(n) for DTMC I similarly

to (3) and the expected retransmission cost E[~roupz] according to (4) with c = 2 (due to local multicasting of packets).

To achieve the expected retransmission cost for Group3 E[Roroup3] we proceed similarly to Groupz. The respective Markov chains become a little bit larger since there are three receivers in Group3' The overall retransmission cost for receiver

originated retransmissions are given by E[R] = E[~roupd + E[~roupz] + E[~roup3] '


6 ANALYSIS OF ROUTER-ORIGINATED RETRANSMISSIONS

The analysis of the router-originated retransmission strategy is very simple now because it can be viewed as a composition of several trees with sender-originated strategy. We distinguish between two scenarios. In the first, we call it RouterA,

retransmissions are performed by sender S and by the multicast routers MR2 and

MR3. In the second scenario (RouterB) all routers are involved in retransmissions.

For analysis of scenario RouterA we divide the multicast tree (see fig. 5) into

three disjoint subtrees (rooted at S, MR2 and MR3, respectively) and analyze each

subtree separately (similar to the sender-originated analysis). The cost parameter c for the subtrees are 3 (for the one rooted at S), 2 (for the MRrsubtree) and 4 (for the

MRrsubtree). We get E[R] = E[Rs] + E[RMR2] + E[RMR3] for the expected overall

retransmission cost. In the same way scenario RouterB results in expected retransmission cost of E[R]

= E[Rs] + E[RMRd + E[RMR2] + E[RMR3] + E[RMR4] where the cost parameter c must

be set to 1 for the sender-subtree and to 2 for all other subtrees.

7 NUMERICAL RESULTS

We first examine how the expected retransmission cost for sender-originated, receiver-originated and router-originated protocols varies with the loss probabilities Pi := P, i.e. with the geographic spread of the multicast group. The results are shown in fig. 9 (the right diagram is just an enlargement of the bottom left corner of the left one).

500 I - -, 10 - . s.xMir

I 400 ......... Receiver

I T - RouterA I / r: 0 300 I ! :: - Roulere

I f ~ ~2OO / / ~

/ ./ [f w / ..... /

100

... ~ .. < .. ::. ..........

......... A.cliver

:1 ~ 5

I

0 0 0.2 0.4 0.6 0.8 0.02 0.04 0.06 0.08 0:

P (loss probability) P (loss probability)

Figure 9 Retransmission cost when varying all Pi.

Obviously the cost of sender-originated protocols soon becomes unacceptable in our multicast tree. Even for small loss probabilities the retransmission cost is rather


high. The improvement achieved by the receiver-originated approach is only marginal. In comparison to this both router-originated scenarios perform well. especially scenario RouterB. where all routers are responsible for retransmissions. This approach results in acceptable cost even for loss probabilities higher than 50%.

However. in real networks the loss probabilities will not be the same for all links. In peak traffic times most links will be rather reliable while only a small number of links will have high loss probabilities at the same time. The results of a corresponding scenario are presented in fig. 10. All loss probabilities (except one varying parameter) have been set to 0.1. a realistic value in a large network with high traffic.

100 - , Stndtr

......... R"-

-_rA

0.2 0.4 0.6 0.8 pl (loss probability)

100

- -......... Roc_

-RouIoIB

I I I

/) // ... /.

/' -'

..... =: ... :::::-... :.:::: .. ::: ... ::::: ... : ........................ .

o~~~~~~:=~~ o 0.2 0.4 0.6 0.8

p9 (loss probability)

Figure 10 Retransmission cost if the loss probability varies on one link only left: Pi = 0.1 (i = 2 ..... 9). PI varies. right: Pi = 0.1 (i = 1 ..... 8). P9 varies.

As can be seen an unreliable link near the source (fig. 10 left) has more impact on the cost for sender-originated and receiver-originated protocols than an unreliable link near a receiver (fig. 10 right). In contrast to this the cost of the router-originated protocol is hardly influenced by the location of the unreliable link since error recovery is handled locally. The performance is very well in both cases.

8 CONCLUSIONS

In this paper we have analytically examined different retransmission strategies for reliable multicast protocols. Particularly. we have presented a Markov chain model for calculating the retransmission cost of sender-originated. receiver-originated and router-originated protocols. An important feature of our analysis is that we allow a dependence between packet loss events for different receivers. Moreover. packet loss probabilities may be defined on a per link basis. Thus our method yields more realistic results than previous work in this context. Numerical results have shown that the cost for sender-originated protocols are only acceptable in the local area where loss probabilities are low. With growing size of the network and increasing


geographic spread of the groups (high loss probabilities) either receiver-originated or even better router-originated protocols have to be used instead.

9 REFERENCES

Deering S. (1988) Multicast Routing in Intemetworks and Extended LANs. Proceedings of ACM SIGCOMM.

Hermanns, o. and Schuba, M. (1996) Performance Investigations of the IP Multicast Protocols. Computer Networks and ISDN Systems 28, 429-39.

Armstrong S., Freier A. and Marzullo K. (1992) Multicast Transport Protocol. RFC 1301.

Heinrichs B. (1994) AMTP: Towards a High Performance and Configurable Multipeer Transfer Service. Architecture and Protocols for High-Speed Networks. Danthine, Effelsberg, Spaniol (Eds.), KIuwer Academic Publishers.

Paul S., Sabnani K. K., Lin J. C.-H. and Bhattacharyya S. (1997) Reliable Multicast Transport Protocol (RMTP). IEEE Journal on Selected Areas in Communications, Vol. 15, No.3, 407-21.

Yavatkar R., Griffioen J. and Sudan M. (1995) A Reliable Dissemination Protocol for Interactive Collaborative Applications. ACM Multimedia '95, 333-44.

Schuba M. (1998) SRMT - A Scalable and Reliable Multicast Protocol. Proceedings ICC'98.

Pingali S., Towsley D. and Kurose J. F. (1994) A Comparison of Sender-Initiated and Receiver-Initiated Reliable Multicast Protocols. SIGMETRICS'94, 221-30.

Stewart W. J. (1994) Introduction to the Numerical Solution of Markov Chains. Princeton University Press

10 BIOGRAPHIES

Marko Schuba has studied computer science in Aachen, where he received his Diplom (the German equivalent to M.Sc.) in 1995. Since then he is with the Computer Science Department of Aachen University of Technology. His research interests include performance modelling and evaluation of computer networks, multicast network and transport protocols, and interworking between connectionless protocols and ATM. Currently, he is working towards his Ph.D.

Peter Reichl has studied mathematics, physics, philosophy and music in Munich and at Cambridge University, where he wrote his Diploma thesis under the supervision of F. P. Kelly. Since 1995 he is with the Computer Science Department of Aachen University of Technology where he is working towards his Ph.D. His current interests include traffic modelling, models for self-similarity and the modelling and evaluation of network protocols.

11 Scheduling Combined Unicast and Multicast Traffic in WDM Networks* Zeydy Ortiz, George N. Rouskas, Harry G. Perros Department of Computer Science North Carolina State University Raleigh, NC 27695-7534, USA {zortizl,rouskas,hp}Gcsc.ncsu.edu

Abstract We study the performance of various strategies for scheduling a combined load ofunicast and multicast traffic in a broadcast WDM network. The performance measure of interest is schedule length, which directly affects both aggregate network throughput and average packet delay. Three different scheduling strategies are presented, namely: separate scheduling of unicast and multicast traffic, treating multicast traffic as a number of unicast messages, and treating unicast traffic as multicasts of size one. The strategies are compared against each other using extensive simulation experiments in order to establish the regions of operation, in terms of a number of relevant system parameters, for which each strategy performs best. Our main conclusions are as follows. Multicast traffic can be treated as unicast traffic under very limited circumstances. On the other hand, treating unicast traffic as multicast traffic produces short schedules in most cases. Alternatively, scheduling and transmitting each traffic component separately is also a good choice.

1 INTRODUCTION

The ability to efficiently transmit a message addressed to multiple destinations has become increasingly important with the emergence of telecommunication services and computer applications requiring support for multipoint communication [1]. These applications include teleconferencing, distributed data processing, and video distribution. Traditionally, without network support for multicasting, a multi-destination message is replicated and transmitted individually to all its recipients. This method, however, consumes more bandwidth than necessary. Bandwidth consumption constitutes a problem since most of the applications requiring multipoint communication support typically consume a large amount of bandwidth. An alternative solution is to broadcast a multi-destination message to all nodes in the network. The problem is that nodes not addressed in the message will have to dedicate resources to receive and process the message. In a multi-channel environment we could arrange

*This work was supported by the National Physical Science Consortium, the National Security Agency, and the NSF under grant NCR-9701113.

Perfonnance of Information and Communication Systems U. Komer & A. Nilsson (Eds.) e 1998 IFIP. Published by Chapman & Hall


for all nodes addressed in a multi-destination message to receive such communication over a previously determined channel. The coordination must be carefully made such that the use of the channels in the system is maximized.

In an optical broadcast network using wavelength division multiplexing (WDM) the available bandwidth is divided into channels. In order to communicate in this multi-channel environment, a transmitter and a receiver of the interested parties must be tuned to a common channel. Also, while the transmission is taking place, no other transmission may be made in that channel, otherwise a collision will occur. With current technology, we must take into consideration the time required for a transceiver to tune to a different channel since this time may be comparable to a packet's transmission time. These three factors contribute to the need for algorithms to appropriately schedule multicast transmissions.

In a previous paper [4], we studied the problem of scheduling multicast traffic in broadcast-and-select networks employing WDM. We found that in this environment we must balance two conflicting objectives: low bandwidth consumption and high channel utilization. Bandwidth consumption can be high if a multi-destination message is always replicated and transmitted separately to each recipient. On the other hand, attempts to coordinate the addressed nodes so that a single transmission of a multicast packet be sufficient can lead to low channel utilization; in other words, it is possible that only a small number of channels carry transmissions at any given time, defeating the original purpose of a multi-channel environment. In [4] we introduced and studied the concept of a virtual receiver which can be used to provide a good balance between the two objectives.

In this paper, we focus on the problem of scheduling both unicast and multicast traffic, since a mixed traffic scenario is the one more likely to be encountered in practice. Thus, the issue at hand is how to schedule traffic in order to efficiently utilize the network resources. In our case, efficiency is measured in terms of the length of the schedule produced: the shorter the schedule length, the higher the overall network throughput and the lower the average delay experienced by a message. The problem of scheduling unicast and multicast traffic has been studied in [5, 2]. However, [5] does not take into consideration the latency associated with tuning to different channels, while in [2] the average number of channels utilized in the network is only one. On the other hand, the scheduling policies presented in this paper are based on an algorithm designed to mask the tuning latency, and they can fully utilize the resources available in the network.

In Section 2 we present the network and traffic models used in this study, and we summarize earlier results. In Section 3, we present three strategies for handling combined unicast and multicast traffic. In Section 4, we compare these three strategies through extensive numerical experiments to determine which one yields the shortest schedule, and we conclude the paper in Section 5.

Unicasl and mullicasllraffic in WDM 139

2 SYSTEM MODEL

We consider an optical broadcast WDM network with a set .N = {I,· .. , N} of nodes and a set C = {Al,···, AG} of wavelengths, where C ~ N. Each node is equipped with one fixed transmitter and one tunable receiver. The tunable receivers can tune to, and listen on any of the C wavelengths. The fixed transmitter at station i is assigned a home channel A(i) E C. Let Xc, c = 1, ... ,C, denote the set of nodes with Ae as their home channel: Xc = {i : A(i) = Ae}. The network is packet-switched, with fixed-size packets. Time is slotted, with a slot time equal to the packet transmission time, and all the nodes are synchronized at slot boundaries. We assume that the traffic offered to the network is of two types: unicast and multicast. We let g ~ .N = {I, 2, ... , N} represent the destination set of a multicast packet and I g I denote its cardinality. Also, we let G represent the number of currently active multicast groups.

In this paper, we assume that there is a ex N unicast traffic demand matrix A = [aej], where aej is the total amount ofunicast traffic destined to receiver j and carried by channel Ae. There is also a C x G multicast traffic demand matrix M = [meg], with meg representing the number of multicast packets originating at nodes whose home channel is Ae and destined to multicast group g. We assume that traffic matrices M and A are known to all nodes. Information about the traffic demands {aej} and {meg} may be collected using a distributed reservation protocol such as HiPeR-l [7].

We let integer .6. ~ 1 represent the normalized tuning latency, expressed in units of packet transmission time. Parameter .6. is the number of slots a tunable receiver takes to tune from one wavelength to another. We note that, at very high data rates, receiver tuning latency becomes significant when compared to packet transmission time. Therefore, unless techniques that can effectively overlap the tuning latency are employed, any solution to the problem of transmitting traffic in a broadcast WDM environment will be inefficient.

The problem of constructing schedules for transmitting unicast traffic in this network environment has been addressed in [6] where arbitrary traffic demands and arbitrary transceiver tuning latencies were considered. The algorithms presented in [6] yield optimal schedules when the traffic demands satisfy certain optimality conditions. A number of heuristics were also presented for the general case, and they were shown to produce schedules of length very close to (and in many cases equal to) the lower bound. In this paper, we will make extensive use of the algorithms in [6]. For presentation purposes, we introduce the following operation: S +- Sched(A, d). The Sched(-) operation takes as arguments a unicast traffic demand matrix A and the transceiver tuning latency .6., and it applies the algorithms in [6] to obtain a schedule S for clearing matrix A.

The authors have previously considered the problem of scheduling multicast traffic in broadcast optical networks [4]. There, a virtual receiver V ~ .N was


defined as a set of physical receivers that behave identically in terms of tuning. Thus, from the point of view of coordinating the tuning of receivers to the various channels, all physical receivers in V can be logically thought of as a single receiver. A k-virtual receiver set V(k), 1::; k::; N, is defined as a partition of the set ./If of receivers into k virtual receivers, V(k) = {V?), V2(k), ... , Vk(k)}. Given a k-virtual receiver set V(k) and a multicast traffic matrix M, transmission of multicast packets proceeds as follows. When a virtual receiver V/(k) is on channel >'e, each transmitter in Xe (i.e., each transmitter tuned to wavelength

>'e) will transmit all its multicast packets to groups 9 such that 9 n V/(k) -=F <P

(i.e., at least one member of 9 has a receiver in V/(k)). All receivers in V/(k) will have to filter out packets addressed to multicast members of which they are not a member, but they are guaranteed to receive the packets for all groups of which they are members.

Given matrix M, our previous work focused on how to select a virtual receiver set so as to achieve a good balance between two conflicting objectives: channel utilization and bandwidth consumption (for more details, see [4]). For presentation purposes, we introduce another operation, V RC), which takes as arguments a multicast traffic matrix M and the tuning latency ~, and which applies the heuristics in [4] to construct a near-optimal virtual receiver set V(k*) for M: V(k*) +- V R(M, ~).

Once the k*-virtual receiver set V(k*) has been determined, we construct a C x k* matrix B= [be,] where bc/ = Lg:gnv/k*);I!<t> meg. An element bc/

of this new matrix represents the amount of multicast traffic originating at channel >'e and destined to virtual receiver V/(k*). Thus, by specifying the k*-virtual receiver set V(k*), we have effectively transformed our original network with multicast traffic matrix M, to an equivalent network with unicast traffic matrix B. This new network has the same number of transmitters and channels and the same tuning latency as the original one. However, it only has k* receivers, corresponding to the k* virtual receivers in V(k*). We can now employ the algorithms in [6] to construct schedules for clearing matrix B in this new network. In summary, the construction of a schedule for the transmission of multicast traffic matrix M, involves three steps: applying the operation VR(M, ~), determining matrix B from the resulting virtual receiver set V(k*), and finally applying the Sched(B, ~) operation. We will use M Sched(M,~) to denote this sequence of operations resulting in a schedule S for M: S +- MSched(M, ~).

3 TRANSMISSION STRATEGIES

In this section we present three different strategies for scheduling and transmitting an offered load of combined unicast and multicast traffic. These are: separate scheduling, treating multicast as unicast traffic, and treating unicast as multicast traffic. These strategies were selected because they provide an

Unicast and multicast traffic in WDM 141

intuitive solution to handling unicast and multicast traffic. We assume that the unicast and multicast traffic demands are given by matrices A and M respectively. Lower bounds on the schedule length for each strategy have been obtained (see [3]) but are omitted due to space limitations.

Strategy 1: Separate Scheduling. Our first strategy for transmitting the combined traffic offered to the network is to separately schedule the unicast and multicast matrices. That is, each traffic matrix is considered in isolation, and the appropriate scheduling techniques from [6, 4] are applied to each traffic component. The two schedules are then used in sequence. This is a straightforward approach and involves the following operations: Sched(A, ~) and MSched(M, ~). Since at the end of the first schedule (say, the one for unicast traffic) the receivers may not be tuned to the channels required to start the next schedule (say, the one for multicast traffic), a sufficient number of slots for receiver retuning must be added between the two schedules. We note that the separate scheduling strategy achieves a lower bound which is equal to the sum of the best lower bounds for each traffic component in isolation (plus ~ slots to account for the retuning between the schedules).

Strategy 2: Multicast Traffic Treated as Unicast Traffic. Our second approach is to treat multicast traffic as unicast traffic by replicating a packet for a multicast group g to all the members of g. In essence, using this strategy we create a new ex N unicast matrix A(2) = [a~;)] where each element a~;) represents the number of packets originating at channel Ae and destined to physical receiver j: a~;) = aej + Lg:j Eg meg. Given A (2), we construct a transmission schedule by applying the operator for unicast traffic, Sched(A(2), ~).

Strategy 3: Unicast Traffic Treated as Multicast Traffic. This strategy, in a sense, is the dual of the previous one. The unicast traffic is treated as multicast traffic by considering each individual destination node as a multicast group ofsize one. Given that initially there are G multicast groups (i.e., matrix M has dimensions C x G), this approach transforms the original network into a new network with multicast traffic only and with G + N multicast groups (the groups of the original network plus N new groups {j}, one for each destination node j). The multicast traffic demands of the new network are given by a new ex (G + N) matrix M(3) = [mW] whose elements are defined as follows:

m(3) = { eg g = 1,···,G g = G+j,j = 1,···,N

(1)

We can then use the new matrix M(3) to obtain a schedule for the combined unicast and multicast traffic: MSched(M(3), ~). The near-optimal k(3Lvirtual

142 Pan Four Multicast

receiver set obtained from matrix M(3), however, will in general be quite different from the k*-virtual receiver set obtained from matrix M.

4 NUMERICAL RESULTS

In this section we investigate the behavior of the three strategies for a wide range of traffic loads and network parameters. Our objective is to determine which strategy produces the shortest schedule. Results are obtained by varying the following parameters: the number of nodes N in the optical network, the number of channels G, the tuning latency ~, the number of different multicast groups G, the average number of nodes 9 per multicast group, and the amount of multicast traffic as a percentage of the total traffic, s.

Specifically, in our experiments the parameters were varied as follows: N = 20,30,40,50 network nodes, G = 10,20,30 multicast groups, G = 5, 10, 15 channels, and ~ = 1,4,16 slots. The average group size 9 was varied so that it accounted for 10%, 25% and 50% of the total number of network nodes N. For each multicast group, the number of members x in the group was selected randomly from the uniform distribution [1, 2g - 1]. Some network nodes may not belong to any of the multicast groups.

The multicast traffic matrix was constructed as follows. Let Peg be the probability that channel Ae will have traffic for multicast group g. Then, with probability Peg, meg was set equal to a randomly selected value from the uniform distribution [1, 20], and with probability 1 - Peg it was set equal to zero. The probability Peg was calculated as follows:

Peg c < lTGTcrJ otherwise

(2)

Parameter s represents the percentage of total traffic due to multicast. It can be obtained as the ratio of the total multicast traffic (as seen by the receivers) to the total traffic in the network:

s GuGm

GuGm+GNa 100% (3)

where m and a denote the average of the entries in the multicast and the unicast matrices, respectively. The percentage s of multicast traffic was varied from 10% to 90%. From the value assigned to N, G, G, m, g, and s, we can


use the above equation to calculate a. Let qcj be the probability that channel Ac has traffic for receiver j. The probability qcj was calculated as follows:

{ c+c-LwZcrJ+l l....L...J

. _ C' C < LNlcJ QC1 - c-L TNkrJ+l

~ otherwise C '

(4)

Then, with probability qcj the corresponding entry of the unicast traffic matrix acj was set to a randomly selected number from the uniform distribution [1, 2a-1J, and with probability 1-qcj it was set equal to zero.

We also investigated the effects of hot-spots by introducing hot nodes which receive a larger amount of traffic compared to non-hot nodes. Specifically, we let the first five nodes of the network be the hot nodes. The average number of unicast packets received by these nodes was set to 1.5a. Therefore, with probability qcj, given by (4), the entry aCj,j = 1,,,,,5, was set to a randomly selected number from the uniform distribution [1, 2(1.5a)-1J, and with probability 1-qcj it was set to zero. The remaining N - 5 nodes receive an average number of unicast packets equal to (N;'!s5)a. For these nodes with probability qcj, the entry acj, j = 6"", N, was set to a randomly selected value from the uniform distribution [1, 2( ~-'!s5)a - 1)], and with probability 1-qcj it was set equal to zero. Note that the overall average number of unicast packets remains equal to a, as in the non-hot-spot case.

For each combination of values for the input parameters N, G, C, il, g, and s, we construct the individual multicast groups, the multicast traffic matrix, M, and the unicast matrix, A, using random numbers as described above. When constructing a case, we require that all nodes receive transmissions (unicast and/or multicast packets) and that all channels have packets to transmit. Based on all these values, we then obtain 8(i) , the schedule length of the i-th strategy, i = 1,2,3. Let fiI' be the schedule length of the strategy with the lower schedule length, i.e., fiI' = min {8(1), 8(2),8(3)}. Then, for each

strategy i, we compute the quantity D(i) = s(ii:s* 100%, which indicates how far is the schedule length of the ith strategy from the best one. Due to the randomness in the construction of the multicast groups and of matrices M and A, each experiment associated with a specific set of values for N, G, C, il, g, and s is replicated 100 times. For each strategy i, we finally compute b(i) = I~O L:J~OI D;i), where Dy) is obtained from the j-th repli

cation. All figures in this section plot b(i), i = 1,2,3, against the percentage s of multicast traffic offered to the network.

4.1 Detailed Comparisons

The results are presented in Figures 1-12. In each figure, we plot D(i), i = 1,2,3, against s indicated as "% Multicast Traffic". In other words, the fig-


ures present the performance of the various strategies relative to each other. Confidence intervals are also shown in each figure. For presentation purposes, we use the following abbreviations for the names of the three strategies in the figures and tables:. Strategy 1 is referred to as "Separate", Strategy 2 is referred to as "Unicast" and Strategy 3 is referred to as "Multicast".

Figure 1 gives the results for the case where N = 20, G = 30, C = 10,.6. = 4, and g = 0.25N. We note that Strategy 2 is the best strategy for s < 50%, but that Strategy 3 becomes the best one for s ~ 50%. This figure represents our base case. Figures 2 to 12 give results in which only one of the parameters has been changed while the remaining parameters are the same as those in Figure 1. Specifically, Figures 2 and 3 show the cases in which we vary g. In Figures 4 and 5 we varied .6.. The number of channels is varied in Figures 6 and 7, while the number of multicast groups is changed in Figures 8 and 9. The next three figures, namely 10, 11, and 12, show results when the number of nodes is increased. Below, we discuss the results presented in Figures 1-12 for each strategy separately. More detailed explanations that take into account the various lower bounds can be found in [3].

Separate Scheduling. Even though the behavior of Strategy 1 (relative to the others) appears to be unaffected by the different parameters, we noticed changes related to the tuning latency, as expected. When .6. was increased, D(1) had a tendency to increase. Recall that .6. slots are added to the optimal bounds for unicast and multicast traffic, while the lower bounds for the other two strategies do not have this component. It is thus expected for jj(l) to be sensitive to this parameter. Increasing s or C did not change the behavior of D(l), except for large values of .6. (.6. = 16). In these cases, the increase observed can be attributed to the large .6..

Multicast Traffic Treated as Unicast Traffic. For this strategy, we note that as s or g increases, the difference from the best strategy, jj(2), increases (and in some cases it increases dramatically). This behavior can be explained by noting that in this strategy, all multicast packets are replicated to every member of a multicast group and transmitted independently. Therefore, it is only natural to expect that the schedule length increases when there is more multicast traffic or more recipients per packet. Similar observations apply when N is increased.

We also note that changes in parameter .6. do not significantly affect jj(2).

Finally, as C increases, jj(2) tends to decrease. For the traffic matrices considered here, the network is in the bandwidth-limited region [6] when this strategy is used. Therefore, an increase in the number of available channels results in a shorter schedule length.

Unicast Traffic Treated as Multicast Traffic. This strategy is not the best choice when we have a large amount of unicast traffic (compared to


..

Figure 1 Comparison for N = 20, G = 30, C = 10, Ll = 4, 9 = 0.25N


"


f ! 30

! I ~ •


..

/ t····+·· l ..... , ...... /. 10

~ °oL-~1O--~m--~~~ .. ~~~--L~~ML=~~~~~~,00 "AUiclsI TrafIi::


.. s:r.:::: / --..

I J/

/

.{ /

':L;;:~=····:!:··=······J·t=·····::1··· .. =······=······t=· ... t! .. =.! .. ~ .. = ..... :1.~.= ... :j .. I~ o 10 ~ 00 ~ ~ ~ ~ ~ ~ 100

"" ...... Tratllr:


146 Pan Four Multicast

20

Figure 7 Comparison for N = 20, G = 30, C = 15, ~ = 4, 9 = 0.25N

/ .J'/

~ ~ ~ ~ M ~ ~ 00 't.MUlicastTr.Hic

'00


i SeJ::'~ ::::: / Mu~icasl t&-1

J ..

i

..

20 r //

,/

X

r ..-

I ... ~" t··· I ··l ......... !,,/

30 '" S<l 60 70 80 90 '00 "MlAIicaslTralfic


."

f ~ l ~

j 20

, 10 !

···f ---r-' f·····. 20 40 50 60

't,lolutlCllslTrafllC ""


f j 30

! i 20

i5 , /

,/ I

20 40 50 60 'XoMlJticasiTraNIC

1/ Separale ........ , Unicasl ...........

! '-Iu~lcasl~

70


S<l

J SeJ:!: ::::: t.tlttieasll&--l

! !

f ..

l l

30

! I 20 l ~ .' , / .r

.J.':'/! ". t + !/ .. .. t· ..... ..... 0

0 30 '" S<l 60 80 % MUlicaslTrattic


.. I 30

J J I ~ #-

, .

Unicast and multicast traffic in WDM

• ~~ __ ~~ __ ~~ __ ~-····=···2· = .... = .... ~ .. = ... ~ .... ~ .. ~~ • ~ ~ 30 .. ~ • ~ • • ~

.... _T_ Figure 13 Comparison with hotspots for unicast traffic (N 20, G 30,C = 10,~ = 4,g = 0.25N)

147

multicast traffic). For small values of s, it starts as the worst strategy, but it becomes the best one for larger values of s. Changing any of the other parameters did not affect the performance of this strategy significantly. This behavior indicates that we could use this strategy in every circumstance since, even for small amounts of multicast traffic (small s), its performance is not significantly worse than that of the best strategy.

Hotspots. Finally, in Figure 13 we show the behavior of the three strategies for the hotspot pattern described earlier. Except for the unicast traffic matrix A, the remaining parameters are the same as those in Figure 1. We note that the results obtained in Figure 13 are not different from those in previous figures where all nodes were identical (no hotspots). This result was observed for a wide range of values for the various system parameters. We conclude that, although the existence of hotspots will certainly affect the schedule length, it does not affect the relative performance of the various strategies.

In Table 1, we present the percentage of time that each strategy produced a schedule of length within 5% of the best schedule, for various values of 9 and s and for all values of the other parameters N, G, C, and~. Tables 2 and 3 present similar results for different values of N, G, and N, C, respectively. The strategy that produced the shortest schedules in each case corresponds to the one with the highest percentage shown. A strategy whose schedule length was within 5% of the best schedule length was also considered to be the best strategy. The 5% margin, though somewhat arbitrary, provides us with an insight into the performance of the strategies. When deciding which strategy to implement in an actual system, we may settle for one that produces the shortest schedules under most conditions while producing schedules within 5% of the best under other conditions. Below, we discuss under what conditions


s = 10,20,30% s = 40,50,60% s = 70,80,90%

Separate 64% Separate 31% Separate 23% 9 = lO%N Unicast 82% Unicast 36% Unicast 22%

Multicast 54% Multicast 97% Multicast 100%

Separate 90% Separate 76% Separate 59% 9 = 25%N Unicast 57% Unicast 20% Unicast 4%


Separate 98% Separate 93% Separate 78% 9 = 50%N Unicast 35% Unicast 6% Unicast 0%


Table 1 Best strategy when 9 and s are varied

G = 10 G= 20 G = 30

Separate 33% Separate 49% Separate 46% N = 20 Unicast 51% Unicast 54% Unicast 66%


Separate 53% Separate 72% Separate 74% N=30 Unicast 29% Unicast 32% Unicast 33%


Separate 61 % Separate 80% Separate 87% N=40 Unicast 20% Unicast 18% Unicast 21 %


Separate 68% Separate 87% Separate 90% N = 50 Unicast 21% Unicast 14% Unicast 15%


Table 2 Best strategy when Nand G are varied

each of the three strategies is best.

Separate Scheduling. Overall, separate scheduling is effective in producing short schedules. Compared to Strategy 3, this strategy is better when there is a larger amount of unicast traffic, when there are many multicast groups (G is large), and when the number of channels is small compared to the number of nodes in the network.


C=5 C= 10 C = 15







Separate 91% Separate 81 % Separate 69% N=50 Unicast 3% Unicast 16% Unicast 25%


Table 3 Best strategy when Nand C are varied

Multicast Traffic Treated as Unicast Traffic. Strategy 2 is best when there is a small amount of multicast traffic in the network and the size of the multicast groups is small (see Table 1). This result is not surprising since replicating a multicast packet increases the requirements in the network and it can only be used efficiently in very limited situations. Also, this strategy is useful when the ratio of nodes to channels is small, i.e. N /C is close to 1 (see Table 2). In this case, the network operates in the tuning limited region [6].

Unicast Traffic Treated as Multicast. Strategy 3 produces schedules of short length in most situations. Even when the strategy does not produce the best schedule, the resulting schedule has a length no more than 20% larger than that of the best schedule (see Figures 1-13). Strategy 3 gives good results when G is small, i.e., G::; N/2, when C is large, i.e., C ~ N/2, and when the amount of unicast traffic is small, i.e., s ~ 40%.

5 CONCLUDING REMARKS

We studied the problem of scheduling unicast and multicast traffic for transmission in a broadcast-and-select WDM network. Our goal was to create schedules that balance bandwidth consumption and channel utilization in order to efficiently use the system resources.

We presented three different strategies for scheduling a combined load of unicast and multicast traffic. These strategies are: separate scheduling, treat-


ing multicast traffic as unicast traffic, and treating unicast traffic as multicast traffic. As expected, multicast traffic should be treated as unicast traffic under very limited circumstances. More specifically, this strategy is useful only when there is a small amount of multicast traffic in the network and/or the multicast groups are small. On the other hand, if we treat unicast traffic as multicast traffic with a multicast group of size 1, the resulting schedule has a shorter length (when compared with the schedules produced by the other strategies). This is the case especially when we have a large number of channels in the system, i.e. C 2: N /2 or when the number of multicast groups is small (G :S N /2). Scheduling and transmitting each traffic separately also produces schedules of short length. Finally, one must also take into account memory and processing time limitations when considering which of the best two strategies to use. In particular, Strategy 3 requires storage for the C x (G + N) multicast traffic matrix when forming the virtual receiver sets, while for Strategy 1 the scheduling algorithms in [6] must be run twice, once for unicast traffic and once for multicast traffic.

REFERENCES

[1] M. Ammar, G. Polyzos, and S. Tripathi (Eds.). Special issue on network support for multipoint communication. IEEE Journal Selected Areas in Communications, 15(3), April 1997.

[2] M. Borella and B. Mukherjee. A reservation-based multicasting protocol for WDM local lightwave networks. In Proceedings of ICC '95, pages 1277-1281. IEEE, 1995.

[3] Z. Ortiz, G. N. Rouskas, and H. G. Perros. Scheduling of combined unicast and multicast traffic in broadcast WDM networks. Technical Report TR-97-09, North Carolina State University, Raleigh, NC, 1997.

[4] Z. Ortiz, G. N. Rouskas, and H. G. Perros. Scheduling of multicast traffic in tunable-receiver WDM networks with non-negligible tuning latencies. In Proceedings of SIGCOMM '97, pages 301-310. ACM, September 1997.

[5] G. N. Rouskas and M. H. Ammar. Multi-destination communication over tunable-receiver single-hop WDM networks. IEEE Journal on Selected Areas in Communications, 15(3):501-511, April 1997.

[6] G. N. Rouskas and V. Sivaraman. Packet scheduling in broadcast WDM networks with arbitrary transceiver tuning latencies. IEEE/ ACM Transactions on Networking, 5(3):359-370, June 1997.

[7] V. Sivaraman and G. N. Rouskas. HiPeR-C: A fugh Performance Reservation protocol with Cook-ahead for broadcast WDM networks. In Proceedings of INFOCOM '97, pages 1272-1279. IEEE, April 1997.

PART FIVE

Admission and Traffic Control

12 A family of measurement-based admission control algorithms Z. Thranyi, A. Veres, A. Ol6.h Ericsson, Traffic Analysis and Network Performance Laboratory POB 107, 1300 Budapest, Hungary e-mail: {Zoltan.Thranyi.Andras.Veres.Andras.Olah}@lt.eth.ericsson.se Fax: +36-1-4377219, phone: +36-1-4377735

Abstract In this paper we identify a set of the requirements for an efficient admission control algorithm and propose new algorithms. These methods need only aggregate traffic measurements, work with simple FIFO scheduling and take only minimal assumptions on the pattern of the traffic. The requirements define a family of measurement based admission control algorithms of which three key members are discussed. We give effective bandwidth formulae for buffered and bufferless systems with token bucket and peak rate limited sources. It is also shown how the utilization can be improved by measuring the variance of the traffic rate while avoiding the limitations of MBAC methods based on the Central-limit theorem.

The theoretical background of this work is the effective bandwidth definition introduced by Gibbens and Kelly which has its roots in the Chernoff bounds.

Keywords Measurement based admission control, effective bandwidth, large deviation, token bucket, integrated services

1 INTRODUCTION

Measurement Based Admission Control (MBAC) has drawn considerable attention recently as it uses only simple and probably loosely fitted descriptors and by measuring the actual traffic it increases the network utilization.

Previous approaches proposed for MBAC can be categorized into two main groups: simple heuristic methods [CKT96, JJB97, JDSZ97] and mathematical bounds [Flo96, GAN91, GibKeI97]. The problem with the first group is that there is little or no clue about how to parametrize the algorithms, whether it would meet a certain QoS or not, or how it would behave if the traffic pattern changes (this happens frequently in the Internet). Members of the second group are more complex but they have the benefit of their parameters being

Performance of Infonnation and Communication Systems U. Komer & A. Nilsson (Eds.) © 1998 IFIP. Published by Chapman & Hall

154 Part Five Admission and Traffic Control

usually direct QoS metrics. However the underlying assumptions (such as independency, traffic models like MMPP or a certain queue length distribution [KWC93]) may limit their use. Also the bounds are usually very conservative.

It is very important that the knobs which we can tune an algorithm by be in direct contact with actual QoS parameters such as delay or loss. The resulting QoS should be independent of the traffic type and close to the required value as much as possible. This wayan administrator do not have to change the settings of the AC algorithm when traffic changes. The simple reference algorithm [JJB97] for example does not fulfill these expectations because its parameters are hard to set to achieve a certain QoS (e.g loss) and depend on the burstiness.

We would like to underline the related work of Brichet and Simonian [BriSim98]. They consider a leaky bucket descriptor and make a conservative Gaussian bound based on that the long-term mean rate of the flows will be always smaller than the submitted bucket rate. This gives an upper bound on the variance and leads to a tighter bound than Hoeffding's.

If we are to implement an MBAC, we face the problem of accurate measurements. It was shown in the literature [GroTse97] that the QoS bounds are very sensitive to measurement errors. These errors can be reduced by measuring the aggregate traffic rather than each flow individually. Aggregate traffic measurements are both scalable and easy to implement.

The above requirements define a family of AC algorithms:

• the required descriptors are as simple as possible, • as few assumptions on the traffic as possible, • should not rely on per flow traffic measurements, • the tuning parameters should reflect and control QoS directly.

In addition the algorithm should be easy to implement and closed form solutions are preferred even if they are suboptimal.

In this paper we develop three MBAC algorithms with different types of flow descriptors and measured parameters, each fulfilling the above requirements. The first is based on our improvement of the Hoeffding bound and uses admitted peak rates and measured average rate (Section 2). The second measures the variance as well and gives a tighter bound. (Section 3). The third algorithm utilizes a leaky bucket traffic descriptor per flow and gives bounds for guaranteeing maximum delay (Section 4). Conclusions are given in Section 5.

2 A TIGHTER BOUND FOR MBAC - FOPT

One very simple member of the family was already proposed for MBAC by Sally Floyd [Fl096]. It uses the Hoeffding bound requiring to admit only the peak rates of the entering flows. For a supplementary parameter the mean of

Measurement-based admission control algorithms 155

the aggregate traffic rate is measured. The theoretical basis of the bound is the concept of effective bandwidth [KeI96]. In this section we give a tighter effective bandwidth using the same information.

2.1 An tighter bound on the effective bandwidth

We use the following expression for the effective bandwidth of the aggregate traffic

N

BW(s) = L.Bk(S) + '1. S

k=l

where (1)

hk and mk are the peak and mean rates of flow k respectively, 'Y = - In (€), and € is the saturation probability (see [KeI96, GibKeI97]). In this expression we need information for the individual values of mk, in other words we need per flow measurements. Fortunately the average of individual flows sums up so if we can find a bound where only the sum of the measurements is present then only aggregate average measurement is needed. We bound the effective bandwidth of each flow in the form .Bk (s) ~ 8k (s) = fmk + Ck (s) where f must be the same for all flows and Ck depends only on s or hk but not mk. With this approximation the expression of the effective bandwidth of the aggregate traffic fulfils this requirement:

N N

BW(s) ~ BW(s,J) = {Lmk + 2:>k(S) + ~ k=l k=l

(2)

.Bk (s) is a concave function of mk so its tangent of slope f is an upper bound. The special choice of f = 1 leads to the Hoeffding bound, details can be found in [GibKeI97, Fl096]. The tangent of slope f is the following:

(3)

For the particular traffic mix on figure 1 the optimal choice is around f ~ 1.4 and at this point it is significantly less than what we get using the Hoeffding bound (J = 1). The question is how to find the optimal slope for a certain traffic mix with parameters hk and mk. BW(s, J) is convex in f and so the optimal f where it is minimal can be calculated by differentiating the sum of 8k (s) on f. Substituting this into BW(s,J) we get BWjopt(s).

N 1 fopt = - N ( h)

S L:k=l mk + eOh':_l


650

., ,g 500 F-----~ ..... ~ w

450

400 '--_---'---_---'-__ --L---'------'--_---:--'=-::-_--:-' 0.50 0.75 1.00 1.25 1.50 1.75 2.00

Slope of tangent (f)

Figure 1 BW(s, f) as a function of f, 100 sources mk = 2, hk = 10 Mbit/s, s = 0.2, 'Y = 12.

N [""N . ""N ~ h 1 _ 1 "" ~j=l m J + ~j=l ~i eS k - 1 'Y BW/opt(s)--L..,.ln N . h +-

S k S k=l

Notice that we need the average of the aggregate traffic only. The peak-tomean ratio influences fopt. If the traffic is biased towards high or low peakto-mean ratios then this optimal choice of f will largely differ from 1.

2.2 Finding an optimal value for s

In this section we give a closed form solution for s. For obtaining an estimation of the optimal s we approximate BW/opt(s) using Taylor series and differentiate in s.

( )2) N IN 211 N 1 N 'Y BW (s) = "" m . + - "" h· - - . - ("" m' - - . "" h· . s + -appro:!! L..,. J 8 L..,. J 2 N L..,. J 2 L..,. J S

j=l j=l j=l j=l

Sopt = 'Y

In an implementation first we calculate Sopt to get an estimate for optimal s and substitue it to BW/opt(s). Then we admit the new flow if there is enough capacity between BW and the link rate C. In figure 2 we can see a typical BW/opt and its approximation as an example.


800

700

i .800 J>

.~

~ 500

<00

/ /

- BWlopl - - - BW approx

3000.':-0 --0:':.2~----:"0."--< --:0:'7.6---:':0.6:------:',.0

Figure 2 BW!opt and BWapprox as a function of s, 100 sources mk = 2, hk = 10 Mbit/s.

! 0.95

~ j 0.90

!!>

:i 0.85

i ~ 0.60

10 mean

Figure 3 The ratio of the margins Hoeffding and !opt methods add to the mean as a function of the mean. 100 sources, hk = 10 Mbit/s.

If we want to compare our bound with the Hoeffding bound it is clear that the greatest difference arises when! is far from 1. This is only the question of the traffic mix. On figure 3 it is visible that for small or large peak-to-mean ratios the gain can be in the range of 5-15%. Large peak-to-mean ratios mean bursty traffic or loosely fitted descriptors; these are the situations where this MBAC has its strength over traditional AC algorithms and algorithms based on the Hoeffding bound.

3 MBAC USING MEASUREMENT OF THE VARIANCE

So far we used only the measured aggregate mean and the admitted peak rate of the flows. Theoretically the more infomation we have about the distribution of Xks the tighter bound can be given. In this section we give a closed form effective bandwidth formula with an extra parameter which is the measured variance of the aggregate traffic rate. The validity of this bound does not depend on the number of flows unlike bounds based on the Central-limit theorem [GAN9I]. The variance - similarly to the mean - sums up, so an expression with the sum of the variances of the flows can be replaced with the variance of the rate of the aggregate traffic.

The bound (1) containing only the mean and the peak rates (!Jk(S)) is the same as if we assumed on/off sources [GibKeI97]. On/off sources have the worst possible variance for a given peak and mean rate and apparently a large part of the real-life traffic will not be on/off, so a measurement on the variance may lead to a tighter bound.

First rewrite (}:k(S) as (for definition of (}:k(S) see [KeI96]):


(4)

for hk ~ mk, X k ~ O. Using the above formula the effective bandwidth is smaller than

Here we have both the mean and the variance in the expression. Following the logic of the calculations in the previous section we can obtain the aggregate effective bandwidth and the corresponding optimal s as

svar _ opt -

See figure 4 for an example how (7 influences the effective bandwidth. As we can see the closed form approximation we use to obtain s~;[ is not very good for small (7 values. For small variances numerical optimization should be used.

Another effective bandwidth estimation is used in the literature based on the normal distribution [GAN9l, GroTse97]. They assume that the aggregate traffic rate can be approximated with the normal distribution and so the effective bandwidth is given as BW ~ m + (7-/2,,{ -ln27r, where m is the average and (72 is the variance of the aggregate traffic rate. ~

This expression uses the same information as Bwvar, but BW is only an approximation while Bwvar is an upper bound. Also unlike Bwvar , BW assumes normal distribution (number of flows is large) which reduces robustness.

4 MBAC WITH LEAKY BUCKET

In the previous sections we investigated the bufferless case. Now we analyze a buffered system. If the sources are able to provide more information than the peak rate such as a leaky bucket, we can do more efficient admission control.

Denote Xk[t], k = 1 ... N the number of bits sent by flow k into the network

Measurement-based admission control algorithms

\ \ \ \ \ \ \

--- BWvar (closed lonn) - BWvar (numerical optimization) - - - BW using nonnal distribution - Hoeffding bound

\

' ...................... . ."".,.,.,,..

~~

°O~~~10--~-2~O--~~~--~~~----~50

std. dev. 01 aggregate traffic rate [Mbills]

159

Figure 4 The effective bandwidth - mean calculated using Hoeffding bound, normal distribution and BWtlor as the function of the aggregate u. 100 sources, hk = 10 Mbitfs, f = 10-5 .

during a time interval of length t. IT flow k is controlled by a leaky bucket policer, we can give an upper bound on the maximum number of bits entering the network during any time interval of length t: 0 ~ Xk[tj ~ Uk + Pkt, or if a peak rate is given as well: 0 ::; Xk[t] ::; min(hkt, Uk + Pkt).

4.1 Effective bandwidth for leaky bucket policed sources

IT we assume that Xk[tj are independent and stationary random variables then we can give a very simple bound for the probability that the aggregate traffic exceeds a certain number of bits B entering during a time interval of length t, i.e. Pr (~Xk[tj ~ B) ~ f.

Using the Chernoff bound the effective bandwidth for f can be written as:

",,1 'Y BW(s,t) = L.J -Ok(S,t) +-

t ts where

Ok(S, t) relates to the number of bits sent by flow k to the network [Ke196]. We do not know the probability distribution of Xk[tj but we know that it

is limited by the leaky bucket and we can measure the average number of bits entering the network during time t (E mkt). Considering that

if


O(s, t) can be bounded as

Note that a similar line of reasoning led to (1). The requirement for aggregate mean rate measurement suggests to bound

the effective bandwidth with a slope f linear function of mk. For simplicity we write the final effective bandwidth of the aggregate traffic for f = 1 which leads to a form of the Hoeffding bound:

or if the peak rate is available as well:

~ L min(hkt, Uk + Pkt)2 k

(5)

(6)

The value of t is the length of the interval over which the amount of incoming load is bounded. Furthermore t also gives the interval over which we limit the peak rate of the flows and measure the average rate.

If t is small, the effective bandwidth depends only on the admitted peak rates and we get back the original Hoeffding bound using only the peak rates. On the other hand a larger t leads to smaller effective bandwidth as the averaging interval is longer.

4.2 Guaranteeing maximum delay

As we have a buffered system we may allow larger bursts into the network and temporarily the link rate can be exceeded. A certain choice of t limits the maximum amount of bits to be accumulated in the buffer and so the maximum buffering delay. In the next sections we give three admission control methods that build on the concept of BW(t) and statisfy a certain maximum delay requirement dmaz with probability f.

(a) Method 1 This very simple method is applicable to both cases when we have or do not have information on the peak rate (BW1 (t) and BW2 (t)). We try to control the delay by limiting the length of the busy periods. Let C be the link rate. If the length of a busy period (during which the server is continuously busy) is longer than t then during the first t seconds of the busy period more than Ct


bits arrived. Thus if the arriving number of bits during any time interval of length t is smaller than Ct then all busy periods are shorter than t seconds. In other words the length of the busy periods is bounded by t with probability f

if BW(t)t :s; Ct. If the length of the busy periods are bounded by dma:z: then the maximum delay is also bounded by dma:z:, thus the guarantee is met if:

BW(dma:z:) :s; C. (7)

On figure 6 we can observe that under a certain delay limit the peak rate is in effect and the number of admitted flows is much higher than if only the leaky bucket descriptor were available. If we know the peak the result is identical with the bufferless case for low delays. However if the allowed maximum delay is larger then the number of admitted flows increases significantly and the statistical multiplexing gain is larger than in the bufferless case.

(b) Method 2 In methods 2 and 3 we control the delay without limiting the length of the busy period. Method 2 applies if we do not have information on the peak rate (we use BW1 (t». The link can carry at most Ct bytes during time t. During a busy jeriod t seconds after the start of the busy period the buffer occupancy is Ek=l Xk[t] - Ct. The buffer occupancy cannot exceed Cdma:z: to guarantee the delay limit so if within all busy periods and for all t

(8)

then the buffer overflow probability will not exceed f. If we find the maximum of b1(t) in t, we can decide whether the flows fit into the link or not. It can be shown that b1 (t) is a convex function of t. If limt-too b~ (t) < 0 (eq. 9) then its supremum is at t --+ O. If limt-to b1(t) < Cdma:z: as well (eq. 10) then the buffer occupancy will always be under Cdma:z:. The above conditions can be written as:

N

Lmk+ k=l

N

~ L u~ < Cdma:z:. k=l

(9)

(to)

Thus we separate the meaning of the leaky bucket parameters. Pk is used to determine if the link can carry our traffic on the long run as a kind of an asympthotic test, and Uk controls the delay. The AC algorithm is very simple, it just checks (9) and (10), and if both pass then the new connection can be


--- Method 2 (Ioaky buclcot only) - Method 3 Oaaky bucIcot _ peak)

,[rna]

Figure 5 b1,2 (t) for a particular traffic mix. The traffic mix contains two kinds of sources 2300 and 200 from each type respectively: h = 1,7; U = 0.02,0.1; P = 0.5,1.5; m = 0.3,1; 'Y = 12; C = 1000 in Mbit.

Figure 6 The number of admitted flows as a function of the delay requirement. The sources are identical hk = 5 Mbit/s, Uk = 0.1 Mbit, Pk = 1 Mbit/s, mk = 0.5 Mbit/s. 'Y = 12, C = 1 Gbit/s.

admitted. We can observe some similarities between (9) and the Hoeffding bound. See figure 5 for an example of b1,2(t).

(c) Method 3 IT we have information about the peak rate of the flows as well, we can give a tighter bound than (10). The problem is that b2 (t) = (BW2 (t) - C)t is not a convex function. We must look for its maximum and see if it is under Cdmaz • We partition the domain of the function into intervals by points tk = uk/(hk - Pk). We call these breakpoints. This way within each interval for any flow either hkt or Uk + Pkt is greater. Within one interval we can write an expression for ~(t) that does not contain the min operator. We define two sets, those flows belong to set A where hkt < Uk + Pkt within that interval, and those belong to set B where it is the other way. Then in that interval

It can be shown that this is a convex expression. Thus within an interval b2 (t) is always below the value at one of the two breakpoints. So b2 (t) takes its global supremum value either

1. at t = 0 (then the supremum is 0) or 2. at one of the breakpoints or 3. it has no supremum, it diverges to positive infinity after the last breakpoint.


After the last breakpoints b2 ( t) = b1 (t), so item 3 can be checked as before in (9). By checking b2(tk) < Cdmax for all k = 1 ... N we can decide if b2(t) < Cdmax for t > O.

On figure 5 some properties of ~(t) can be observed. b2 (t) ~ b1 (t) especially for small t values. In this case the supremum is not necessarily in t = 0 (as in the case of b1 (t)) but in a breakpoint instead.

Checking the value of b2 (t) in several breakpoints may be computationally expensive. The number of breakpoints is not greater than the number of different descriptors, so if several flows share common descriptors then calculation takes less time. On the other hand one class of flows can have several leaky bucket descriptors for several timescales giving a more detailed traffic description [ZhaKni94]. For example the ATM VBR descriptors (PCR,CDVT) and (SCR,MBS) are one example of such a multilevel descriptor.

On figure 6 we plotted how many identical flows can be admitted using the various methods. One can observe that supplying peak rate besides a leaky bucket improves the utilization considerably. It can be seen that a deterministic guarantee [PaGa93] is much worse as it does not exploit statistical multiplexing gain.

5 CONCLUSION

A set of requirements for efficient admission control algorithms was given. These requirements define a family of measurement-based admission control algorithms of which we worked out a few representative members. These MBAC algorithms differ in the set of information required from the sources upon flow setup and in the measurements performed on the multiplexed traffic. The algorithms are based on the Chernoff-bound with direct QoS metrics such as loss and delay as tuning parameters. In sections 2 and 3 we used a model which does not give explicit guarantees on delay. These algorithms can offer a Controlled Load Service. In section 4 we used a buffered model and gave probabilistic delay bounds. This method can be applied for the IETF Guaranteed Service.

In all methods we assume only FIFO buffering discipline so there is no need for expensive hardware with sophisticated scheduling algorithms. While the information of the admitted flows are stored for each flow, the per-packet work -the measurement- is done on the aggregate traffic making these methods scalable to tens of thousands of flows. To decrease the computational costs and delay of admission control decisions all bounds are expressed in closed form.

REFERENCES

[BriSim98] F. Brichet, A. Simonian, "Conservative Gaussian models applied


to Measurement-based Admission Control", submitted to IEEE INFOCOM '98, San Francisco, March. 1998

[CKT96] C. Casetti, J. Kurose, D. Towsley, "A New Algorithm for Measurement-based Admission Control in Integrated Services Packet Networks", emphProtocols for High Speed Networks '96, INRIA, Sophia Antipolis, Oct. 1996

[Flo96] S. Floyd, "Comments on Measurement-based Admissions Control for Controlled-Load Service", unpublished, available at ftp:/ /ftp.ee.lbl.gov/papers/admit.ps.Z

[GAN91] R. Guerin, H. Ahmadi, M. Naghshineh, "Equivalent capacity and its application to bandwidth allocation in high-spped networks" , IEEE Jurnal on Selected Areas in Communications, 9(7), pp. 968-981, Sep. 1991

[KeI96] F. P. Kelly, "Notes on Effective Bandwidths", In F. P. Kelly, S. Zachary and 1. B. Ziedins, Stochastic Networks: Theory and Applications, Royal Statistical Society, Lecture Note Series 4, p 141-168, Oxford Univ. Press

[GibKeI97] R. J. Gibbens, F. P. Kelly, "Measurement-Based Connection Admission Control", International Teletraffic Congress 15, Jun. 1997

[GroTse97] M. Grossglauser, D. Tse, "Towards a Framework for Robust Measurement-based Admission Control", SIGCOM '97, Cannes, September 1997.

[JamShe97) S. Jamin, S. Shenker, "Measurement-based Admission Control Algorithms for Controlled-load Service: A Structural Examination", Internal report, Apr. 1997

[JDSZ97] S. Jamin, P. Danzig, J. Shenker, L. Zhang, "A Measurement-Based Admission Control Algorithm for Integrated Service Packet Networks", IEEE/ACM Transactions on Networking, vol. 5. no. 1. Feb. 1997

[JJB97] S. Jamin, C. Jin, L. Breslau, "A Measurement Based Admission Control Algorithm for Controlled-Load Service with a Reference Implementation Framework", Internet draft, Nov. 1997

[KniZha95] E. Knightly, H. Zhang, "Traffic Characterization and Switch Utilization using a Deterministic Bounding Interval Dependent Traffic Model", in Proc. IEEE INFOCOM '95, Boston, April 1995

[ZhaKni94] H. Zhang, E. Knightly, "Providing end-to-end statistical performance guarantee with bounding interval dependent stochastic models" , Proc. ACM SIGMETRICS '94, pp. 211-220.

[KWC93] G. Kesidis, J. Walrand, C. Chang, "Effective Bandwidths for Multiclass Markov Fluids and Other ATM Sources", IEEE Trans. Networking, Vol. 1, No.4, pp. 424-428, Aug. 1993.

[PaGa93) A. Parekh, R. Gallager, "A generalized processor sharing approach to flow control in integrates services networks: The multiple node case" , Proc. INFOCOM'93, San Francisco, CA, Mar. 1993.

13 Resource reservation in a connectionless network

A. Eriksson Ericsson Telecom Dialoggatan 1, S-126 25 Stockholm, Sweden

phone: +46-8-719 2253, fax: +46-8-7196677 e-mail: [email protected]

Abstract This paper describes a new signalling protocol that supports resource reservation for unicast traffic in a packet network. The key feature of the protocol is that resources can be reserved on a per connection basis without introducing connection states in the network. This is accomplished by the combination of connection state handling in the hosts and link state handling in the network. The handling of link states rather than connection states allows for a connectionless mode of operation in the network, which is attractive from a complexity and scalability point of view.

Keywords Resource reservation, connectionless, Internet, Quality of Service, scalability

Performance of Information and Communication Systems U. Komer & A. Nilsson (Eds.) © 1998 !FIP. Published by Chapman & Hall


1 INTRODUCTION

The Internet Engineering Task Force is standardizing the Resource Reservation Protocol RSVP (Braden et al. 1994 and 1997). This protocol introduces connection states into the previously connectionless Internet. These states are used to store information in the network nodes about bandwidth, buffer parameters, identity and status on a per connection basis. However, the simplicity of the connectionless architecture is perceived as one of the key features of the Internet. The introduction of a connection-oriented protocol, such as RSVP, may lead to poor scalability properties. Possibly a complexity of the same magnitude as for the connection handling functions of a traditional telephony exchange must be added to an IP router that supports resource reservation.

One important objective for RSVP is the support of multicast applications where each user is able to make a separate resource reservation. Moreover, RSVP is designed to support bearer service classes with a tight control of transi t delay and delay variation. These objectives necessitate a connection-oriented network.

The Ticket Protocol described in this paper is based on the assumption that the major part of the real-time traffic is generated by either two-party calls, or multi-party calls with only a small number of parties. For these cases unicast connections are sufficient. As long as the number of parties is small, the multi-party calls can be supported by a mesh of unicast connections. These assumptions imply that the network should be optimized for unicast connections. Multicast real-time traffic can then be supported by an overlay network of RSVP multicast routers which are interconnected by means of tunnels over the underlying unicast network.

The Ticket Protocol is also based on the assumption that absolute guarantees on the maximum network latency are not needed for most real-time applications. Interactive applications such as telephony and video conferencing do not require a firm upper bound on the delay, but rather a service that, with rare exceptions, offers a small delay.

The objectives for the Ticket Protocol are certainly more relaxed than for RSVP. As a result, the Ticket Protocol can operate over a connectionless network as described in this paper. The connectionless mode of operation is a major simplification compared to the connection-oriented RSVP. However, this simplification also implies some limitations, for example with regard to routing, packet scheduling and policing. These limitations will also be described in the paper.

Resource reservation in a connectionless network 167

2 DESCRIPTION OF THE TICKET PROTOCOL

2.1 Overview

The TIcket Protocol addresses the problem of offering traffic contracts with a QoS better than best-effort over a wide area connectionless network. Since no connection identities can be stored in a connectionless network, the service differentiation is based on the use of priority bits in the IP header. However, in a public connectionless network, there is a problem of controlling the amount of traffic using the high priority levels. Possibly everyone could be using the highest priority, resulting in no improvement compared to the best-effort service. To avoid this problem, the usage of the high priority levels must be controlled by the network. By limiting the aggregate bandwidth of the high priority traffic to a fraction of the total bandwidth on every link, a controlled QoS can be achieved.

Before a connection can use a specific priority level and bandwidth, a traffic contract is set up. This is done by means of a resource reservation request from the user that must pass admission control in the network. Traditionally the handling of the admission control and the traffic contract would be based on connection states in the network. However, it is desirable to retain the simplicity of a connectionless network. This is achieved according to the following description of the TIcket Protocol.

When initiating a unicast connection with a controlled QoS, the source sends a message to the network with a request for a specific traffic contract, i.e. a permission for a specific source to use a specific priority level with a specific bandwidth to a specific destination during a specific time. This request message is routed across the network and is subject to admission control at every router and its associated output link, see Figure 1. If the admission control is successful, the request will reach the destination host; otherwise it will be dropped. The destination host returns the request to the access router at the source. The access router recognizes that the request for a traffic contract has passed the admission control successfully, and translates it into a so called ticket message, which is sent to the source. This message contains all data about the traffic contract.

Since there may be an incentive for the user to forge the ticket message in order to get access to more bandwidth or a higher priority level than admitted in the traffic contract, the information in the ticket message is protected by the network with a digital signature. The mechanism described in (Atkinson, 1995) and (Braden et al. June 1994) can be used for this purpose.

The sender periodically transmits the ticket message to the network by inserting it in the user data packet flow. The ticket message follows the same end-to-end path across the network as the user data. The network can thus use the ticket message to extract all the information that is needed about the traffic contract of the connection (e.g. bandwidth, priority level, QoS parameters, time of expiry). Therefore, the network does not have to store a copy of the traffic contract and can operate in a connectionless mode.


Admission Control

/ REO-N= REQ-U + signature

User Data + .~~ __ ...... .:.. ___ +-__ Tickets

Polic ng

r---------~~_REL ____ ~----------~

A

AR R REL REQ-N REQ-U

Internet

Access Router Any other router Release Reservation Network Reservation Request User Reservation Request

Figure 1 Overview of the Ticket Protocol signalling messages.

The network uses the information in the periodically recurring ticket messages to calculate the aggregate amount of resources that have been reserved per priority level and per link. This information is used by the admission control when deciding if a new resource reservation request should be accepted or rejected. The calculation of the aggregate amount of reserved resources requires link states, but not connection states.

The information in the ticket message is also used when specific connections are policed. For example, connections that are using a specific priority level and bandwidth without including a ticket message with a permission to use these resources should be dropped at the edge of the network.

Policing requires that a network state machine is set up for the policed connection. If policing is done on a sample basis, the number of state machines will be small. However, if policing of all connections is desired, the edge router must have a state machine per connection. The edge router then uses the Ticket Protocol in a connection-oriented mode, see section 2.5, while the core network uses the Ticket Protocol in a connectionless mode.


2.2 Detailed Description of the Ticket Protocol

Functionality The Ticket Protocol is used for signalling between the user and the access node as well as for signalling between network nodes. This means that it supports the same type of functions as RSVP or ATM UNIINNI signalling, that is:

• set up of a traffic contract between user and network for a specific connection; • request for and reservation of end-to-end network resources for a specific

connection; • admission control; • providing information from the user to the network for routing, policing and

charging; release of the resource reservation.

Operation The operation of the Ticket Protocol is described below. The numbers in the text below are references to specific signals or events in Figure 2, which is an elaboration of Figure 1.

The user sends a REQ-U message to the network with a request for reservation of network resources for a connection with a specific bandwidth, priority level and destination.

2 The access node translates the REQ-U message to a REQ-N message by adding a time of expiry parameter and a digital signature. The time of expiry is needed because the reservation is always made for a limited time interval Tt

with a length in the order of seconds. The digital signature is used to protect the REQ-N message from being changed by the receiving user when it is looped back to the sender.

3 The REQ-N message is routed across the network based on the destination address and priority level in the IP header. Every router along the end-to-end path performs an admission control on the outgoing link based on the information in the REQ-N message. If the requested bandwidth and priority level can be supported by the link, then resources for the connection are reserved on the link for a time period ofTt, and the REQ-N message is forwarded along the link to the next router. If resources are not available on a specific link, the admission request is rejected and the REQ-N message is discarded.

4 If the admission control is successful on all links along the path, the REQ-N message will arrive at the destination host, which will loop it back to the sender unchanged, except for the addition of an acknowledge information element. In case the receiver is not interested in a connection, there is also an option not to return the acknowledgement.


5 When the looped back message, ACK(REQ-N), reaches the access router serving the sender, the digital signature and the time of expiry are checked. If they are correct, the ACK(REQ-N) is translated to a ticket message, which is transferred to the sending host. The ticket message is protected by the network by a digital signature, so that the sending user shall not be able to code a larger bandwidth or a higher priority level than admitted by the network.

6 The ticket message is inserted in the user packet flow, and is routed along the same path as the user data across the network. It is either inserted in every user data packet, or sent as a separate packet with a period of Tt •

7 The access router checks the digital signature and the time of expiry. The access router may also use the information in the ticket message for policing of the corresponding user connection.

8 The receiver acknowledges the ticket message in the same way as the REQ-N message.

9 When the access router receives the ACK(Ticket) message, a new ticket message is issued every period Tt by the access router with a new time of expiry, which is the value of the current time of expiry parameter plus Tt• The digital signature is recalculated taking the new time of expiry into account.

By the cyclic renewal of the ticket based on the acknowledgement of the old ticket from the receiver, a ticket loop is formed. By means of this ticket loop, network resources are reserved, even if user data are temporarily not sent. The ticket loop thus supports a per connection reservation of network resources, even though all per connection states are kept in the hosts. By inspection of the signal flow it can be confinned that the network states are related to the aggregate reserved bandwidth per priority level and per link, and that there are no per connection states in the network.

Please note the two-fold function of the ticket message in Figure 2. A ticket message valid for a time period T1 - T2 is used both to prove that access has been admitted for that period, and also to reserve resources for the next time period T2 - T3.

The ticket message is used by the routers along the path as a source of information about the parameters of a connection, such as bandwidth, token bucket rate, source, destination and priority level. The network nodes thus do not need to maintain states for every connection, thereby being able to operate in a connectionless mode. However, also a connection-oriented mode of operation can be supported, see section 2.5.

When the sender or receiver wishes to terminate the reservation, they can do so by discarding the ticket message. The ticket loop is then broken, and no new tickets are issued. Due to the termination of the ticket loop for a connection, the links along the path of the connection will calculate a decrease in the reserved bandwidth, and thus they will have more bandwidth available for new resource reservations.

Old tickets cannot be reused due to the time of expiry parameter. Resources for a new connection can only be reserved by issuing a new REQ-U message.

T1

time


Admission

REQ-U ... -.t:landwidth

priority level des!. address

2 Control y.

REQ-N = REO-U + signature

A

AR R REQ-N REQ-U

X • Figure 2

REQ-N __ .... ~

TICKET 1 ACK(REO-N) .. II .. ' II II II "' II II II II "" II

I"'valid until Tl valid TO - T1 reserve n -T2

TICKET 2 valid n -T2 reserve T2 - T3

TICKET 3 valid T2 - T3 reserve T3 - T 4

Internet

Access Router Any other router Network Reservation Request User Reservation Request issue of the next ticket reservation for the next time slot

TICKET 1 __ o6l

II II II •• 1, ..... 11 II II. II"

TICKET 2. __ o6J • II II II •••• II ,II II II II' II

Signal diagram for the Ticket Protocol.


The ticket loop When performing admission control, the aggregate reserved bandwidth for all connections with a specific priority level on a link is calculated during each consecutive time interval Tt. This is done by addition of the relevant parameters in the ticket messages of the active connections. The ticket message must therefore be sent with a period Tt. Also, in order to avoid that a ticket message is used repeatedly, it must be valid only for one period. The time of expiry parameter in the ticket message must thus be renewed with a period of Tt. The renewal is done by the access router.

If a user fails to send a ticket message during a time interval, then the ticket loop is broken and the reservation is released. The reason is that a missing ticket message for a connection means that the admission control function cannot take the bandwidth of that connection into account, and may grant this bandwidth to an other connection making a reservation request. The sender can check that the ticket loop is not broken by monitoring that a new ticket message for the subsequent time interval is received from the access node. If no new ticket message is received by the sender within a time interval T « Tt after sending the previous one, then the previous ticket message must be resent to request a new ticket.

However, what happens if a ticket message is lost half-way along the path? When retransmitting a ticket message, some nodes will count this message twice. This shows that the estimate of the aggregate reserved resources cannot be based only on the ticket messages. Also the REQ message and the message for the release of reservations must be taken into account. Moreover, the estimate can be improved by measurement of the high priority traffic on the link, see chapter 2.3.

Release of reservations Reservations can be released by stopping sending tickets. The ticket loop will then be broken, and the estimate of reserved bandwidth made along the path of the connection will be decreased by an amount corresponding to the bandwidth of the released reservation. This will be true either if the bandwidth estimate is based on addition of the bandwidth in the ticket messages, or if it is based on the measurement of the aggregate high-priority traffic. In the first case the decrease of the bandwidth estimate will be done within a time period Tt , while in the second case it will take a longer time, since the measurement based estimation requires averaging.

The time of the reservations release can be decreased by means of an explicit release message issued by the sender when the ticket loop is broken.

2.3 Admission control

Admission control is performed link by link based on the information in the REQ message. The admission control procedure takes the bandwidth, token bucket parameters and priority level in the REQ message into account and makes an assessment whether resources can be reserved for the requested new connection while still ful-


filling the service contracts for the already admitted connections. This is done by each router on the outgoing link, and a ticket is only issued if the REQ message passes the admission control on all links along the path.

In order to determine if a new connection with a specific priority level can be admitted on a link, the aggregate resources already reserved for the connections using that priority level must be estimated. In a connection-oriented network, the aggregate resources would simply be calculated by summation of the connection parameters stored in the network. In a connectionless network there are by definition no such parameters stored in the network. Therefore the following methods can be used:

• The aggregate reserved resources for a priority level are estimated by summation of the bandwidth and token bucket parameters obtained from the ticket messages for each connection on the link.

• The aggregate reserved resources for each priority level are estimated by measurement of the traffic on the link (Jamin et al. 1997).

The first method gives a more accurate estimate of the reserved resources, since explicit connection parameters, such as peak bit rate, are available in the ticket messages. However, these messages may get lost in the network, and the second method could therefore be useful as a complement.

2.4 Policing

The policing function checks that a connection adheres to the traffic contract in the ticket message. Also, the integrity of this message is checked by means of the digital signature.

In order to police all connections continuously, state information such as token bucket parameters must be installed for every connection in the access node. This means that the access node would operate in a connection-oriented manner. If a fully connectionless network is preferred, then the policing must be done on a sample basis, i.e. a fraction of the connections are picked out for policing. The criterion for picking out a connection for policing could be pretty much the same as in an ordinary customs check, i.e. on a random basis or when an anomaly is detected.

2.5 Connection-oriented operation

The Ticket Protocol can be used in a network where some subnets are connectionless, and some are connection-oriented. The ticket message contains the complete traffic contract, including bandwidth parameters, priority level, time of expiry and destination address. This information is sufficient to set up connection states.


2.6 Handling of the Controlled-Load service

To achieve QoS differentiation. the Ticket Protocol relies on the use of priority bits in the IP header. The content of the header is the only available infonnation when scheduling packets in a connectionless network. Scheduling mechanisms that rely on additional infonnation. such as weighted fair queueing. can not be used on a per connection basis in a connectionless network. As a consequence. priority scheduling must be used in a Ticket Protocol network.

The network latency and packet loss rate provided by a simple priority scheduling mechanism depends strongly on the load of the high priority traffic. The definition of the Controlled-Load service specified by the IETF (Wroclawski. 1997) can be fulfilled if this load is kept below a certain level. The admission control mechanism and the policing mechanism must therefore limit the load of the high priority traffic below this level.

3 QUALITY OF SERVICE AND TYPE OF SERVICE ROUTING

The Ticket Protocol is able to support connectionless operation as well as connection-oriented. These two modes of operation are handled very differently from a routing point of view.

3.1 QoS routing in a connection-oriented network

In a connection-oriented network. each connection can be routed separately based on parameters signalled at connection setup. such as bandwidth and delay requirements. The load conditions of the network are also taken into account when making the routing decision. The QoS for the connection as well as the network utilization can thus be optimized. For example. if a link along the primary path selected by the routing protocol is congested. the routing protocol can select an alternate path. This reduces the blocking probability and improves the network utilization.

3.2 Type of Service routing in a connectionless network

In a connectionless best-effort network. the routing is nonnally only based on the destination address. In order to support an improved QoS. additional infonnation such as the 1Ype of Service (ToS) bits in the IPv4 packet header can also be used. These four bits are used to infonn the routing protocol that the routing decision should optimize either for low delay. high bandwidth. high reliability. or low monetary cost (Almquist. 1992).

For parallel packet flows with identical source and destination addresses. only the ToS and precedence bits can be used to differentiate the routing in a connectionless network. As a consequence. the routing protocol cannot select an alternate path if a


link along the primary path cannot support the requested bandwidth and QoS. In this case a reservation request must be rejected by the admission control mechanism. This will limit the performance of the Ticket Protocol when used in combination with ToS routing in a connectionless network.

3.3 Handling of route changes

The routing tables are updated quite frequently, for example due to routine traffic management procedures, a change in the network topology, or a link failure.

In a connectionless network, a router immediately reroutes all the traffic related to a specific entry in the routing table when that entry is updated. This works for besteffort traffic but is not allowed for already established connections with reserved resources, which first must pass an admission control along the new path. Therefore a mechanism must be introduced to prevent this immediate rerouting of traffic with reserved resources. The following mechanism is proposed.

Prior to the replacement of an output link in a ToS routing table, the ToS traffic on the link is stopped by discarding all tickets, thus breaking the ticket loop. Moreover, the priority bits in the rerouted packets are reset to a best-effort value, so that high priority connections are not rerouted along a new path, on which admission control has not been passed. The router which has made the rerouting continues to reset the priority bits until the ticket loop has been broken and the reservation thus has been released. The user is thereafter only allowed to send best-effort packets and must initiate a new reservation to obtain permission to send high priority packets.

The need for the user to initiate a new reservation after a path change is of course a limitation. However, this limitation exists also in most connection-oriented networks, e.g. the PSTN. If a failure occurs in the PSTN that requires updates of the routing tables, already established connections along a failing route must be re-established along a new route.

Re-establishment of the connection by the user may be sufficient if route changes are rare. However, if route changes are made several times per day, which is the case in some networks (Paxson, 1997), then a mechanism is needed to handle the route change without intervention by the user.

4 RELATED WORK

The Scalable Resource Reservation Protocol SRP (Almesberger, 1997) is designed to be independent of connection states in the network, as the Ticket Protocol. However, a major difference is that the TIcket Protocol passes the connection parameters to the network in explicit messages, while the connection parameters (e.g. bandwidth) are implied in the characteristics of the user data flow in the SRP. The availability of explicit connection parameters in the Ticket Protocol facilitates admission


control and the operation in a connection-oriented mode as an alternative to the connectionless mode. Moreover, the explicit connection parameters in combination with the digital signature facilitates policing.

5 CONCLUSION

A new resource reservation protocol, the so called Ticket Protocol, for the support of a controlled QoS over a connectionless network has been described. As shown in the paper, this can be achieved in a simplistic and scalable manner without the complexity of a connection-oriented network. Key features and limitations have been discussed.

6 REFERENCES

Almesberger, w.; Le Boudec, 1.; Ferrari T. (1997) Scalable Resource Reservation for the Internet, IEEE Protocols for Multimedia Systems: Multimedia Networking '97.

Almquist, P. (1992) Type of Service in the Internet Protocol Suite, IETF RFC 1349. Atkinson, R. (1995) Security Architecture for the Internet Protocol, IETF RFC 1825. Braden, R; Clark, D.; Schenker, S. (1994) Integrated Services in the Internet

Architecture: An Overview, IETF RFC 1633. Braden, R; Clark, D.; Crocker, S.; Huitema, C. (June 1994) Report of lAB

Workshop on Security in the Internet Architecture, IETF RFC 1636. Braden, R; Zhang, L.; Berson, S.; Herzog, S.; Jamin, S. (1997) Resource

Reservation Protocol (RSVP) - Functional Specification, IETF RFC 2205. Jamin, S.; Schenker, S.; Danzig, P. (1997) Comparison of Measurement-based

Admission Control Algorithms for Controlled-Load Service, INFOCOM'97. Paxson, V. (1997) End-to-End Routing Behaviour in the Internet, SIGCOMM'97. Wroclawski,1. (1997) Specification of the Controlled-Load Network Element

Service, IETF RFC 2211.

7 BIOGRAPHY

Anders Eriksson received his Master of Science degree in 1979 from the Royal Institute of Technology in Stockholm, Sweden. In the same year he joined Ellemtel AB to work on N-ISDN prototype development. In 1987 he joined Ericsson Telecom where he has been active in various areas, including ATM switching and IP routing. He is currently working on IP traffic management.

14 Buffer analysis of the explicit rate congestion control mechanism for the ABR service category in ATM Networks

C. Blondiat , O. Casal;, B. Van Houdtt t University of Antwerp, Dept. Math. and Computer Science Universiteitsplein, 1, B-2610 Antwe1p - Belgium, t Polytechnic, University of Catalunya, Computer Architecture Dept., Cj Gran Capitan, sjn Campus Norte, D6, E-08071 Barcelona - Spain, {blondia,vanhoudt}Guia.ua.ac.be, olgaGac.upc.es

Abstract In this paper we consider an ABR traffic stream which shares an output port of a switch with delay sensitive CBRjVBR traffic. Congestion control of the ABR traffic is achieved by means of an Explicit Rate congestion control scheme. The occupancy of the ABR-buffer in the switch is analytically evaluated. Application of the analysis on numerical examples illustrates the influence of the following system characteristics on the buffer occupation. From this study some guidelines and engineering rules are derived for the ABR service category in ATM networks.

Keywords ATM, Traffic Management, Congestion Control, Available Bit Rate, Explicit Rate Congestion Control

1 INTRODUCTION

In order to allow for different service types, each with their specific QUality of Service (QoS) requirements, the Asynchronous Transfer Mode (ATM) needs adequate traffic management mechanisms. For real-time service categories, such as CBR and rt-VBR traffic services, the network applies preventive open loop control mechanisms. CAC, UPCjNPC and Traffic Shaping belong to this class of traffic control mechanisms. Open loop control requires an adequate prediction and control of the traffic volume and its profile. This is achieved by means of a traffic contract established between the source and the network at call set-up. For data traffic services, such a prediction is difficult (if not impossible), and therefore open loop schemes are not efficient in this case, as

Performance of Infonnation and Communication Systems U. Komer & A. Nilsson (Eds.) @ 19981FIP. Published by Chapman & Hall


they may result in a considerable waste of network resources. For this class of traffic services, a closed loop control scheme seems to be more appropriate since it may use the remaining bandwidth more efficiently. Such a closed loop scheme dynamically regulates the cell rate of a connection based on feedback information from the network. For the ABR service class, there are strict QoS guarantees towards the Cell Loss Ratio (CLR), but no guarantees towards delay or delay variation. The network and the source may agree upon a Minimum Cell Rate (MCR) and a Peak Cell Rate (PCR). Between MCR and PCR, the network guarantees a low CLR, as long as the Source End Station (SES) adapts its cell rate to the feedback information received from the network. Since the notification process involves a round trip delay of twice the distance between SES and switch, the network has to provide large buffers in the switches to cope with the low cell loss guarantees in the presence of this notification delay. Within the ATM Forum ([1]), a number of congestion control mechanisms for the ABR service class have been proposed, which differ in the way the feedback is realized. The Binary Feedback Congestion Control mechanism and the Explicit Rate Congestion Control scheme are the most important ones. Although the ATM Forum traffic management specifications allow the older switches with binary feedback, the newer explicit rate switches will provide better performance and faster control. In this last class of schemes, switches compute the rate a source should use to emit cells, called Explicit Rate (ER), and this rate is communicated to the source by means of Resource Management (RM) cells. From this ER, the source determines the Allowed Cell Rate (ACR) according to an algorithm specified by the ATM Forum (see [1]). This rate always satisfies the relationship M C R ~ AC R ~ PC R. Several ways of computing the ER have been proposed; e.g. Enhanced Proportional Rate Control Algorithm (EPRCA), Explicit Rate Indication for Congestion Avoidance (ERICA) and the new version named "ERICA+", the Congestion Avoidance using Proportional Control (CAPC), etc ... (see [7, 8, 9, 2) ). Several authors have proposed analytical models to derive the throughput and buffer requirements for ABR traffic when switches with binary feedback are used (see [5, 6, 12, 13, 14, 18)). In this paper, we evaluate the required buffer space to guarantee a low cell loss (e.g. < 10-9) for the ABR traffic (see Figure 1). The switch used is based on the ERICA scheme ([8))), where the Allowed Cell Rate is updated on a periodical basis (every P timeslots). We consider two traffic sources, a CBR/VBR traffic source and an ABR traffic source, both connected to a switch. The CBR/VBR traffic source generates a variable bit rate traffic, modeled by means of a D-BMAP (see [3,4)), while for the ABR traffic source two cases are considered, namely a greedy (or persistent) ABR traffic source and an on/off ABR traffic source. The model takes the distance between ABR-SES and switch (27 timeslots) into account. We derive the queue length distribution of the ABR queue in the switch. Two different cases are considered, each involving a different approach for the analysis : 27 ~ P and 27 > P. In numerical examples, we investigate the influence

Explicit rate congestion control mechanism 179

of the following system characteristics on this performance measure: (i) the distance between the ABR source and the switch, (ii) the variability of the CBR/VBR traffic, (iii) the frequency by which the Allowed Cell Rate of the ABR source is updated, (iv) the burstiness of the ABR traffic.

2 THE QUEUEING MODEL

2.1 System Configuration

We evaluate the ABR buffer occupation in a system consisting of two end stations and a switch, a CBR/VBR SES and an ABR SES. Both the ABR and CBR/VBR traffic are input to the switch and are competing for the bandwidth of the same output port in the switch. The switch acts as a virtual destination station for the ABR traffic. The distance between the ABR-SES and the switch is T time slots, where a time slot is the time needed to process a cell in the switch (and chosen as time unit).

2.2 Source and Switch Behavior

a. CBR/VBR Traffic Model The CBR/VBR traffic is modeled by means of a discrete-time Batch Markovian Arrival Processes (D-BMAP), a generic traffic model for VBR traffic in ATM networks (see [3],[4]). In particular, the superposition of on/off processes, a model for VBR video traffic, belongs to this class. Consider M discrete-time on/off sources, with geometrically distributed on period (mean on period p time slots), geometrically distributed off period (mean off period q time slots) and a probability of I/d to generate a cell in a slot during the on period. The superposition of these on/off sources can be modeled as a D-BMAP with matrices D n , n ~ 0, where the matrix Do with elements (do);,j governs transitions without arrivals, while the matrices Dn with elements (dn)i,j, I ~ n ~ M, govern transitions that correspond to arrivals of batches of size n.

b. ABR Traffic Model We consider two cases : case A where the ABR source is a persisteni (or greedy) source, i.e. this source has always cells to transmit and will do so at maximal allowed cell rate, and case B where the ABR source is an on/off source. This on/off traffic is characterized by three parameters: the mean on period, the mean off period and the cell rate while in an on period. The rate at which cells can be transmitted is called the Allowed Cell Rate (ACR). The ACR varies between the Peak Cell Rate (PCR) and the Minimum Cell Rate


(MCR), both values being defined at call setup. Every P time slots, the ABRSES receives a notification of the new ACR to be used during the next P time slots from the switch by means of the value in the ER field in a backward RM cell. The interval P is called an observation period. It determines the time scale according to which the ACR adapts to the state of the network. We simplify the behavior of the SES as we let the ACR be completely determined by the ER, not taking into account additive increase and multiplicative decrease factors (see [1]). In case A, the ABR-SES generates traffic according to the allowed rate ACR, while in case B, the actual rate that is used depends on both the allowed rate ACR and the state of the ABR source.

c. Switch Behavior The behavior of the switch shows many similarities to the ERICA switch described in [71. During an observation period of P time slots, the switch counts the number of arrivals from both the CBRjVBR traffic source and from the ABR traffic source. Denote these numbers by Nc , resp. Na . The total input rate of the switch during this observation period is then i = (Nc + Na)j P cells per slot. Let the desired utilization of the output link of the switch be TCR (Target Cell Rate). Then the overload factor is given by 0 = ijTCR. The explicit rate communicated to the SES is given by r = min [PCR, max [MCR, Nao1P11 .. We let the range of possible rate values be discrete and chose the value closest to r. We assume that ABR traffic is guaranteed a service rate of at least MCR.

------------P----------------- 21:-----

nP nP+2 "t' (n+l)P SWITCH .

~r ,/:-," old ,/ I

r i,

-----l!'..

new \'\,

ACR \'.

new \'.\

ACR \'

ABR-SES , " , . '.

nP+'t

, . , . '.

(n+l)P+ 2't

(n+l)P+ "t

Figure 1 The interaction between Switch and ABR-SES, 2r ~ P

2.3 Buffer Occupation

The performance measure to be evaluated is the occupation of the ABR buffer in the switch. In particular we are interested in the 10-9 -quantile of the queue length distribution of the ABR traffic.


3 ANALYSIS OF THE QUEUEING MODEL

3.1 The Buffer Occupation in case 27::; P

(a) Evolution of the Process Figure 2 illustrates the interaction between the ABR-SES and the switch in case 2r ~ P. Observe that during an observation period of length P, two rates for the ABR traffic apply. Indeed, consider the interval [nP, (n+ 1)P[: Denote the rate during the interval [(n - 1)P + 2r, nP + 2r[ by TOld(n) and Tnew(n) the rate during the subinterval [nP + 2r, (n + 1)P[. Let us describe the system at the end of each observation period, i.e. at instances nP, n = 1,2,3, ... , by means of the following vector S(pc(n),Pa(n), TOld(n), Tnew(n)) = S(n), with

• Pc (n) is the phase of the CBR/VBR traffic at instant nPj • Pa(n) is the state of the ABR traffic source at instant nP - rj

• TOld(n) is the ACR computed by the switch at the end of the observation period [(n - 2)P, (n - 1)P[j

• Tnew(n) is the ACR computed by the switch at the end of the observation period [(n - 1)P, nP[j

We compute the transition S(n) ----t S(n + 1). Let S(n) = (io,io, f.J,o, vo). (i) First we compute the joint distribution of the number of CBR/VBR arrivals and the phase of this process. Denote Nc[to, tl] the number of CBR/VBR arrivals during the interval [to, tl [. Then it is possible to compute this probability directly from the matrices Dn, as P{pc(n + 1) = i l , Nc[nP, (n + 1)P] = l I pc(n) = i o}. (ii) (this step is only necessary in case B) Compute the joint distribution of the number of ABR arrivals and the state of the ABR source during an interval of length P: P{Pa(n + 1) = il, Na[nP, (n + 1)P] = k I Pa(n) = io}. (iii) Clearly Told(n + 1) = Tnew(n). (iv) Now we compute Tnew(n+ 1). We need to compute the number of ABR arrivals during [nP, (n + 1)P[. First we consider case A. As two ACRs apply, we compute the two corresponding components separately. During [nP, nP + 2r[ the rate Told(n) = f.J,o applies, hence the number of ABR arrivals during that period equals 2rf.J,o. Similarly, the number of ABR arrivals during the interval [nP + 2r, (n + 1)P[ is given by (P - 2r)vo. Hence, the total number of ABR arrivals is Na[nP, (n + 1)P] = L2rf.J,O + (P - 2r)voJ. In case B, the number of ABR arrivals is given by the computation in (ii). If there are Nc[nP, (n + 1)P] CBR/VBR arrivals (see (i)), then the new ACR is given by Tnew(n + 1) = min [peR, max [MeR, '"N:::;~ TeR]], with Ntot = Nc[nP, (n + 1)P] + Na[nP, (n + 1)P].


(b) Buffer Analysis From the above analysis, we know the number of ABR cells that have arrived at the ABR queue in the switch during an interval [nP, (n + I)P[. Let this number be denoted by Na . The CBRjVBR traffic has priority, i.e. is served first, but such that ABR traffic has a guaranteed service rate of MCR, i.e. of every P slots there are M C R x P slots reserved for ABR cells (if there are ABR cells available). Hence, if Nc cells of CBRjVBR traffic arrive during [nP, (n+ l)P[, and taking into account Remark 1, the number of slots available for serving ABR cells, is given by B = max [MCR x P, P - Nc]. Denote by Q(n) the queue length of the ABR buffer in the switch at instant nP. Then we can describe approximately the evolution of the queue length as follows: Q(n + 1) = max [0, Q(n) + Na - B]. The process Q(n) forms a Markov chain with the following transition matrix. Let Ci the matrix describing the transition of the variables (Pc, Pa, r old, r new) giving rise to a growth i in number of ABR cells during an observation period P. Clearly - P ::; i ::; L PC R x P J ::; P. The transition matrix is given by

I:~=-P C i C 1 C p 0 0 0

I:::-P C i Co Cp- 1 C p 0 0

p= C_p C-P+1 Co C 1 Cp-l Cp

Remark that P is finite, but for simplicity reasons the boundary matrices are ommitted. By grouping the matrices Cj in the appropriate way, a Quasi-BirthDeath (QBD) process is obtained, which can be solved by a classical algorithm e.g. the folding algorithm ([17]) or the logarithmic reduction algorithm ([IOD. In both algorithms a rate matrix R is needed, of which the calculation can be improved using the specific structure of P. The method is an extension of the matrix geometric algorithm introduced in [15] and can be found in [16].

3.2 The Buffer Occupation in case 27 > P and p < < P

(a) Evolution of the Process Now we consider the case where 27 > P, but with the additional assumption that the ON period of the CBRjVBR traffic is small with respect to the observation period. The interaction between the ABR-SES and the switch is illustrated in Figure 3. By choosing 27 a multiple of P, say 27 = L x P, we notice that the ACR during each observation period remains the same. The basic idea is to use L + 1 buffers for the ABR cells in stead of one. During the time intervals of the form ](27 + P)n + (i - l)P, (27 + P)n + iP[ we will use the ith buffer i.e. ABR cells that arrive during this interval will line up

Explicit rate congestion control mechanism

round trip delay

Observation period

-------•

nT+t (n+1LT+t

Figure 2 The interaction between Switch and ABR-SES, 2r > P

183

in the ith queue and only cells of the ith queue will depart during such an interval. Notice that the behavior of these L + 1 buffer is somewhat different compared to the single buffer. Still given that each buffer contains at least one element it behaves exactly the same i.e. when a cell arrives or departs for the global queue so does one cell in the system with L + 1 buffers. This allows us to believe that the tail of both distributions are very similar and it can be used when considering the cell loss ratio. To solve the system with L + 1 buffers we start by noticing that these L + 1 buffers all have an identical distribution and given that p « P they may be considered as independent. Thus once we have this unknown distribution the results are obtained by a simple convolution. This distribution is found by observing the system on the time instances n(2r+ P) by means of the following vector S(pc(n),Pa(n) , r(n)) = S(n) , where pc(n) resp. Pa(n) is the state of the D-BMAP used for modeling the CBR/VBR resp. ABR traffic at time n(P+2r) and r(n) is the ACR for the time intervalln(2r+P), n2r+(n+l)P[. The transition from S(n) = (io,jo,j.£o) to S(n + 1) is similar to 3.1.

(b) Buffer Analysis The method used to solve the system introduced in section 3.2.1 is very similar to the one in section 3.1.2 and we can use the same technique. Since the dimensions of the matrices Cj are reduced by a factor v, with v the number of discrete values used for the ACR, the computational effort now is smaller.

4 NUMERICAL EXAMPLES

4.1 Impact of the Burstiness and Observation Period Length on the Buffer Occupation

In what follows we investigate the impact the burstiness of the CBR/VBR traffic and the duration of the observation period P have on the ABR buffer occupation in the switch. In all the examples, by buffer occupation is meant


the number of places in the buffer needed to guarantee a CLR ~ 10-9 .

Example 1 : Consider the following system. The CBR/VBR traffic is modeled as a single ON/OFF source in order to better control its bursty nature. Let the ON period have a geometrically distributed duration with mean p and let the OFF period have the same distribution with mean q = 1.25 x p. While in the ON state, the CBR/VBR traffic source generates a cell in each slot. Hence, the CBR/VBR traffic generates a load of 0.44. Furthermore, we consider a greedy ABR traffic source with parameters TCR=0.9, PCR=0.9 and MCR=0.3. The range of discrete values of the ACR is [0.3 0.45 0.6 0.75 0.9]. We let the round trip delay be T = 1. We investigate the buffer occupation for variable mean ON period duration p and variable observation period length P .

f I .. I "

'" .. --.. ,

Figure 3 The buffer occupation as function of P and p, p ~ 16

..•...... .. " .....

.~~,--~--~--~ .. ~-7.--~--~ --Figure 4 The buffer occupation as function of P and p, p ~ 16

Figure 4 shows the impacts for mean ON periods smaller than 16 when P = 20. In this case the buffer occupation grows with the length of the ON period. As soon as the mean ON duration p is larger than 16 as shown in Figure 5, the buffer occupation as function of p shows a decreasing tendency. Note that 16 is about the same magnitude as the length of the observation period P. This observation is confirmed in Figure 6, where the buffer occupation is depicted as a function of the mean ON period duration p for different values of the observation period length P = 20,60,120. From this figure we conclude that the buffer occupation reaches a maximum for values of p around or just before the length of the observation period P. In Figure 7, we show how the buffer occupation reaches slowly a stable value (and slightly decreasing thereafter) when the observation period duration P is increased. Moreover, we see that the convergence is slower for higher burstiness of the CBR/VBR traffic source.


1'20 "

1,00 ! I .. '

, , ,

p",,,

~~~~~~.~~.~~'m~~~~~ co __

Figure 5 Maximal Buffer Occupation for P = 40, 80 and 120.

PO'

Figure 6 The Buffer Occupancy for High Values of P

4.2 Impact of the Burstiness and Round-Trip Delay on the Buffer Occupation

Let us now investigate the impact ofthe round-trip-delay 7, and the burstiness of CBR/VBR traffic on the ABR buffer occupation. Example 2 : 27 ~ P: We consider a system similar to the one in Example 1. The observation period length is chosen to be constant and equal to P = 20. The round trip delay 7 varies between 1 and P /2. Hence we apply the analysis of Section 3.1. Figure 8 illustrates the fact that from a certain value of the

~~~~~~~~~--~~--~--~~ ~alCSAMIA...a.

Figure 7 The Buffer Occupation as function of 7

... -......... ..

. ....... .

10 '1 IIInIIia aI the CBIWBR tr.II~

Figure 8 The Buffer Occupation as function of 7 and P

burst size of the CBR/VBR traffic, the buffer occupation remains constant (or even slightly decreases). From the figure it follows that this point is situated just before 20 + 2 x 7. This rule can be generalized as follows. In a system with observation period P and round trip delay 7, the buffer occupation remains constant for mean ON period values p ~ 2 x 7+P. This property is illustrated in Figure 9, where the buffer occupation is shown as a function of the burstsize,


for variable P and 7. Example 3 : 27 > P: Consider again the system described in Example 1 and let 7 vary between 0 and 120, incrementing in steps of 20. Furthermore, we let P = 20 and P = 40 and we let the on period of the CBR/VBR traffic be p = 2 and p = 4. Figure 10 shows the that increasing 7 leads to large buffers.

~L' __ ~ __ ~ __ ~~~~~==~~ n.~"""T

Figure 9 The Buffer Occupancy as function of 7 for different values of P

-----------------

30

100 ISO ....... oHperIocIaI .. A8RMI&IIa.

Figure 10 Modeling ABR traffic as bursty or as greedy

Even for high values of 7 with respect to p, the required buffer size is still increasing for growing 7. This is in contrast with the corresponding results for P (see Figure 7). An important conclusion to be drawn from Figure 10 is that the value of P becomes irrelevant for values of 7 much larger than P.

4.3 Modeling ABR as Greedy or Bursty Sources

To conclude this set of numerical result we turn our attention to the modeling aspect of the ABR traffic. It is clear that incorporating burstiness of the ABR traffic into the model increases its complexity. In the following example we investigate when we may ignore the bursty character of the ABR traffic. Example 4: Consider a system consisting of the following components. A CBR/VBR traffic source which has an ON/OFF behavior with mean on period p = 50, mean on period q = 62.5 and probability of generating a cell when ON equal to 1, resulting in a load of 0.44. The ABR traffic has parameters TCR=0.9, PCR=0.9 and MCR=0.15. The round trip delay is assumed to be 7 = 0, while P = 40. Now let the ABR have increasing mean ON period, where the value infinity corresponds with a greedy source. Multiple numerical results have shown (see e.g. Figure 11) that the needed buffer capacity is approximated very well by a greedy source as soon as the mean ON period of the ABR traffic reaches the value 2 x 7 + P, even for small ABR loads.


5 CONCLUSIONS

This paper presents an analytical evaluation of the buffer occupancy of ABR traffic in a switch when sharing the outgoing link with CBR/VBR traffic and using an Explicite Rate congestion control scheme. From the numerical examples we may draw the following conclusions and derive some engineering rules. • The burstiness of the CBR/VBR traffic has a strong influence on the required buffer capacity. As long as P + 2r is longer than the mean burstsize, the ABR buffer occupation increases with increasing CBR/VBR burstiness. IT the mean burstsize is larger than 2r + P, then the burstiness has no real impact on the used buffer space. It follows, that in order to find the maximum value of the buffer occupation it is sufficient to consider CBR/VBR traffic with mean burst duration of the order of 2r + P. • When selecting the length of the observation period P, one may take into account the following observation. The larger P the more buffer space is needed to guarantee a low CLR, thus we can gain buffer space by reducing the length of the observation period this at the price of increasing the number of RMcells i.e. the network overhead. But no relevant gains in buffer occupation can be made by changing its length P as long as is stays well above the mean length of the burstsize of the CBR/VBR traffic. • The longer the distance between the ABR-SES and the switch, the more buffer space is needed even when the mean burst size is much smaller than the delays considered. • In networks with large-round trip delays relative to the observation period, no gain can be made by adapting the length of the observation period, but such that it remains small compared to the round-trip delay. • When modeling the Explicit Rate congestion control scheme, on may replace the bursty ABR traffic by the more simple model of greedy sources in case the mean ON periods of the on/off ABR traffic are larger than the sum ofthe length of the observation period P and the round-trip-delay 2r, even if the load of the on/off sources is well below the value of 0.1.

Acknowledgements This work was supported in part by the Commission of the European Union, under project ACTS AC094 "EXPERT". The first author was also supported by Vlaams Actieprogramma Informatietechnologie under project ITA/950214 "Design and Control of Broadband Networks for Multimedia Applications".

REFERENCES

[1] ATM Forum, ATM Forum Traffic Management Specification, Version 4.0, April 1996.


[2] A. W. Barnhart, Explicit Rate Performance Evaluation, ATM Forum document AF -TM -94-0983Rl.

[3] C. Blondia, O. Casals, Performance Analysis of Statistical Multiplexing of VBR Sources, IEEE Infocom'92, Florence (Italy), 1992.

[4] C. Blondia and O. Casals, Statistical multiplexing of VBR sources: A matrix-analytic approach, Performance Evaluation, 16 (1992) 5-20.

[5] C. Blondia and O. Casals, Analysis of Explicit Rate Congestion Control in ATM Networks, Proceedings Australian Telecommunications Networks and Applications Conference (ATNAC '96), December 1996, Melbourne, Australia, 1996

[6] C. Blondia and O. Casals, Throughput analysis of the explicit rate congestion control mechanism, Proceedings 10th ITC Specialist Seminar, Lund, Sweden, 1996

[7] R. Jain, S. Kalyanaramam and R. Viswanathan, The EPRCA+ scheme, ATM Forum document 94-1173

[8] R. Jain, A sample switch algorithm, ATM Forum document 95-0178R1 [9] R. Jain, S. Kalyanaramam,R. Goyal, S. Fahmy and R. Viswanathan, ER

ICA switch algorithm: A complete description, ATM Forum document AF-TM-96-1172.

[10] G. Latouche and V. Ramaswami, A logarithmic reduction algorithm for Quasi-Birth-Death processes, J. of Appl. Prob., 30 (1993) 650-674

[11] M.F. Neuts, Matrix-Geometric Solutions in Stochastic Models, The John Hopkins University Press, Baltimore, 1981

[12] H. Ohsaki, M. Murata, H. Suzuki, C. Ikeda and H. Miyahara, RateBased Congestion Control for ATM Networks, ACM SIGCOM Computer Communication Review, (1995) 60-72

[13] M. Ritter, Analysis of Feedback-Oriented Congestion Control Mechanisms for ABR Services, ITC Specialist Seminar on Control in Communications, Lund (Sweden), 1996.

[14] M. Ritter, Network Buffer Requirements of the Rate-based Control mechanism for ABR Services, IEEE INFOCOM'96 proceedings, San Francisco, (1996) 1190 -1197

[15] K. Wuyts and R. K. Boel, A matrix geometric algorithm for finite buffer systems with B-ISDN applications, ITC Specialist Seminar on Control in Communications, Lund (Sweden), 1996.

[16] K. Wuyts and B. Van Houdt, Matrix geometric analysis of discrete time queues with batch arrivals and batch departures, in preparation

[17] Jingdong Ye and San-qi Li, Folding Algorithm, A computational method for finite QDB processes with level-dependent transitions, IEEE Trans on Comm., 42(2/3/4) (1994) 625-639

[18] N. Yin and M.G. Hluchyj, On Closed-Loop Rate Control for ATM Cell Relay Networks, IEEE INFOCOM'94, Toronto.

15 A New Traffic Control Algorithm for ABR Service

A. Bak and W. Burakowski Warsaw University of Technology Institute of Telecommunication ul. Nowowiejska 15119 00-665 Warsaw, Poland fax: +48226607564 tel: +48 22 25 21 60 e-mail:[email protected]

Abstract

In this paper we present an Explicit Rate (ER) ABR flow control algorithm. It directly measures the available link capacity as well as takes into account the ABR buffer occupancy. More specifically, the explicit rate calculated by the switch is proportional to the difference between predefined threshold and the actual state of the queue. Therefore, the algorithm can be regarded as the one based on a proportional control scheme. The effectiveness of the approach was verified by simulation. The paper includes sample results illustrating transient behaviour, queue occupancy, connections throughput and fairness.

Keywords

A TM Networks, ABR Service, explicit rate algorithm, flow control

Perfonnance of Infonnation and Communication Systems U. Korner & A. Nilsson (Eds.) © 1998 IFIP. Published by Chapman & Hall


1 INTRODUCTION

The ABR (Available Bit Rate) service is presently discussed by the A1M Forum (A1M Forum, 1996) as a promising solution to serve, so called, elastic non-real time applications, e.g. computer data traffic. The implementation of this service assumes that the reactive traffic control scheme is used to control the traffic volume offered to the network. For this purpose, the ABR source sends periodically Forward-RM cells along the connection. These cells are then sent back by the destination to the sender as Backward-RM cells. Initially the source inserts its current ACR (Actual Cell Rate) and PCR (Peak Cell Rate) parameters into the RM cells (the second parameter corresponds to the desired cell rate of the connection). In the case of Explicit Rate algorithms the switch can reduce the value of the desired cell rate (the ER field in RM cells) to match the source sending rates to its current traffic conditions. Additionally the ABR source can use the guaranteed bandwidth allocation by declaring the minimum cell rate (MCR) parameter in the call set-up phase.

Numerous proposals for the ER class algorithm were submitted (e.g. (Jain, 1994a), (Jain, 1996), (Ghani,1997), (Ait-Hallal, 1997), (Hernandez-Valencia., 1997), (Zhao, 1996)). It is worth mentioning ERICA (Jain, 1996), CAPC (Barnhardt, 1994) and EPRCA (Roberts, 1994), which are often considered by the A 1M Forum as possible solution for the standardisation. The ERICA algorithm assumes that the load corresponding to the high priority traffic (required guaranteed bandwidth) as well as the ABR traffic is measured in the predefined intervals. Additionally, in ERICA+ (Jain, 1996), the queue occupancy is taken into account. On the basis of these measurements the ER value is calculated with respect to each connection. In the CAPC method, only the total traffic load entering the switch is measured. The switch runs an estimate of ER value, which is updated proportionally to the difference between the measured load and assumed target utilisation. Similarly to the CACP method, the EPRCA algorithm measures also the total traffic load of the switch but the ER value is calculated on the basis of weighted average of the CCR (Current Cell Rate) values refereeing to ABR connections.

This paper describes an ABR flow control algorithm which considers both the link utilisation and ABR buffer occupancy. The proposed scheme, called the ER-PR (Explicit Rate - Proportional Regulator), belongs to the explicit rate class and assumes that the ER parameter is a function of the current queue size. The ER value, calculated by the switch, is proportional to the difference between predefined queue length threshold and the actual state of the queue. Therefore, the algorithm can be regarded as the one based on a proportional control scheme. This algorithm requires measurements of the load corresponding to both the high priority traffic and to the ABR traffic (only for constrained connections) and the number of non-constrained ABR connections being in progress.

The paper is organised as follows. Section 2 describes the proposed ERPR algorithm in details. The exemplary numerical results showing the effectiveness of the approach are presented in section 3. Finally the appendix A gives the pseudo-code of the modelled switch.

A new traffic control algorithm/or ABR service 191

2. THE ER-PR ALGORITIIM

It is assumed that an A TM switch handles two types of traffic, with and without bandwidth allocation, denoted as TBA and mBA, respectively. The TBA traffic is transferred via network with highest priority then the mBA traffic. The switch stores cells belonging to these traffic classes in separate buffers. The mBA buffer is served only in case there are no cells in the TBA buffer waiting for transmission (nonpreemptive priority).

Assuming the fluid flow model of the ABR connections we can make an analogy between the ABR buffer and a bucket (see Fig .1), where the buffer is filled by a number of input streams (ABR connections). Considering that the ABR traffic is of the mBA type the capacity available for ABR connections depends on the current load of the TBA traffic. Therefore, the output rate of the ABR buffer, denoted CADit), depends upon the time (it can change in the range from 0 to link capacity).

ACR!.(t) ===, .. ___ AffiN(t)

ACBl(t) J I ..... ' t ~-- KAJB(t)

i-------lx

Ya(t) •

.... RmA(t) 'OLA--

pC + Figure 1. ABR buffer model.

Let's choose the occupancy of the ABR buffer, x, as the state variable in our system. Denoting the input flows of the ith ABR connection as ACRj(t), i=I, ... N, the state equation can be written in the following form:

dx(t) N -= LACR;(t)-CABR(t)=u(t)

dt ;=) (1)

Note that the difference between the input and the output flows constitutes the control signal, u(t), in the system. The knowledge of this signal enables determination of the future states of the ABR buffer. From (1), we can see that the ABR buffer works as an integrator, i.e. it integrates the signal u(t) converting it to the buffer occupancy.


Denoting the instant carried TBA traffic by 14aA(t) the output rate of the buffer can be expressed by:

C ABR(/) = pC - Rm.t(t) , (2)

where p is the overall link utilisation and C is the link capacity. The problem under consideration belongs to the N-input-one-output linear

system class. It can be treated as the one-input-one-output system assuming that the cumulative ABR traffic stream is controlled as a whole and then equally distributed among N ABR connections. This approach is intuitively in accordance with fairness criteria but is not effective in the case when some ABR connections are bottlenecked in other switches. The ABR connections served by a switch can be divided into two groups, i.e. constrained and non-constrained connections, depending on whether they are bottlenecked or not in this switch. Notice that the switch controls only the rate of the non-constrained connections. Therefore, we can rewrite (1) in the following form:

dx(/) = R~R (I) + R~R (I) - C ABR (I) = U(/) , dl

(3)

where R+ABR(t) and R-ABR(t) denote the aggregate rate of non-constrained and constrained connections, respectively.

In order to control the rate of the non-constrained connections a simple proportional regulator was used. Its objective is to stabilise the ABR buffer occupancy at the predefined threshold and, as a consequence, it gives a chance of achieving high link utilisation.

Assuming that the decision delay is produced on the output of the controller, we can write the control rule. in the following form:

{K\ ·(xo -x(t--r», whenxo ~x(t--r)

u(t) = K2 . (xo -x(t --r», when Xo < x(t--r) (4)

where K1,2 are the gains of the proportional regulator and Xo is the buffer threshold value.

The block diagram of the control scheme is shown in the figure 2. The difference between the observed buffer state x(t) and Xo is multiplied by K\ or K2 and the result constitutes the input signal u(t). Therefore, the rate of ABR traffic (non-constrained traffic) is proportional to the difference between the assumed and observed buffer state. With parameters K\ and K2 we can adjust the performance of the algorithm for the cases when the queue is below and above the predefined threshold.

A new traffic control algorithm/or ABR service

regulator D(t)

u(t) + + + ~O

Figure 2. Block diagram of the control system, D(t) disturbance.

Taking into account that:

itt(/) u(/)=-

dt ,

we arrive at the following formula:

R~ (t) + R~R (t) - C ABR (t) = K J•2 • (xo - x(t --r»

193

(5)

(6)

Assuming that the value of explicit rate (ER) parameter is calculated at the switch we can write:

R;BR (t) = L ACR, (I) = N+ . ER(/--r) ~ , m

where 1f denotes the number of non-constrained connections and Z is the set of non-constrained connections. So finally the value of the ER parameter can be expressed by:

pC - RTBA. (I) - R;BR (I) + K J 2 • (Xo - X(/» ER(/) = .

N+ (8)

The implementation of the control scheme given by (8) requires the measurements of the TBA traffic rate (RnA)' the constrained ABR connections traffic rate (R'AIIR) and the number of non-constrained ABR connection (1f). This is done in the measurement intervals. The explicit rate in the interval kth is calculated in the following way:

(9)

The TBA traffic rate can be calculated by counting the number of TBA cells served by the switch in the measurement interval. In order to reduce the influence


of the TBA traffic variability on the ABR control algorithm, the weighted averaging of consecutive measurements can be used:

RTBA (k) = (1- a)RTBA (k -1) + a rTBA (k -1) , (10)

where rTBA(k) denotes the TBA traffic rate measured in kth interval and a denotes the averaging constant.

In order to measure the constrained connections traffic rate (R'ABR) and the number of non-constrained connection (N'), the switch has to know which ABR connections are constrained and non-constrained. It can be done in the following way. A switch inserts into the FRM (or BRM cells) cells its unique identifier when it updates the ER value. An ABR connection is marked as non-constrained when the switch identifier equals to with the value read-out from the BRM cell. Unfortunately, it requires a slight modification of the RM cell format. Knowing which ABR connections are constrained and non-constrained the measurements of tv' and RABR can be done in straightforward way. The pseudo-code of the algorithm used in the simulations is presented in Appendix A. Two extensions of the basic scheme described above are implemented. First to avoid transient overloads, when constrained connection becomes unconstrained, the following modification in the explicit rate calculation was introduced:

pC-RTBA(k)-max(O,R~BR(k)-CCR)+KI2 ·(xo -x(k» ER= .

N+ +1 (11)

where CCR is current cell rate for this connection. Secondly for the same reason in the case of newly established connection (first

seen by the switch) the explicit rate is calculated in the following way:

pC - RTBAk) + KI 2 • (xo - x(k» ER= .

N , (12) where N is the total number of ABR connections.

3 PERFORMANCE STUDIES

The effectiveness of the algorithm was checked by simulation. The exemplary performance characteristics representing transient behaviour, throughput, queue size and fairness are included in this section. All presented results were obtained with 95% confidence interval.

We assume two basic test network topologies, which are usually used to study the effectiveness of ABR service, i.e. the bottleneck (BNT) and simple parking lot (PLT) configurations depicted in figure 3.


a) Bottleneck topology - BNT

e tp' IVB~ 1 ... ·· .. · .. lv;'NI

I ~NI t-1_15_5M_b_it/_s_-II··~2 .... I·::::~ S~ \;. tp __ ~

I v~·~"I· .. ·· .. ···lv·~R'NI .... · .... Links with no propagation delay

- Links with propagation delay

b) Parking lot topology -PL T

8 """'~--"

e·················· : ............ .g ..... _....1··'·8

VBR', VBR', Figure 3. Studied network topologies.

195

The BNT topology consists of two ATM switches connected with 155 Mbps link. The traffic served by the network is a mixture of TNBA and TBA streams. The TNBA traffic is generated by 5 ABR sources while the TBA traffic is produced by 40 homogenous ON/OFF sources. The ON/OFF sources have geometrically distributed ON and OFF periods and are characterised by peak cell rate (30 Mbps), mean cell rate (3 Mbps) and ON period duration (100 slots). Each ABR source is connected to the switch with access link of propagation delay tPi (i=I, .. ,5). The EFCI mode was disabled by setting RIF=1 and RDF=infinity. Other ABR source parameters were set to default values.

The PLT topology consists of three A TM switches connected with 155 Mbps links. The network serves 3 groups of ABR and 2 groups of TBA sources. The ABR sources belonging to the group no.l (SES 1 in the figure. 3) generate traffic, which is served by switches Nt, N2 and N3. The sources belonging to the group no.2 (3) (SES 2 (3)) generate traffic which is served by switches Nl (N2), N2 (N3).

The parameters of the algorithm were chosen as follows: the controller gain Kl=~=0.0002, the queue thresholds xo=O cells and the measurements interval T=250 slots. Setting xo>O we can obtain higher link utilisation at the expense of longest queue. In case of nonzero queue threshold the factor Kl*XO should be kept constant e.g at 5% of link capacity. In the following experiments weighted averaging of TBA traffic was omitted (a= 1). The target rate p was fixed at 1.


3.1 Transient behaviour

The transient behaviour of the algorithm was studied by using the BNT network. In the following simulations the TBA was not present. In this experiment each ABR source has different access link propagation delay ranging from 1 up to 10000 slots (see table 2). Initially, the value of the ACR parameter for each ABR connection is set to 1 Mbps (lCR). Figure 4 shows the behaviour of ABR connections. One can observe that all connections reach the maximum ACR value (approx. 30 Mbps) after the RTT (Round Trip Time delay with minor oscillations.

180 160 ---ACRI

140 - - -ACR2 120 - - - - - 'ACR3 100 - - - -ACR4 80 - - - -ACR5 60 40 I!

20 I . 0

-20 10000 20000 30000 40000 50000

Figure 4. ACR transient characteristics.

3.2 Queue size and throughput characteristics

The queue size and throughput characteristics are studied using the BNT network fed by both TNBA and TBA traffic. The mean rate of TBA traffic is 60 Mbps while the ABR traffic is the same as in previous case. Additionally, is assumed that the propagation delay is the same for each ABR connection.

The queue length characteristics are presented in terms of the required queue size (RQS) and the coefficient of the variation, c2 (c2=Var[x]/Mean[x]2, where x is a random variable describing queue length). The RQS_worsCcase is evaluated assuming the step unit function (changing from zero up to link capacity) as the background traffic (Bak, 1997) while RQS_sim is obtained by simulation with TBA traffic generated by ONOFF sources. These characteristics vs. RTT are depicted in figure 5 and 6, respectively.

The curve in figure 5 shows that the RQS_worsCcase mainly depends on the RTT. The resulting RQS value is a function of the signalling delay (RTT * link capacity) and delay corresponding to the reaction time of the algorithm. The RQS_sim is always below the RQS_ worsCcase and the difference between these curves strongly depends on the TBA traffic pattern.

14000

12000

10000

8000

6000

4000

2000


Queue

- - - - - 'Rqs_sim

---Rqs_ worst_case

Rtt ___ •. .• __ ........................ _ ........................................ .a

O~------~-------.-------.--------.-------.

o 2000 4000 6000 8000 10000

Figure 5. RQS vs. RTf.

197

The characteristic of the c2 referring to the queue length as a function of the RTf is depicted in figure 6. It can be noticed that for RTf <1Ooo (LAN and MAN networks) the variability of queue length is decreasing while for RTT>l000 slots (WAN networks) it is slightly increasing (but is close to 1). This result proves that the algorithm is stable at least for this range of RTf.

1.4 V/A"2

1.2

0.8

0.6

0.4

0.2 Rtt

O+--------.--------.--------.--------.-------~

o 2000 4000 6000 8000 10000

Figure 6. Square coefficient of variation for Queue State vs. RTf.

Figure 7 shows the utilisation of the inter-node link vs. RTf. One can observe that (for the considered range of RTf) the obtained link utilisation is about 97% link capacity. For small value of RTf the throughput slightly increases (RTf<1000) while for greater values of RTf the throughput decreases but it is still above 96% of link capacity.


0.985 Rho

0.98

0.975

0.97

0.965

0.96

0.955 Rtt

0.95

0 2000 4000 6000 8000 10000

Figure 7. Throughput vs. RIT.

3.3 Fairness

The ABR algorithm should fairly allocate the available bandwidth between active ABR connections. The fairness of the ABR algorithms is usually defined in terms ofmax-min-faimess criteria (Jain, 1994).

In order to show the fairness of the ER-PR algorithm the results from two simple experiments are presented. In the frrst experiment the BNT network was used with 60 Mbps TBA traffic in inter-node link. Five ABR connections (unconstrained) with different propagation delay were simulated. The throughput obtained by these connections is shown in table 1. The difference between the lowest and highest allocated rate is about 0.6 Mbps. It is not too much considering the differences in RIT delays. This result can be improved by choosing greater measurements intervals.

Table 1. Simulation results for BNT network

Connection No. 1

RIT [slots] 1

Throughput [Mbps] 17.6

Expected throughput 18

2

10

17.6

18

3

100

17.8

18

4

1000

18.2

18

5

10000

18.2

18

In the second experiment the case with constrained and unconstrained ABR connections was considered. For this purpose a simple paring lot (PL T) network was used. The cell rate of TBA traffic was equal to 60 Mbps on each inter-node link leaving about 60% of link capacity for TNBA (ABR) traffic. The RIT delay for each link is 1000 slots. Two cases were simulated. In the first case the ABR connection group 2 has 10 connections while remaining groups have 5 connections. The connections belonging to group 1 and 2 are bottlenecked in node

A new traffic control algorithm for ABR service 199

Nl while the group 3 is bottlenecked in node N2. In the second case the group 3 has 10 connections while the remaining group have 5 connections. Now the connections of group 1 are bottlenecked in node N2. The average throughput obtained by connections of group 1-3 is shown in table 2. It can be noticed that in the first case the connections of group 3 get twice as much bandwidth as connections of group 1 and 2. Similar results were obtained for second case. As one can see the available bandwidth is fairly allocated.

Table 2. Simulation results for PL T network

Group No. 1 2 3

Number of Conn. 5 10 5

Throughput [Mbps] 5.77 5.80 11.4

Expected throughput 6 6 12

Number of Conn. 5 5 10

Throughput [Mbps] 5.7 11.5 5.73

Expected throughput 6 12 6

4. CONCLUSIONS

The distributed explicit rate ABR algorithm based on queue observation and traffic measurements has been proposed. The ABR buffer state in the form of proportional control flow is used in the calculation of explicit rate parameter. This assures the stability of the algorithm. The scheme can effectively operate in the presence of TBA traffic. The included exemplary numerical result shows that the algorithm gives high link utilisation and satisfies fairness criteria.


LITERATURE

Ait-Hellal, O. and Altman, E. (1997) Rate Based Flow Control with Bandwidth Information" , European Transactions on Telecommunications, Vo1.8, No.2.

ATM Forum, (1996) ATM Forum Traffic Management Specification Version 4.0. ATM Forum, 95-0013Rll, 1996.

Bak, A. Burakowski, W. and Kopertowski, Z. (1997) Evaluation of Required Queue Size to Support ABR Service", Document of the COST 257 project, Helsinki, September 1997

Barnhart, AW. (1994) Explicit Rate Performance Evaluation, ATM Forum 94-0983Rl.

Ghani, N. and Mark, lW. (1997), "Meaurement Based Flow Control for ABR Services in A TM Networks" , European Transactions on Telecommunications, Vo1.8, No.1, 1997.

Hernandez-Valencia, E.J. Benmohamed, L. Nagaraj an, R. and Chong, S. (1997) Rate Control Algorithms for the A TM ABR Service, European Transactions on Telecommunications, Vo1.8, No.2.

Huges, D. and Daley, P. (1994) More ABR simulation Results, ATM Forum 94-0777.

Jain, R. Kalyanaraman, S. and Viswanathan, R. (1994a) The OSU Scheme for Congestion Avoidance using Explicit Rate Indication, ATM Forum 94-0883. Jain, R. (1994b) Fairness: How to measure quantitatively?, ATM Forum 94-08981. R. Jain et al, (1996) ERICA Switch algorithm: A Complete Description, ATM

Forum 96-1172. Roberts, L. (1994) Enhanced PRCA (Proportional Rate-control Algorithm, ATM

Forum 94-0735Rl. Siu, K.Y. and Tzeng, H.Y. (1995) Intelligent Congestion Control for ABR Service

in A TM Network, Internal Report of the Dept. of Electrical & Computer Engineering University of California, Irvine.

Zhao, Y. Li, S.Aand Sigarto, S. (1996) A Linear Dynamic Model for Design of Stable Explicit Rate ABR Control, A TM Forum 96-0606.

Appendix A Switch pseudocode

A new traffic control algorithm/or ABR service 201

if ( End of Measurement Interval) R_TBA = (I - A VF)*R_TBA +

A VF*(TBA_Count I MI); R_ABR = ABR_Count I MI; TBA_Count = 0; ABR_Count = 0; QS = cum:nt queue length; C_ABR = RHO*LCR-R_TBA;

if (Queue not empty) if (TBA connection) TBA_Count++; else if (Cell is RM cell)

if(Cell->DIR=O) Process FRM cell if (Cell->DIR=I) Process BRM cell

else /I Data cell if (Constrained connection)

ABR_Count++;

/I Forward RM cell if(First Seen Connection)

Mark this connection as transient; NUP++; if( Cell->Switch_ID=null)

Cell->Switch_ID=SWITCH_ID; switch( Connection type) case Transient:

ER = (C_ABR + QueueFunction( QS» I (NUP+NON);

case Non-constrained: ER = (C_ABR - R_ABR + QueuePunction( QS» I NUP;

case Constrained: ER = MAX( 0, R_ABR -Cell->CCR); ER = (C_ABR - ER + QueuePunction( QS» I (NUP+ 1);

ER = MIN(LCR,ER); ER = MAX(O,ER); if( (Cell->ER) > ER)

Cell->ER = ER; Cell->Switch_ID = SWITCH_ID;

/I Variables MI -length of measurements interval A VF - averaging factor KI,2 -gain X. - queue threshold RHO - target utilisation TBA_Count - TBA cells counter ABR_Count - Constrained connections cells

counter - measured TBA traffic rate - constrained connections rate - queue state at the end of measurement interval - ABR capacity - Explicit rate - number of constrained connections - number of non-constrained and transient connections

/I Backward RM cell if (Cell->Switch_ID=SWITCH_ID)

if (Constrained Connection) NUP++;

else

NON--; mark this connection as non-constrained;

if (Non-constrained or transient connection) NUP--; NDN++;

mark this connection as constrained; if (Constrained connection) ABR_Count++;

/I Queue function - proportional control QueuePunction( QS)

if(QS < X.) retum«x" - QS)*KI);

else retum« X. - QS)*K2);

PART SIX

Video over ATM

16 On the efficiency of statistical-bitrate service for video

G. Karlsson Swedish Institute of Computer Science Box 1263, SE-164 29 Kista, Sweden

G. Djuknic Lucent Technologies 67 Whippany Road, Room 1A-234 Whippany, NJ 07981-0903, U.S.A.

Abstract

The provisioning of quality of service by means of statistical multiplexing has been an alluring research idea for the last decade of teletraffic research. In this paper we question the efficiency of statistical bitrate service which is the standardized representation of this operational mode for ATM networks. Our argument is that the amount of information needed about a traffic source in order to· attain a fair multiplexing gain is beyond what is captured in the standard's three-parameter traffic descriptor.

Keywords

Statistical bitrate, variable bitrate, deterministic bitrate, ATM, video, teletraffic

1 INTRODUCTION

Statistical multiplexing with quality guarantees is often seen as the prime service offering of asynchronous transfer mode networks that should justify the introduction of

Performance of Information and Communication Systems U. Korner & A. Nilsson (Eds.) © 1998 IFIP. Published by Chapman & Hall

206 Pan Six Video over ATM

ATM in relation to existing detenninistically multiplexed telephony networks as well as statistically multiplexed networks without quality guarantees, such as most local area networks and internet protocol based wide area networks. There has consequently been a remarkable interest in the research community on the definition and evaluation of this operational mode.

Statistical multiplexing has been successfully used for data communication during the last three decades and more recently in radio networks. In both cases there is a division of responsibility: the network provides fair access to the transmission capacity and routing; the end-equipment is responsible for the quality of the transmission by means of retransmission and forward-error correction. ATM is breaking this division by asking the network to provide quality guarantees for statistically multiplexed channels. The implicit assumption is that the guarantees would come at only a small loss in multiplexing efficiency, which still would leave a large efficiency gain compared to the use of detenninistic multiplexing. We will consider this latter comparison of statistical and deterministic multiplexing for the case when quality of service is required but the information about source behavior is limited to that provided by a leaky-bucket descriptor. Our main interest is video communication.

The Telecommunication Standardization Sector of the International Telecommunication Union has made Recommendation 1.371 for the choices of traffic control mechanisms in B-ISDN. We will use the tenninology of the Recommendation and refer to statistical multiplexing with quality guarantees as the statistical-bitrate service (SBR) and the deterministic multiplexing as deterministic-bitrate service (DBR). The ATM Forum has chosen the terms variable-bitrate service and constantbitrate service for these two services.

For video communication over ATM networks there are primarily two causes of information loss to consider: quantization loss in the source coder, and cell loss due to multiplexing overload in the network. In general the quantization loss can be made less perceptual than the cell loss for comparable levels. This, in tum, means that it is better to reduce the bitrate by source coding and allowing at most a small amount of cell loss, compared to nearly lossless source coding and more cell loss in order to get more efficient multiplexing. For example, Heeke reports that the statistical multiplexing gain increases 20 percent for a video conference scene and 40 percent for a television scene when increasing the cell loss rate seven orders of magnitude from

10-9 to 10-2 [6]. An equally large increase in distortion caused by source coding would most likely allow a much higher reduction in needed transmission capacity for the signal.

The idea has been that going from a truly lossless network service to a virtually lossless one would open up for a reasonable statistical multiplexing gain without compromising the quality which ought to be determined by the source coding loss. In this study we show that this idea, although appealing, cannot always be realized. The ensuing risk is that the more complex SBR service is implemented and yet it does not give any performance improvements compared to a simpler DBR provisioning. The main reason why this risk is not negligible is that the call-acceptance control would need a fair amount of information about the source characteristics in order to ensure

On the efficiency of statistical-bitrate service for video 207

quality at a high multiplexing efficiency. The recommended traffic parameters are often insufficient for this purpose. For example, Heeke's work relies on the measured average rate and its standard deviation in order to calculate the number of identical but independent streams that could be multiplexed onto a link. In reality the procedure would have been that the sender estimates a few traffic parameters for the traffic stream, and the call-acceptance control chooses the number of streams based on those parameters (where different calls would of course have different parameter values). The mean and standard deviations would thus have been calculated from the traffic descriptors, rather than being the true values of the source.

2 ATM TRANSFER CAPABILITIES

According to ITU Recommendation 1.371 we may pose the following requirements on the parameters that would be used to describe a forthcoming call: they should be understandable by user or terminal to make conformance possible; they should be useful for the call-acceptance control to meet performance requirements, and finally, the parameters should be enforceable for user and network parameter controls.

Source parameters The peak rate is a mandatory parameter to specify for all calls.!t is simply given as the inverse of the minimum cell distance, measured in time from first bit to first bit (Tpcr)' The time is treated as a continuous variable despite the fact that ATM transmission is slotted (idle times are filled by empty cells to maintain link synchronization of cell boundary detection at the physical layer). However, the peak rate specification is quantized to 1 638 444 distinct rates (from 1 cell up to 4.3 X 109 cells per second).The peak rate is coupled to a tolerance value for the cell-delay variation which specifies the maximum deviation from the minimum cell-interarrival time specified by the peak rate.

The second rate-tolerance pair is the sustainable rate and the intrinsic burst tolerance ( I/T.br and f ibt)' They are defined by a generic cell rate algorithm. There is also a tolerance value for the cell-delay variation with respect to the sustainable rate. The burst tolerance is measured in seconds. An equivalent burst measure in terms of cells,

the so called maximum burst size, is given by 1 + l fib'/(T.br - Tpcr)J. The worst admissible behavior of a source that is specified by sustainable and peak

rates and an intrinsic burst tolerance is an on-off behavior, transmitting fibt seconds

at peak rate followed by an idle period of fibt(T.brlT per - 1) seconds [13]. We will assume that the parameters describing a source are the peak and sustain

able rates (in bits per second) and maximum burst size (in bits) and denote it by the

triple (R, R, b). We will disregard the two rate-tolerance values. No further informa

tion about the source can be assumed by the call-acceptance control. The bound can be illustrated by a so-called arrival curve: Let R(t) denote the number of bits sent by

208 Part Six Video over ArM

a source from time 0 to time t, then the arrival curve is given by

a('r) = SUPt:2:0 !R(l' + t) - !R(t). It is consequently a bound on the number of bits the source can generate in a period of l' seconds. The leaky bucket gives an upper bound to the arrival curve consisting oftwo lines, as shown in Figure 1.

A

bits R Xl' RXl'+b

a(l')

b a(l') s min(R Xl', R Xl' + b)

r Figure I An arrival curve for a source bound by a leaky bucket.

Statistical and deterministic bitrate services As mentioned before, there are two types of transfer capabilities that we consider in this study: the deterministic bitrate service and the statistical bitrate service. The for-

mer requires specification of the peak rate and will subsequently be denoted (R, R, 0)

(i.e., R = R); the latter is specified by the full parameter triple (R, R, b). Determin

istic bitrate service means that the connection is assigned a capacity that is at least equal to the peak rate. The lTD Recommendation does not state the associated quality of service but loss-free service with low maximum delay is possible, and will henceforth be assumed [9]. The peak rate cannot be renegotiated during the session by any other means than signalling and network management procedures.

The statistical bitrate service means that a rate R < R· < R is allocated for the connection. The parameters are fixed for the duration of the call, or renegotiated by signalling or management. The number of algorithms for call-admission control in the literature is large [2]. Yet none, to our knowledge, handle call requests based on the leaky-bucket descriptor when not all calls have the same parameter values. Our study is consequently based on a homogeneous situation with identical and independent calls. The algorithm we have chosen considers only the peak and sustainable rates in the acceptance decision.

For the sake of discussion, we briefly describe the ATM block transfer capability (ABl) although it is not a part of our study. A block consists of a group of cells between two resource management (RM) cells. The first RM cell establishes the block cell rate for the group, which essentially is a peak rate for the block. The second RM cell releases the resource or changes the reserved rate to suit the following block. The service is therefore a DBR service with piecewise fixed rates. The parameters for a connection are: the overall peak cell rate that never may be surpassed by the block cell rate, the peak cell rate for the RM cells which gives the minimum renegotiation interval, and the sustainable cell rate. The sustainable rate can be used to lower the blocking probability for the renegotiations: if the mean rate up to a renegotiation


point is below the SBR, then an increase will be accepted without blocking. The rate may be set to zero.

The ABT is a flexible service that can be well suitable for video [3]. However, it is not clear how the sender would be able to choose appropriate renegotiation intervals and sustainable rate for a live transfer. We will discuss the ABT option further in the final conclusions.

3 THE VIDEO SYSTEM

A video communication system is shown in Figure 2. The digitized video is first passed to a source coder. It is often built with three system components: energy compaction, quantization and entropy coding [10].

The energy compaction aims at putting the signal into the form most amenable to coarse quantization. Common methods for video include discrete cosine transform, subband analysis, and prediction, possibly motion estimated. The quantizer reduces the number of permissible amplitude values of the compacted signal and introduces round-off errors. The entropy coding, finally, assigns a new representation to the signal which represent the data more efficiently but there is no longer a constant number of bits per picture, and the bit rate becomes temporally varying.

/sackpressur~ l Digita

video - Energy compaction

Source coder

Entropy Bit- rate Quantization I--

coding regulation ~

Figure 2 The sending side of a a video communication. The bit rate regulation consists of a smoothing buffer with back pressure to avoid overflow.

The bit-rate regulation is used to adapt the varying bit rate to the channel in the network. The regulation flattens the bit-rate variations by buffering and may regulate the compression to avoid overflow. The feedback reaches the quantization of the encoder and enforces a higher step-size with increased round-off error as a consequence. If the quantizer step-size is throttled frequently and heavily it may lead to visible quality fluctuations in the reconstructed signal.

Leaky bucket descriptors have recently been studied for regulated video. It is clear that the feedback makes it possible to regulate the bit rate from the coder in order to fit any choice of leaky-bucket parameters. Whether a particular set of parameters is good or not can only be determined by subjectively evaluating the encoding quality. Hsu et al. have established that a smoothing buffer of size Bsbr together with the

leaky-bucket descriptor ( fl., R, b) yields the same quality as a system with a buffer of

size Bdbr = Bsbr + b and the single upper bound descriptor (R,R,O) (again, this

210 Part Six Video over ATM

notation means that R = If) [8]. The gain is therefore a lower delay in the former case since the buffer can be b bits smaller without any effect on quality. It should be noted, however, that the first case also requires a higher capacity allocation due to the allowed burstiness, and it is the issue we are considering in this study.

Allocatl!d ratl!S /MblsJ

12,---------------------------------------------,

IO~----------------------------------------~

8r-----------------------------~r__4

6 r-------------------------~

4 t-----------=:------i

2

o 2 4 6 8 /0 12 14 16 18

Pl!ak ratl! /MblsJ

Figure 3 The allocated rate as a function of the source's peak rate. The sustainable rate is 1.8 Mb/s, and the link rate is 150 Mb/s for white bars and 620 Mb/s for grey bars.

4 COMPARISON OF EFFICIENCY

We now study the two cases given above. For the leaky-bucket characterized source, one cannot justify any helpful assumptions about the variations within the bounds and an on-off pattern must consequently be assumed to be safe (even though such behavior is not observed for variable bit rate video) [13]. Following Hamdi et at. [5], the allocation for identical connections can be approximated as R* = C / N, where N is the largest value such that the target loss probability is not exceeded:

I. (jR - C)(~)(R/Rn 1 - R/R(-j j- rc/Rl

Ploss = ----:--....:..----------N-=R=------------

This expression assumes a fluid-flow model of the traffic and a bufferless multiplexer (thus, b is not appearing in the expression; it could, however, be considered in a tariff structure if call acceptance would be based on this formula) . It follows that the

utilization is R/R* < 1 when R > Ii. A unity utilization would mean that all connections are allocated their sustainable rates. This should not be mistaken for the actual usage of the link which could be arbitrarily much lower since the declared sustainable rate might be well above the actual mean rate due to uncertainty in the sender's parameter estimation. The allocations needed for a cell loss probability of 10-6 are plotted in Figure 3 as functions ofthe peak rate for link rates of 150 and 620


Mb/s. We only consider the 150 Mb/s link rate in what follows since it is more realistic for access links, which easily become the bottlenecks for video services.

A valid question is what gain can be achieved by SBR over DBR for a given source. If delays are not of primary importance then obviously DBR is more efficient than SBR in terms of capacity allocation (and quality of service) since it requires an allocation of R compared to RO > R for SBR. Recall that the encoding quality of the two cases is comparable if Bdbr = B,b, + b. The delay difference is at most b/R seconds, if we assume that the network delays are as short for SBR as for DBR.

A more interesting comparison is to keep the capacity allocation- equal in the two cases and to compare the resultant smoothing delays. Thus, for DBR we have a des-

criptor (RO, RO, 0) and for SBR the usual (R, R, b) descriptor which also leads to an

allocation of RO. We would like to determine the buffer size B db, and the buffer plus

burst size, B,b, + b, such that p(Q > Bdb, I RO) = p(Q > B,b, + b I R). This means that the probability of the queue exceeding B db, serviced at a rate RO should be equal the probability of exceeding B ,b, with a burst of b bits when serviced at rate R. Functions like P(Q > B I R) have been studied by Chong and Li under the name probabilistic burstiness curves [1]. Given the values for Bdb, and B,b, + b, we can determine the difference in smoothing delay for a given maximum burst size.

Instead of using the more general probabilistic burstiness curves, we restrict our comparison to the equivalent capacity for a two-state Markov chain. The formula by Guerin et al. is well-known [4]:

ail. - B + .j (aR. - B)2 + 4aBR. R =--------~~----------. ~ , where

a = - (lnploss) lis (1 - R,/R.).

The subscript's' signifies that the parameters are for the source, and not the connec

tion. In general we may expect that R. ~ Rand R, < R. The latter is simply a stability condition for the smoothing buffer. The parameter li, is the average burst duration (in seconds) for the two-state chain.We solve the expression for the two cases

R.q. = {RO, R} to find the corresponding buffer sizes B = {Bdb" B.b, + b} for the given loss probability.

Figure 4 shows the resultant buffer sizes for R. = 0.7 R, R. = R and b. = 40 ms (the frame duration for European video formats). The actual utilization of the sustainable rate is consequently 70 percent. The quality in terms of loss has been fixed in the calculation (to Ploss = 10-6 which could be the probability of overflowing the smoothing buffer or of regulating the quantizer). The delay for the SBR and DBR cases would be equal if B.b,/R = Bdb,/R·. This gives the value for B.b, and from the buffer values in Figure 4 for B .b, + b we find the minimum value of b for which SBR yields as low smoothing delay as DBR. These values are plotted in Figure 5 for in-

212 Pan Six Video over ATM

creasing peak: rates. SBR is more efficient than DBR in terms of smoothing delay when the declared burst size of the leaky bucket is above the line in the plot.

Buffer sizes 1Mb) 30.---------------------------------------------.

251----------------------------------------~

201------------------------------~_r--~

151--------------------------~

101----------------==--~

5 I------------j

OL...------'---'--'------'---'--'-2 4 6 8 10 12 14 16 18

P~aJc rat~ IMb/s}

Figure 4 The needed buffer sizes for a given equivalent capacity. White bars are for Bsbr + b and grey bars for Bdbr•

Maximum burst size 1Mb)

15

(b) (a)",...-

/ ..,/ ',;'

V V (C) .........

/ / V -./ -""

25

20

/ V ". ~ L..---'"

10

~

L ~ ~ 5

o o 2 4 6 8 10 12 14 16 18

Peak rate {Mb/s] A

Figure S The maximum burst size, b, as a function of peak: rate R. The parameters

are R = 1.8 Mb/s, R. = Rand bs = 40 ms. The average source rates are (a)

R. = 0.7R, (b) Rs = 0.9R and (c) Rs = O.SR.

5 CONCLUSIONS AND DISCUSSION

We have given a straightforward example to illustrate that a DBR service may in many cases outperform an SBR service for variable bitrate sources, such as video. A given quality of service can always be assured at a lower allocation of capacity with DBR than SBR if delay is not of prime importance. The allocation for SBR service


would be R" > II for a call described by the leaky-bucket parameters (R. R, b),

while the DBR allocation would be II at the cost of bIll seconds of more delay. If the burst size is considered by the call-acceptance control then the comparison could be skewed further in favor of DBR service since R" would increase with increasing b.

By keeping the allocations equal and instead comparing delays we also show that DBR outperfonns SBR for some reasonable parameter choices. We have used an onoff Markov model for the source which fits the on-off behavior that is assumed by the call-admission control. Yet the results show that SBR is not always yielding a lower delay than DBR. For instance, a call with 1.8 Mb/s sustainable rate and 8 Mb/s peak rate (a 5: I peak-ta-mean ratio is common for VBR video [6]) would require a declared maximum burst size of nearly 9 Mb in order to yield lower smoothing delay than a DBR connection with the same allocated capacity. This only assumes an average source rate that is 70 percent of the sustainable rate. The needed burst size depends on both the utilization, as can be seen in Figure 5, and on the average burst duration for the source. For lis = 10 and 80 ms, the needed burst sizes are 2.2 and 17 Mb, respectively, compared to 9 Mb for the case above (with 70 percent utilization in all cases).

It is not too surprising to find the low efficiency of SBR service for call-acceptance decisions based on leaky-bucket descriptions of the calls. All studies of statistical multiplexing gains have assumed source characteristics that are known to a very high degree: for instance, they could be captured by a stochastic model with parameters fitted to real data [7], or when only the first two moments are used, they are still actual values for a real source [6]. What we have shown here is that a leaky-bucket description of a source does not provide enough infonnation about source characteristics to ensure a reasonable multiplexing gain in many cases. Our finding is supported by the study presented in [11].

Even such a simple descriptor as the triple (i, 1f, b )causes problems for the sender

to detennine suitable parameter values before a call has commenced. The quality of a call may, on the one hand, not be as good as expected if the values are too small, since the bitrate regulation will ensure that the agreed parameters will not be exceeded. New parameter values can only be established by user signalling, which typically would have to be initiated manually. On the other hand, the call will be unnecessarily expensive if the parameters are only loosely fitted to the actual traffic. Thus, increasing the complexity of the descriptor is not a good solution: it would allow the network to operate more economically with more statistical multiplexing at the expense of the user who would have more parameters to estimate, allowing more room for misestimation. Methods for estimating even the simple leaky-bucket parameters for a call request are to our knowledge still lacking.

There are three possible solutions to this dilemma. The first is measurement-based admission control which enhances a user-provided traffic descriptor (typically only the peak rate) by infonnation from measurements of on-going calls (there are already several proposals in the research literature, one example is [12]). Any quality


guarantee would be conditioned on the assumption that the measurements provide reliable information for predicting future network behavior.

The second possibility is to use the ATM block transfer capability for which the fixed rate can be renegotiated at need to suit variations in a bit stream, for instance as caused by scene variations in a video program. The study by Grossglauser et al. could serve as a good starting point for further investigations [3]. The third possibility is to offer a combination of only DBR and ABR/UBR transfer capabilities. Such service offering could still be very efficient since reserved but unused capacity of DBR calls would be available to ABR and UBR calls [9]. The sole advantage of ABT over this simple service offering is that ABT calls may share capacity between themselves through the renegotiations. In the simple case, unused capacity allocated to DBR calls is only shared with ABR/UBR calls. It is not clear how important this advantage is in practice.

Although it is not clear what burst sizes are practically permissible in operational ATM networks, we are troubled by the very large sizes that are needed for SBR to compare favorably with DBR in terms of delay at equal bitrate allocations. This certainly weakens the case for promoting SBR, considering also that it is more complex to implement and that it yields an inferior transfer quality compared to DBR service. We hope that this paper may help directing the attention of traffic-control researchers away from the statistical bitrate service towards evaluating the merits and problems associated with measurement-based admission control, ATM block transfers, and the DBR/UBR service structure.

6 ACKNOWLEDGMENT

This study was done when G. Karlsson was visiting professor at the Telecommunication Software and Multimedia Laboratory at the Helsinki University of Technology, Finland. This support is gratefully acknowledged.

7 REFERENCES

[1] S. Chong and S. Li, "Probabilistic Burstiness-curve-based Connection Control for Real-time Multimedia Services in ATM Networks," IEEE Journal on Selected Areas in Communications, Vol. 15, No.6, August 1997, pp. 1072-1086.

[2] E. Gelenbe, X. Mang, and R. Onvural, "Bandwidth Allocation and Call Admission Control in High-Speed Networks," IEEE Communications Magazine, Vol. 35, No.5, May 1997, pp. 122-129. [3] M. Grossglauser, S. Keshav, and D. Tse, "RCBR: A Simple and Efficient Service for Multiple Time-Scale Traffic," ACM Computer Communications Review, Vol. 25, No.4, October 1995, pp. 219-230.

[4] R. Guerin, H. Ahmadi, and M. Naghshineh "Equivalent Capacity and Its Application to Bandwidth Allocation in High-Speed Networks," IEEE Journal on Selected Areas in Communications, Vol. 9, No.7, September 1991, pp. 968-981.

On the efficiency of statisticai-bitrate service for video 215

[5] M. Hamdi, J. W. Roberts, and P. Rolin, "rate Control for VBR Video Coders in Broad-band Networks," IEEE Journal on Selected Areas in Communications, Vol. 15, No.6, August 1997, pp. 1040-1051.

[6] H. Heeke, "Statistical Multiplexing Gain for Variable Bit Rate Video Codecs in ATM Networks," International Journal of Digital and Analog Communication System, Vol. 4, 1991, pp. 261-268.

[7] D. P. Heyman, "The GBAR Source Model for VBR Video Conferences," IEEEI ACM Transactions on Networking, Vol. 5, No.4, August 1997, pp. 554-560.

[8] C.-Y. Hsu, A. Ortega, and A. R. Reibman, "Joint Selection of Source and Channel Rate for VBR Video Transmission Under ATM Policing Constraints," IEEE Journal on Selected Areas in Communications, Vol. 15, No.6, August 1997, pp. 1016-1028.

[9] G. Karlsson, "Capacity Reservation in ATM Networks," Computer Communications, Vol. 19, No.3, March, 1996, pp. 180-193.

[10] G. Karlsson, "Asynchronous Transfer of Video," IEEE Communications Magazine, Vol. 34, No.8, August 1996, pp. 118-126.

[11] B. V. Patel and C. C. Bisdikian, "End-Station Performance under Leaky Bucket Traffic Shaping," IEEE Network, September/October 1996, pp. 40-47.

[12] H. Saito, "Dynamic Resource Allocation in ATM Networks," IEEE Communication Magazine, Vol. 35, No.5, May 1997, pp. 146-153.

[13] T. Worster, "Modelling Deterministic Queues: The Leaky Bucket as an Arrival Process," in Proc. ITC-14, Elsevier Science, 1994, pp. 581-585.

8 BIOGRAPHIES

Gunnar Karlsson works at SICS since 1992. He holds a Ph.D in electrical engineering from Columbia University and a M.Sc. from Chalmers University of Technology. He has been project leader for the Stockholm Gigabit Network and conducts research on packet video communication, quality of service provisioning and switch architectures. He is a member of IEEE and ACM. Goran Djuknic received his Diploma and MS degrees from the University of Belgrade, Yugoslavia, and a Ph.D. from the City College, New York, all in electrical engineering. He is with Bell Laboratories, Lucent Technologies, where he evaluates the potential of satellite-based and other innovative schemes for establishing wireless communications services. He also develops new wireless data applications. He is a member of IEEE and on the Board of the Tesla Society.

17 Predictive shaping for VBR MPEG video traffic transmission over A TM networks

L. de la Cruz, l. l. Alins and l. Mata

Department of Applied Mathematics and Telematics Polytechnic University of Catalonia C/ lordi Girona, 1 i 3. Mbdul C-3, Campus Nord 08034 - Barcelona, SPAIN E-mail: {[email protected] Phone: +34-[3]4016014 - Fax: +34-[3]401 5981

Abstract The use of smoothing techniques to remove the periodic fluctuations of the bit rate generated by the codification modes of the MPEG algorithm is very suitable in video transmission. In this way, the multiplexing gain is maximized and the resource allocation is reduced in A TM Networks. The traffic smoothing can be achieved storing the cells in a buffer. This buffer is allocated between the coder and the user-interface. To reduce the delay introduced in the storage process a new technique to forecast the VBR MPEG traffic is presented. This technique is based on the characterization of bits per frame generated by the MPEG coder as an ARIMA process. In this study the invariance of the ARIMA coefficients is verified for all coded sequences used. In addition, these coefficients are invariant also in front of the changes of the selected image quality in the coder. This characterization allows to propose a new traffic shaper scheme when forecast techniques are applied. Moreover. numerical results allows to compare the smoothing effects introduced. as well as the delays for the classic shaper and the predictive shapero

Keywords ATM networks, MPEG video traffic, ARIMA process, traffic shaping

Performance of Information and Communication Systems U. Komer & A. Nilsson (Eds.) © 1998IFIP. Published by Chapman & Hall

Predictive shaping for VBR MPEG video traffic transmission 217

1 INTRODUCTION

Broadband Networks based on the Asynchronous Transfer Mode (A TM) will support, among others, traffic coming from variable bit rate video (VBR) coders, which are capable of maintaining a constant picture quality of the decoded image. The characterization of such VBR video sources becomes important in the analysis and design of Broadband Integrated Services Digital Networks (B-ISDN). The network architecture and its characteristics, such as cell-loss probabilities, transmission delay, statistical multiplexing gain, buffering, etc., are strongly related to the statistical properties of the sources and the coding schemes involved. Therefore, source models are useful to analyze and to dimension the network components (Nikolaidis, 1992)(Mata, 1996)(Mata, 1994).

On the other hand, a characterization of the traffic generated by a VBR source is necessary in order to allocate resources in A TM networks, as well as to keep a satisfactory quality of service (QoS). In the call establishment phase, service requirements are negotiated between the user and the network to establish a Traffic Contract. The source traffic parameters used to specify the statistical properties are the Peak Cell Rate (PCR), Sustainable Cell Rate (SCR) and Burst Tolerance (BT). The Generic Cell Rate Algorithm (GCRA) is used to provide a formal definition of the traffic conformance. This algorithm depends only on the increment parameter (I) and the limit parameter (L).

The MPEG coding algorithm was developed to achieve a high compression ratio with a good picture quality. MPEG can be used to transmit real-time variable bit rate broadcast video and it is suitable for video-on-demand in A TM networks (Pancha, 1994).

MPEG has two main coding modes: interframe mode and intraframe mode (I). In its turn, two types of frames can be distinguished by the interframe mode, predicted (P) and bidirectionally-predicted (B) frames. The Intra coded frames (I) are coded without any reference to other frames. Predictive coded frames (P) are coded using motion compensated prediction from a past I or P frame. This implies a more efficient coding. Bidirectionally-predicted coded frames (B) provide the highest degree of compression using the previous and next I or P as a reference. A video sequence of pictures (SOP) is divided into groups of N pictures (GOP). A GOP consists of subgroups of M pictures where the first is a reference picture, intra or predicted, and the rest are bidirectionally-predicted. The image quality depends on the values M, N and the selected quantizer step size (Q).

Four levels of coding can also be considered: picture, slice, macroblock and block. A picture (or frame) is a basic unit of display. The frame size in pixels depends on the application. A slice is a horizontal strip within a frame. According to the MPEG standard, each frame is divided into slices of 16 pixels of width, which implies that the frames are divided into 18 slices. A macroblock consists of four 8x8 blocks of luminance pixels and two 8x8 chrominance blocks. The smallest unit is a block which is a 8x8 matrix of pixels.


MPEG codec can be set in an open-loop mode to maintain the subjective quality with a fixed Q, and the coded variable bit-rate (VBR) output stream is delivered to the network. A suitable choice of Q, M, N parameters is important to minimize the traffic bit rate for a fixed subjective quality or for a constant signal-to-noise ratio (SNR). These parameters have to be selected to minimize the traffic rate for a constant signal to noise ratio (Mata, 1996).

The variations of the bit rate generated in the codification are produced by intrinsic and extrinsic reasons. The extrinsic ones are produced by the changes of the complexity and activity of the sequence to be coded. The intrinsic reasons are related, fundamentally, to the codification modes applied on the frames. Thus, the I frames need a higher number of bits than the frames P or B because the I frames only exploit the spatial redundancy using the DCT transform technique. In addition, the P frames tend to generate greater number of bits than B ones, since only motion compensation is applied respect to the previous reference image. Within the codification of the frames, another factor that give rise to variations of the generated bit rate is the exploitation of the entropy using run-length codes.

The extrinsic reasons that produce fluctuations in the bit rate depend on the content of the frames to code. The frames with greater grade of detail or greater texture have a high complexity level and reduce the efficiency of the spatial redundancy exploitation. The high activity scenes with fast camera movements, zooms and plane changes, avoid the use of the predictive compression technique. In this way, these scenes increase the binary rate with respect to smaller activity sequences.

In general, the coders do not deliver directly the traffic to the user interface because, usually, a smoothing system is enabled. The smoothing is carried out through a small storage buffer. The insertion of the buffer introduces a delay in the cells delivered to the network. The use of the smoothing allows to maintain a bit rate approximately constant during a time interval. The smoothing is applied to decrease the variability of the traffic and its peak rate. Likewise, the intrinsic periodic fluctuation of rate generated by the MPEG algorithm can be removed. In this way, the VBR MPEG traffic shaping allows to reduce the allocated resources to the virtual circuit. Moreover, the effect of the periodic arrivals to the multiplexers and switch fabrics are avoided. Therefore, the employment of the traffic shaping maximize the statistical multiplexing gain.

Most of the studies are focused on the modeling and the prediction of the rate generated in a frame interval. The main reason is that the human perceptive system does not appreciate a delay less than lOOms though it is admissible until 200 ms (Garret, 1993). Therefore, the traffic shaper can introduce a delay of only several frames. At the same time, this delay allows to use the Bidirectionally-Predicted mode in the MPEG algorithm for interactive services (Kawashima, 1993).

Depending on the temporal requirements of the service all the generated cells for the GoP can be stored. Afterwards, the cells are delivered to the network at a constant. rate during an interval of the same duration. For services with more


restrictive temporal requirements is essential the reduction of the storage time (about 80 ms). This reduction makes necessary the application of prediction techniques. These techniques permit the reduction of the traffic source burstiness and to satisfy the temporal constrains. The smoothing in intervals of duration one GoP allows to extract the intrinsic variations of the rate introduced by the MPEG algorithm. In this way, the rate generated only depends on the complexity and activity of the scenes.

This paper is organized as follows. In section 2 the ARIMA process is revised for digital filter theory point of view. Analyzing the coder data traces, the VBR MPEG traffic is characterized as an ARIMA process in section 3. Likewise, the perfect capture of the compressed video traffic by the ARIMA process is shown for all the long and short sequences analyzed using residual diagnostic goodness-of-fit tests. This characterization is proposed to forecast the VBR MPEG traffic in section 4. In order to evaluate the temporal response of the predictor, its behavior is also studied in sudden scene changes. The invariance of the ARIMA coefficients for all the sequences analyzed allows to introduce a new traffic shaper for VBR MPEG video in section 5. Finally, the main results of this work are discussed in section 6.

2 THE ARIMA PROCESSES

These processes have been widely studied in the literature and in their more general form are denominated autoregressive, integrative, moving average processes (ARIMA) (Box, 1994). The autoregressive models are used in the context of sources of synthetic traffic or in traffic forecast for the generation of series of rates in intervals of fixed duration (Grunenfelder, 1991)(Yegenoglu, 1993). The ARIMA(p,d,q) models are decomposed in an autoregressive component of order p, an integrative component of order d and a moving average component of order q.

The autoregressive component reflects the dependence between the current generation and the last p generations. Thus, for an AR(p) process the values generated in a time series y=(Yo'Y., .. ,Y.) are obtained from the p past values and an independent factor from the times series. This factor can be modelled as a process with identically independent distributed values W =(wo,w., .. w.). The time series W are denominated residual series. These time series are considered as the prediction error of the following generation of the process. Customarily, the values from the series W are synthesized as the realization of a gaussian variable with an average and a standard deviation directly related with the corresponding moments of the process AR to generate. So that:

y(n)=a.y(n-l )+~(n-2)+ ... +a.,y(n-p )+w(n), (1)

where the terms 8i are constant coefficients.


The MA( q) component of the process reflects the dependency in the generation of the past values of the independent process that contributes in the obtained value. In this way, a MA(q) process would be expressed as:

x(n)=bow(n)+b lw(n-l)+bzw(n-2)+ ... +bqw(n-q), (2)

where the terms bi are constant coefficients.

The integrative contribution allows to capture the non stationarity of the moments of the stochastic process. Although the integrative component can be considered within the AR component by its formulation, its synthesis depends on different factors. Thus, the integrative component also shows the dependence with past values of the series but its synthesis depends on the non stationary moments of the process. The order d of the integrative component is fixed by the order of the highest non stationary moment of the stochastic process. In general, the integrative component can be expressed:

z(n)=clz(n-l )+czz(n-2)+ ... +cdz(n-d)+w(n), (3)

where:

Cj = (~}_l)i + 1 i E {1.2 ..... d}. (4)

For example, a process whose mean is non stationary and the rest of high order moments are stationaries would have an integrative component of order 1. This integrative process is the so-called "random walk". If the behavior of the variance shows a clear trend during long intervals it is convenient to apply a transformation like the Box-Cox (Box, 1994).

The interpretation of a process ARIMA(p,d,q) can be carried out defining the delay operator Z·I (Proakis, 1983). So that, the general expression of an ARIMA(p,d.q) process can be expressed by its Z transform as:

Y(z) = [B(z)A(z)C(z)]· W(z). (5)

Understanding this expression as the relationship between the input w(n) and the output y(n) of a digital filter in a given instant n, the transfer function of the filter H(z) could be define as:

Y(z) H(z) = - = B(z)A(z)C(z) .

W(z) (6)


Note that the roots of the polynomial B(z) correspond to the zeroes of the filter and the zeroes of AI(Z) and C-I(z) to the poles. According to the definition of the cj

values expressed in (4), the integrative order defines the multiplicity of the pole in z=l. This pole generates the instability of impulsional response. The rest of obtained poles (Zk) will be found in the unit circle (Izki< 1) of the Z plane. In Figure

1 a scheme of the ARIMA model is shown. ,------------,

weill MA /x(n)1 AR ~ I ~n) ,I B(z). A(z) I I C(z) I r L ____________ ,

Figure 1. Components of an ARIMA process.

3 CHARACTERIZATION OF THE VIDEO TRAFFIC VBR MPEG AS AN ARIMA PROCESS

The temporal series of the VBR MPEG-I traffic presents a slow variation of the mean rate for several hundred of frames. This variation is related to the activity and complexity of the scene. The long range dependence complicates the development of a predictor because the temporal series shows an apparent non stationary mean. In order to synthesize a good predictor it is necessary to capture this long term effect. In this section, a new ARIMA model for the VBR MPEG traffic has been developed to find the predictor. Three sequences have been used to find and evaluate the predictor, "Live in Central Park" (by "America"), "Jurassic Park", and "Geografia de Catalunya" which are 34000, 174000 and 51000 frames long, respectively. The sequences have been coded using the parameters (Q =9, M= 2, N= 6), (Q= 6, M= 2, N= 6) and (Q= 6, M= 2, N= 6), respectively. The first and the second sequences presents the classic characteristics of activity and complexity, while the third has high complexity levels and short length scenes. Likewise, the results have been contrasted with the ones obtained for the sequence "Live in Central Park" coded with the set of parameters (Q =9, M= 2, N= 4).

In order to develop the ARIMA model, initially, the integrative component is found. The long term dependence produces that the mean rate varies slowly for several hundreds of frames. This variation reaches maximum and minimum levels which are very distant. However, the variance remains almost constant. This allows to conclude that the integrative component of the model should be of order 1 and its associated transfer function C(z)=(1-Z·lrl.

In order to determine which are the values of the AR components and MA, it will be necessary to extract the integrative component of the actual process s(n). According to the scheme presented in Figure 1 the residual ARMA series y(n) and the real series s(n) are related as follows:


Y(z) = _1_S(z) = (1- Z-l )S(z) . C(z)

(7)

In this way, the temporal series y(n) will be obtained at the output of the FIR filter, whose transfer function is (l-Z·I), when it is excited with the temporal series generated by the coder. It can be checked that the temporal series y(n) is a stochastic process with mean 0 and an invariant autocorrelation coefficients. This statistical analysis has been carried out with the three sequences using blocks of 15000 frames and with autocorrelation lags of 100 units. The probability distribution function fits a gaussian distribution in all cases. The difference noted in the three temporal series is the standard deviation. This dissimilarity is related with the variability and complexity of the sequences.

The temporal series y(n) presents a seasonal behavior (Box, 1994) of period N= 4 or N= 6 according to the parameter chosen in the MPEG algorithm. Using the peaks of the autocorrelation function, which appear in mUltiples of N, the AR component can be synthesized. To determine the coefficients of the AR component Least Squares estimation has been employed. The order of the seasonal model found is 2.

The MA component can be analyzed when the AR component of the y(n) series is withdrawn. Using a FIR filter with transfer function AI(Z) the series x(n) can be obtained at the output of this filter when y(n) is applied at the input. To estimate the parameters of the MA process, least square estimation is applied to fit the partial autocovariance function of x(n). The best adjustment is obtained with a MA process with order 13.

The values of the AR and MA filter's coefficients, and a more detailed explication, can be found in (De la Cruz, 1997 b).

The integrative component of the obtained model has order 1. Thus, the integrative and the autoregressive components can be written together in the following way:

A'(Z) = A(Z)C(Z) = A(ZX1-z-1). (8)

The generated series can be expressed as:

s(n) = bow(n)+.·+bqw(n - q)+ alsen -1)+··+a~+ls(n - p -I). (9)

where the a; coefficients are obtained applying the inverse Z transform to A'(z).

4. VBR MPEG TRAFFIC PREDICTION

In this section, the ARIMA predicter for the bit rate generated by a VBR MPEG coder is developed. The predicter is based on the obtained ARIMA model. This


prediction will be used in the next section to shape the traffic before deliver it to the network.

From (9), the (n+l) sample prediction is:

Nevertheless, in the prediction context the values of the w(n) series are unknown. The predicter will have only the previous values of the s(n) series. Moreover, the W(n + 1) is a future value. The forecast value of w(n + 1) will be the mean value of

the w(n) series. In this case, the mean value is O. Thus, the (n+ 1) sample prediction can be written as:

s(n + 1) = bl w(n)+ .. +bq w(n - q + 1) + a;s(n) + a2s(n -1)+ .. +a~+ls(n - p). (11)

On the other hand, from (9) it is also possible to write:

s(n) = boW(n) + qw(n -1)+ .. +bqw(n - q)+ a;s(n-1)+ .. +a~+ls(n - p -1). (12)

Subtracting (12) to (9):

s(n)- sen) = bo(w(n)- W(n»).

As it has been mentioned, the forecast value of W(n) will be 0, so:

s(n)- sen) = bow(n) .

Therefore:

w(n)= s(n)-s(n) . bo

(13)

(14)

(15)

Replacing this value in the equation (16), the (n+1) sample prediction can be written as:

sen + 1) = _1 [i1(s(n)- s(n»)+ .. +bq (s(n - q + 1)- s(n - q + 1»)]+ bo

+als(n)+a2s(n-l)+ .. +a~+ls(n- p) (16)

The derived ARIMA predicter is shown in Figure 2. The predicter supplies the estimated value for the (n+l) sample as a function of the n previous ones. This set


of samples can be used also to obtain a prediction of the samples "2 ahead", "3 ahead", etc. Running the predicter with the (n+j) sample estimation, it supplies an estimated value of the (n+j+ 1) sample.

;(,,+1)

Figure 2. ARIMA Predicter.

In order to evaluate the behavior of the above transfer function, an analysis of the forecast errors has been done for all sequences. Figure 3 presents the residuals autocorrelation and the 99% confidence intervals. The residual diagnostic determines that the forecast errors are very uncorrelated. Therefore, the ARIMA model fits well the behaviour of the VBR MPEG traffic at frame level. This model could not be used to synthesize VBR MPEG traffic because the temporal series generated has a variant unbounded mean. In order to observe the temporal response of the prediction, a sudden scene change is analyzed. This response is shown in Figure 4.

0.75

0.'

0.25

autocorrelation index

"uve in Central Park"

"Geografla de Catalunya"

"}urask Park"

Figure 3. Autocorrelation function of the forecast errors using the ARIMA predictor.

:::,------="'-----,--,--.,-------, ·-.. ·····_"d __ ••••

... Codor_

:::

Figure 4. Unit step response of the ARIMA predictor.


5. VBR MPEG TRAFFIC SHAPING

The use of video compression algorithms like MPEG-I causes the variation of the generated bit rate for the images according to the coded mode I, P or B . In order to minimize the variability of the generated rate, traffic shaping is needed. This traffic shaping could be achieved for several images. To smooth the generated traffic, a number of images have to be stored in the buffer until the mean rate required is determined. This mechanism could only be applied to services which accept a transmission delay higher than the required time introduced in the stored process.

To avoid high delays for interactive services the use of prediction techniques is suitable. In this section a new VBR MPEG traffic shaper based on these techniques is introduced. It performance is studied for all the sequences under study. Moreover, it is compared with the classic storing systems. These systems are presented in the first place.

5.1 Storing systems

The most classic smoothing system is based on the storing of a number of frames. Later, the frames are delivered to the network at a constant rate. This rate will be the mean rate obtained for all the stored pictures. This kind of smoothing has been called "ideal smoothing" in previous works (Lam, 1996). Generally, the number of pictures used to calculate the mean rate is N, that is, the number of pictures in a GoP. Let S(n) be the n picture size. Thus, the ideal shaper will deliver the information of the previous GoP at the following rate:

S(n)+S(n+l)+ .. +S(n+N -1) r= ,

N-r (17)

where 't is the frame period. The main disadvantage of this shaper is the introduced smoothing delay. Observe

that for a given frame, the delay in the buffer can reach (2N't) seconds. For instance, in a system working at 25 pictures per second and N=6, a given picture can be delayed even 480 miliseconds. This delay can be admissible for broadcast services, but it is not suitable for interactive services. In Figure 5, the results of the ideal shaper for a section of the "Jurassic Park" sequence is shown. The selected section presents sudden transitions of scenes. The introduced delay is presented in Figure 6. The unit chosen to represent the delay has been the frame period.

Another kind of smoothing consist of update the obtained mean for every frame. That is, the picture n will be delivered to the network at the following rate:

S(n-N)+S(n- N + 1)+··+S(n-l) ~~= ,

N-r (18)


In this method, the rate is updated for every frame, so it is possible to call it "sliding smoothing". Note the main difference between the two methods presented: in the fonner, the window used to calculate the mean is static for every frame in a same GoP, while in the latter this window is varies for each frame. Figures about this kind of shaping can be found in (De la Cruz, 1997a).

1~r---------------------------------~

14<XXXl

40000

20000

o~~~~~~~~~~~~~~~~~~

15913172125293337414549535761656973778185899397

frame number

Figure 5. Ideal smoothing

_8

~ 7

~.g 6

-i '5 "CI 11/ 4

~ 3 =2 ~ ~ H ~ ~ = ; ~ ~ = ; : ~ = ; = • ~ :

frame nulTber

Figure 6. Delay introduced by the ideal smoothing

Some of the numerical results obtained are shown in Table 1. In this table, the two previous methods are compared. In both cases, there is a great reduction in the quadratic coefficient of variation, C,2, and in the burstiness, B,. These parameters measure the variability of the rate, and they are defined as follows:

B = 'peak r _. (19) ,

In the worst case, B, is reduced in a 20%. This will give rise to a considerable improvement in the resources allocation over A TM networks.

The main disadvantage for the two previous methods is the delay. For the sequences under study, the worst case presents a maximum delay of 10.2 frame


periods, that is, 408 miliseconds for the systems working at 25 pictures per second. Note that the QoS will be fixed for this maximum delay.

On the other hand, the shaping goodness can be studied also in terms of the autocorrelation function. This function is shown in Figure 7 for the ideal smoothing. Results for sliding smoothing are very similar. In both cases, the extraction of the periodic peaks is verified. Therefore, both kind of shaping presents good characteristics for services without strong delay constraints. However, these shapers are not suitable for interactive services.

0.9

C 0.8

j ~: 11/ :: 0.5

go., ; 0.3

" 0.2

0.1 ---Ortgiml ................ -Ideal o~+-+-__________ ~~~~-+-+-+-+-+ ____ ~

o I 2 3 .4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

lag

Figure 7. Ideal shaping autocorrelation

Table 1 Shaping methods comparison

Shaping C2 , B, Min. delay Max. delay Mean delay

None 0.52 5.96

Ideal 0.27 4.73 4.5 9.6 7.4

Sliding 0.28 4.77 3.0 10.2 5.6

Predictive 0.28 4.77 3 2.03

5.2 Predictive shaping

In the previous section, two shaping methods have been studied. They are based on the stored samples. In this section, a predictive shaper scheme is presented. The main goal of the new scheme is to achieve a small and bounded delay. The


predictive shaper is based on the developed ARIMA model to forecast the future samples.

In Figure 8 the structure of a generic traffic shaper is presented. This structure contains a buffer to temporarily storage the information generated by the coder. This information will be packetized and delivered to the network at a given rate. This rate is calculated for the controller. In the methods studied in the previous section, this controller is mainly an averager. The mean of the N previous pictures is used to obtain the output rate. With the ideal smoothing, this rate will be constant for all frames in the same GoP. When the sliding shaping is applied, the output rate is calculated for each frame.

The controller for the new predictive scheme is presented in Figure 9. In this case, the controller use K samples to determine the output bit rate. The K samples are distributed in the following way: LJ samples from the past and L2 samples forecast by the ARIMA predicter. The current sample is included in LJ' so K=LJ+L2• With these K samples, the controller calculates the mean value. This value will be the output rate supplied to the buffer.

SHAPER .- - - - - - - - - - - - - - -I 1

..... ___ ---II--';(-n )...,.I-r---.. ••• 11 MPEGCODER

Figure 8. Traffic shaper.

r;(n)

To(n)

: . : .....................•

J ------------Figure 9. Predictive controller.


In particular, in the presented controller it will not be necessary a number Ll greater than one. All the needed information about the past is included in the current sample and in the buffer fullness b(n-l). The controller will use this quantity in order to calculate the minimum rates necessaries to keep the delay under a given value.

On the other hand, the minimum number needed of future samples will be the necessary to complete a GoP, that is, (N-1) samples. Thus, the controller has the information about all the I, P and B frames in a GoP, in order to calculate the mean rate. In previous works (Lam, 1996), the possibility of working with a number of predicted samples greater than N has been refused. Here it is possible to corroborate this assumption, since the prediction of a second GoP will be practically the same than the first one. Thus, it will not introduce any difference in the output rate. Nevertheless, the prediction chosen in (Lam, 1996) for a given picture is the bite rate of the equivalent picture in the previous GoP. That is, the bit rate estimated for the (n+ 1) picture is the bit rate of the (n-N+ 1) one. This prediction is very accurate when there is not scene changes. However, when a sudden transition occurs, the prediction is not accurate. The difference is shown in Figure 10.

2rom,------------------------------------,

---0-- Original sequence " .. -0. " .. Prediction based on p-evious GoP .•. -<>- . .. ARIMA prediciton

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 A' flame nwd»er

Figure 10. ARIMA prediction and. "previous GoP" prediction.

As it has been mentioned, the buffer fullness information will be employed by the controller. This information is necessary when the shaper has to offer a given QoS, that is, a maximum smoothing delay. Using the buffer fullness, the shaper can obtain a minimum rate for each frame in order to keep its delay under a minimum. This minimum rate will be calculated as a function of the picture size S(n), the buffer fullness b(n-l), and the maximum delay allowed D:

( ) _ S(n)+b(n-l) Tmin n - ,

D-r (20)

where D is expressed in frame periods.


The controller will work normally in the same manner explained previously. Nevertheless, it will have in memory a minimum output rate for every picture which has not been yet completely extracted of the buffer. Therefore, the minimum output rate will be the maximum of these bounds. This mechanism can be called "rate corrector".

A section of the sequence "Jurassic Park", and its predictive smoothing with D=4, D=5 and D=6, are presented in Figure 11. Note that if the maximum delay allowed is D=I, the shaped sequence is the same than the original one. The section chosen for both figures presents a sudden negative transition. It is possible to observe that the smoothing is better when the allowed delay D is greater. The introduced delay in every case is presented in Figure 12. In this figure, it is shown that maximum delay is not exceeded in any case.

~r---------~--------------------------~

7!XXXl t.A.../J,...J.J,-A-M-H~ ~6!XXXl ~5OCXX) ;; <0000

~3<XXXl ;S2!XXXl

1!XXXl

----Olgrd _ •• _ •• -[).4

••••••••• ().6

().6

I 3 5 7 9 II 13 15 17 19 21 23 25 27 :29 31 33 35 37 39

Irame number

Figure 11. Predictive shaping in a negative transition.

11-1 ••••••••• D ... - ----- ---- -

Figure 12. Delay in a negative transition.

Analyzing the previous results, the worst cases appears when sudden negative transitions occurs. This is due to the following reason. In these moments, the predicter will calculate a low output rate, according to the low new rate coming from the coder. However, there is still in the buffer a lot of information. It is the remaining information from de previous frames. These frames were coded with a great number of bits, but now the shaper tries to extract them out of the buffer at a


low bit rate. At these moments it becomes necessary to correct the output rate, with the "rate corrector" mentioned above.

The numerical results obtained with this new shaper are presented at the end of Table 1, for the sequence "Jurassic Park" and for D=3. As with the previous kinds of shapers, the quadratic coefficient of variation and the burstiness are strongly reduced. However, the introduced delay is smaller and perfectly bounded. This characteristic permits the use of this kind of shaping with all the services.

The final test to determine the goodness of the new scheme consist of checking the autocorrelation function, in order to observe if the periodicity of the sequences is extracted. In Figure 13, this function is presented for the cases D=1 (that is, the original sequence), D=2 and D=3. It shows that for D=I, the sequence has a great periodicity. This periodicity is strongly reduced for D=2, but it is still possible to observe some peaks every (iN+l) lags. This peaks are completely extracted for D=3. The obtained functions for D greater than 3 are not presented because they are very similar with the case 0=3. From this figure, this analysis permits to conclude that the maximum decorrelation of the output sequence is achieved for values of D greater or equal than 3. This will give rise to an improvement in the statistical multiplexing gain over A 1M networks. For stronger delay constraints, the shaper could be used with D=2. In this case, the improvement in the resources allocation is reduced.

The different tests has been carried out also with the sequences "America" ("Live in Central Park") and "Geografia de Catalunya", with very similar results .

............... .. c~:\ /\ ...................... _ .. _ ..... _ .. , ..

i" \ t tl / \ 1\ A \ /\ j\ ' \ I~ V V V V / V V \ V \

01 ---[)'l ---t><1 ......... o.'l

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

lag

Figure 13. Predictive shaping output autocorrelation

6. CONCLUSIONS

In this paper, a new VBR MPEG traffic shaper is presented. This shaper use prediction techniques to smooth the traffic. In this case, the applied technique is based on the characterization of real traffic as an ARIMA process. The long range dependence of the VBR MPEG traffic can be approximated with the integrative component of the ARIMA process. In this way, the predictor is very accurate in a short temporal range. This short temporal dependence is captured from the autoregressive and the moving average components of the ARIMA predictor. A


result of this work is the invariance of the ARIMA coefficients obtained for all the real data sequences analyzed. Moreover, the invariance is also presented from the quantizer step set on the MPEG VBR coder. This invariance allows to apply the VBR MPEG traffic shaper to coders which vary the image quality according to the congestion level in the A TM networks.

The new shaper scheme has been compared with the classics storing systems. The main disadvantage of these systems is the delay introduced in each frame. Nevertheless, the new scheme has a smaller and bounded delay. This characteristic allows to employ this shaper for interactive services, where small delays are needed.

In order to synthesize artificially VBR MPEG traffic an integrative component as H-I/2

(1-z-l) can be applied. In this way, the Hurst parameter (H) define the persistence of the process. This persistence or self-similarity is associated to the long range dependence of the process. Future works will be focused in this sense using fractional ARIMA process to obtain a new model with bounded mean.

7 REFERENCES

Box, G.E.P., Jenkins, G.M. and Reinsel, G.C. (1994) Time Series Analysis. Prentice Hall, New Jersey.

De la Cruz, L., Alins, J., Pallares, E., Fernandez, M. and Mata, J. (1997a) Conformaci6n predictiva de trafico de video VBR MPEG a partir de su caracterizaci6n como proceso ARIMA, Jornadas de Ingenierfa Telematica JITEL'97, 197-208.

De la Cruz, L., Alins, J. and Mata, J. (1997b) Prediction Techniques for VBR MPEG Traffic Shaping. Proceedings of IEEE GLOBECOM'97, 3, 1434,39.

Garret, M.W. (1993) Contributions Toward Real-Time Services on PacketSwitched Networks. Ph.D. Dissertation CUlCTRffR 340-93-20, Columbia University, New York.

Grunenfelder, Cosmas, Manthrope and Odinma-Okafor (1991) Characterization of Video Codecs as Autoregressive Moving Average Processes and Related Queueing System Performance. IEEE J. on Selected Areas in Communications, 9, no. 3, 284-92.

Kawashima, K., Chen, c., Jeng, F. and Singhal, S. (1993) Adaptation of MPEG Video Coding Algorithm to Networks Applications. IEEE Transactions on Circuits and Systems for Video Technology, 3, no. 4, 261-9.

Lam, S.S., Chow, S. and Yau, D.K.Y. (1996) A Lossless Smoothing Algorithm for Compressed Video. IEEElACM Transactions on Networking, 4, no. 5, 697-708.

Mata, J. and SalIent, S. (1996) Source Traffic Descriptor for VBR MPEG in ATM Netwoks, in Multimedia Communications and Video Coding (ed. Plennum Press).


Mata, J., Pagan, G. and SalIent, S. (1996) Multiplexing and Resource Allocation of VBR MPEG Traffic on ATM Netwoks. Proceedings of the IEEE ICC'96, 3, 1401-5.

Mata, J., SalIent, S., Balsells, J., Zamora, J. and Van der Kolk, A. (1994) Statistical Models for MPEG Video Standard. Proceedings of lEE EUSIPCO'94, 1, 624-7.

Nikolaidis, I. and Akyildiz, I.F. (1992) Source Characterization and Statistical Multiplexing in A TM Networks. Paper of the College of Computing. Georgia Institute of Technology, Atlanta, USA.

Pancha,P., and EI Zarki, M. (1994) MPEG Coding For Variable Bit Rate Video Transmission. IEEE Communications Magazine, 32, no.5, 54-66.

Proakis. (1983) Digital Communications. McGraw-Hill, New York. Yegenoglu, F., Jabbari, B. and Zhang, Y. (1993) Motion Classified Autoregresive

Modeling of Variable Bit Rate Video. IEEE Transactions on Circuits and Systems for Video Technology, 3, no. 1,42-53.

ACKNOWLEDGEMENTS

This work has been developed using the Global A TM Standard Simulator (GLASS) and supported by the SIGLA (GLASS) Project [Spain CICYT, TEL 96-1452].

18 Circulant matching method for multiplexing ATM traffic applied to video sources *

K. Spaey c. Blondia University of Antwerp Department of Mathematics and Computer Science Performance Analysis of Telecommunication Systems Research Group Universiteitsplein 1 B-2610 Wilrijk - Belgium { spaey, blondia} @uia.ua.ac.be

Abstract In this paper a method is proposed, called circulant matching method, to approximate the superposition of a number of discrete-time batch Markovian arrival sources by a circulant batch Markovian process, while matching the stationary cumulative distribution and the autocorrelation sequence of the input rate process. Special attention is paid to periodic sources. The method is applied to the superposition of MPEG video sources and the obtained results are validated through experiments.

Keywords Multiplexing, circulant matching method, periodic sources

1 INTRODUCTION

Defining appropriate models for traffic streams in ATM networks has been the subject of intensive research during the past ten years. Several models, together with the corresponding queueing systems, have been proposed. In this paper, a matrix-analytical approach is followed, by choosing discete-time batch Markovian arrival processes (D-BMAPs) (see (Blondia 1993)) as model for ATM traffic. A basic problem in traffic engineering of ATM networks is the computation of the buffer occupancy and waiting time distribution of a single server queue with deterministic service time (i.e. the time needed to transmit a cell) and input consisting of a superposition of processes modeling ATM traffic streams. A major problem encountered when solving this system

"This work was supported by the Commission of the European Union, under the project ACTS AC094 EXPERT

Perfonnance of Infonnation and Communication Systems U. Komer & A. Nilsson (Eds.) @ 1998 IFIP. Published by Chapman & Hall

Circulant matching method for multiplexing ATM traffic 235

is the explosion of the state space when the number of input sources takes values that are typical for real life situations.

In this paper, a solution is proposed which reduces the state space of this model drastically. This method, called circulant matching, is based on an approach proposed in (Hwang et al. 1995) and makes use of a traffic spectral representation, which was first introduced to queueing analysis by S.Q. Li et al. (see e.g. (Li et al. 1992)). A number of independent D-BMAPs form the input process of a single server queue. The exact superposition of these processes is again a D-BMAP, with number of states equal to the product of the number of states of the individual D-BMAPs. The idea is to replace this D-BMAP by a D-BMAP with a smaller circulant transition matrix which matches two important statistical functions of the exact input rate process, namely the stationary cumulative distribution and the autocorrelation sequence (characterized in the frequency domain by means of the power spectrum). The transition matrix is chosen to be circulant in order to avoid solving an inverse eigenvalue problem. Once the circulant D-BMAP is found, the problem is reduced to solving a D-BMAP/D/1/K+1 queue, for which efficient methods to compute the stationary queue length distribution are available (see e.g. (Blondia et al. 1992)).

The proposed approach is illustrated by means of the evaluation of the cell loss ratio (CLR) in a multiplexer that is fed by a number of video sources. The CLR values resulting from the circulant matching method are compared with those obtained from a series of experiments (Aarstad et al. 1998) performed within a European project in the ACTS programme, EXPERT.

The paper is organized as follows. Section 2 gives a detailed description of the circulant matching method, emphasising the differences with the approach proposed by S.Q. Li and paying special attention to periodic sources. In Section 3, the results are applied to the superposition of video sources, in particular to an MPEG source type model. Comparison with the experimental results is made in Section 4. Finally, conclusions are drawn in Section 5.

2 MULTIPLEXING OF DISCRETE-TIME BATCH MARKOVIAN ARRIVAL PROCESSES

2.1 Discrete-time batch Markovian arrival process

A class of stochastic processes which is often used to describe the stochastic nature of an ATM source is the class of processes which are modulated by a Markov chain. A discrete-time process which belongs to this class is a discretetime batch Markovian arrival process (D-BMAP) (Blondia 1993).

A D-BMAP is characterised by a sequence of matrices (Dk)k>O and can be defined as follows: the matrix D = L~o Dk is the transition "i"natrix of a discrete-time Markov chain of dimension m + 1. Suppose that at time n this


chain is in some state i, 0 ~ i ~ m. At the next time instant n+ 1, there occurs a transition to another state j, 0 ~ j ~ m with probability (D)i,j at which a batch arrival mayor may not occur. The matrix Do governs transitions that correspond to no arrivals while the matrices Dk, k 2: 1, govern transitions that correspond to arrivals of batches of size k. Let 11' be the stationary distribution of D, i.e. 11' D = 11' and 1I'e = 1, where e is a column vector of 1 'so The mean arrival rate). of the process is then given by ). = 1I'(L:~o kDk)e. For more details and properties, see (Blondia 1993).

2.2 Multiplexing of D-BMAPs: problem description

The superposition of M independent D-BMAPs (Dii)k~o, can again be de

scribed by a D-BMAP (Dkh?o with D = ®:!1 D(i), Do = ®:!1 D~i), D1 = (1) (101M (i)) (IOIM-1 (i)) (M) D1 ® lOIi=2 Do + ... + lOIi=l Do ® D1 , ... where ® denotes the

Kronecker product. It is clear that this superposition leads to a state space explosion, which implies that in practice, (Dkh?o is not usable. Therefore, the exact aggregate arrival process is replaced by another, but simpler process, which matches the exact one as close as possible for some important statistical functions. Preferable, the new process is again a D-BMAP, such that it is possible to keep on working within the same framework.

In (Hwang et al. 1995), it is proposed to replace the superposition of continuous-time Markov modulated Poisson processes (MMPPs) by a MMPP with a special structure, called circulant modulated Poisson process (CMPP). This process has a completely different Markovian structure from the superposition, but approximates two important statistical functions of the input rate process: the cumulative distribution representing the stationary statistics and the autocorrelation function in the time domain or equivalently the power spectral function in the frequency domain representing the second order statistics. In the next section it will be demonstrated that this method can be adapted for discrete-time Markov models such as D-BMAPs without too much difficulties, and leading to the result that the superposition of D-BMAPs can be replaced by a circulant D-BMAP. Simultaneously, the method will be extended such that the periodicity which is often noticed in the transition matrix of D-BMAPs, and thus also in their exact superposition, is preserved. Examples of periodic Markov sources are the MPEG model which will be used in section 3 and the model to describe the traffic profile of a tagged CBR connection after it has been jittered by background traffic (Blondia et al. 1995). Recent works studying and capturing periodicities present in real-time applications are e.g. (Lazar et al. 1993) and (Landry et al. 1997).

2.3 The circulant matching method

The input rate process of a D-BMAP (Dk)k>O which is assumed to be irreducible and diagonalizable is defined by rem), with rem) = r i while the

Circulant matching method/or multiplexing ArM traffic 237

Markov chain is in state i at the m-th time slot. The input rate in a slot is thus a stochastic variable r which takes the values r o, ... , rN-l with probabilities 1I"0, ••• ,lI"N-l, where

N-l 00 00

r i = L (LkDk) .. = (LkDke) .. j=O k=O '.3 k=O '

(1)

The autocorrelation sequence R[n] of the random process r(m) is defined as R[n] = E[r(m)r(m + n)]. This gives for a D-BMAP

R[O] = 7r [ (~kDke ) 0 (~kDke) ] , (2)

00 00

R[n] = 7r(L kDk )D1nl-l (L kDk )e, n#O k=O k=O

where 0 denotes the element-by-element product of two vectors. As D is supposed to be diagonalizable, D can be written as D = E:-:~l AIglh/, where Al is the l-th eigenvalue of D and gl' resp. hi, is the corresponding right column, resp. left row, eigenvector such that hlgl = 1, from which

N-l 00 00

R[n] = L (A/)lnl-l1/J/, n#O 1=0

with 1/J/:= 7r (L kDk )glhl (L kDk) e. (3) k=O k=O

Remark that if Al = 1, V1fii is the mean arrival rate. Since D is the transition matrix of an irreducible Markov chain, IA/I ~ 1, VI, and 1 is always a simple eigenvalue of D which will be given the index zero: AO := 1. For each eigenvalue, denote Al = IA/leiw, and 1/JI = I 1/Jdeill, and define n to be the collection of all eigenvalues of D: n = {>.o, ... , AN-d. By distinguishing between the different types of eigenvalues, from (3) one derives after some manipulation that

.\,E(OnR\{O,l,-l} ) ",E(OnC) 1(",»0 1"11<1

where I{a} is the indicator function of event a.

",E(OnC) 1(",»0 1"11=1

l1/Jd cos(lnlwl) +

(4)

Remark that the second and fourth term in this expression disappear if the transition matrix D is aperiodic, since only periodicity of D implies the existence of eigenvalues different from 1 on the unit-circle.

The autocorrelation sequence in the time domain is equivalently characterized in the frequency domain by its power spectrum P(w) = Et~oo R[k]e-ikw , which is the discrete-time Fourier transform of the autocorrelation sequence.


Since P(w) is periodic in w with period 21T, only angular frequencies (expressed in rad/sec) in the range -1T < W ~ 1T need to be considered. By using (4), a formula for P(w) is obtained from which the contribution of each eigenvalue of D to P(w) can easily be read:

P(w) = R[O] - tPo + 21TtP06(W) + tPo - 21TtPo6(W - 1T)I{>."eo and ,x,,=-I}

+2 L tP COSW-AI ( \{ }) '1 - 2AI COSW + (A/)2

,x,e OnR 0,1,-1

+ L (-2ItP/I + 21TltPd6(w + WI) + 21TltP/16(w - WI») ~,E(nnC) I(~,»O

l~d=l

+4 ~ lR{tP COSW-AI } L..J '1 + (A/)2 - 2AI COSW

~,E(nnC) I(~,»O

1~,I<l

where 6 is the Dirac delta function.

with - 1T < W ~ 1T,

(5)

As can be seen from this formula, the discrete part in the power spectrum is caused by the eigenvalues with modulus 1.

If now not only one D-BMAP is considered, but M independent D-BMAPs (Dii»k~O' 1 ~ i ~ M, the autocorrelation sequence of the superposition is given by

M M M

R[n] = L R(i) [n] + 2 L L J tP~i) J tP~j) (6) i=1 i=1 j=i+l

and thus

(7) i=1 i=1 j=i+l

This means that the power spectrum of the aggregate process is completely known by all the eigenvalues of the D-BMAPs (Dii»k~O and their contribution to their power spectrum. If now all M D-BMAPs are identical, or can be divided into a limited number of groups of identical D-BMAPs, a lot of contributions to P{w) come from the same eigenvalues and can be merged together. Thus, if a D-BMAP (Qkh:>o could be constructed with as eigenvalues of Q the eigenvalues that contribute to P(w) in (7), a new D-BMAP could be obtained with the same power spectrum Pc{w) provided that it is possible to tune the (tPc)"s of this new D-BMAP.

To avoid the construction of Q to be equivalent to solving an inverse eigenvalue problem, Q must be such that its eigenvalues are known in closed form.

Circulant matching method/or multiplexing ArM traffic 239

As in (Hwang et al. 1995), a N-dimensional circulant is used:

(8)

Its eigenvalues are given by (Ae), = Ef:c/ ajd', where c:= e~. Also the Qk's will be chosen in an appropriate way such that, as in (Hwang et al. 1995) for the CMPP, the approximating process will be completely determined by two vectors, namely a, the first row of Q and a rate vector 'Y. Q k will be ch h (Q ) (-y)ke-'Yi H h Q ' al b osen ere as k:= a(j-i)modN • k! • owever, t e k s may so e chosen differently. As long as E~o kQk = aT 'Y, everything what follows will stay valid. Thus, it is also possible to define only a finite number of Q k 's different from the zero matrix. In any case, the input rate vector r will then equal the rate vector 'Y.

To find a, a set of linear programming problems equivalent with those described in (Hwang et al. 1995) have to be solved until a solution is found. The only difference is that there ae needs to be zero (since a CMPP is a continuous-time Markov chain) while here it needs to be 1, with all aj ~ 0 for 0 ~ i ~ N - 1. In our implementation of this solution method, the faster index search algorithm (ISA) as proposed in (Che et al. 1997) is used instead of the ad-hoc scheme developed in (Hwang et al. 1995).

An extension to periodic transition matrices is made in the following way: if Q needs to have a period d > 1, it suffices to search only for eigenvalues with an argument in [0, 2; [, because the set of eigenvalues of a periodic irreducible matrix, regarded as a system of points in the complex plane, is invariant under a rotation of the plane by the angle 2; (see (Qinlar 1975)). By imposing that all the aj's, with i =I- kd + 1, for some kEN are zero, also the eigenvalues with argument outside [0, 2; [ will automatically be eigenvalues of Q.

Once the solution a is found, the contribution (t/Je)' of each eigenvalue (Ae), to the power spectrum Pe{w) of the approximation has to be found. For

a circulant D-BMAP, (t/Je)' = ~(E.f=;~l'YjC-'j)(Ef=-~/'Yjdj){Ae)I' which

implies that (t/Je)' is a positive real multiple of (Ae),. By defining {3k as {3k = -if E~Ol 'Y,dk , and transforming it to polar notation, (3k = ..f5(keiOtk ,

(t/Je)' can be written as (t/Je)' = X,(Ae),. So, the problem is reduced to finding positive real X, 'so Of course the constructed Q has also other eigenvalues besides the envisaged eigenvalues. To eliminate their contribution to Pe(w), the corresponding X,'s are chosen zero. The X,'s corresponding with eigenvalues of modulus one can be calculated exactly such that the discrete part of the power spectrum which is introduced by those eigenvalues is matched exactly: if

{Ae)O = 1 then Xo := (E:!l J t/Jai ») 2, if (Ae)a = -1 then Xa := - E:!l t/Jii)

and if (Ae), E IC \ lR, I(Ae)d = 1 then X, := E:!llt/Jfi )l. The other t/J, are


found by minimising the difference between the continuous part of the power spectrum of the circulant D-BMAP and of the superposition by using the nonnegative least square method as in (Hwang et al. 1995).

At this point, the transition matrix Q of the circulant D-BMAP and the corresponding values (.,pc)' are determined such that pew) ~ Pc(w). Now, only "y has still to be found such that (Qk)k>O is completely defined. Of course, "Y has to be determined in such a way that the (.,pc)' 's, which depend on "Y, are not changed anymore. The components of "Y can be expressed as function of the Xl'S and the a,'s: if N is odd (N = 2p + 1),

p 2n 'Yt = 50 + 2 L ffm cos(am - N tm), or

m=l

(9)

p-l 2n 2n 'Yt = 50 + 2 L ffm cos(am - N tm) + /Xv cos(ap - N tp) (10)

m=l

if N is even (N = 2p). Remark that the value of N will depend on the outcome of the index search algorithm. The only fact known about N is that it has to be a multiple of the period.

As can be seen from (9) or (10), there is still a degree of freedom left, namely the a,'s. Those will be used to match the stationary cumulative distribution of the input rate process. The stationary cumulative distribution F{x) of r, the input rate in a slot of a D-BMAP (Dk)k>O, is defined as F(x) = p{r ~ x}. Since p{r = rd = ni, F(x) is completely determined by 1r, the stationary distribution of D and the input rate vector r = (ro ... rN_l)T = E~o kDke: F{x) = Er.<z ni· For the superposition

of M independent D-BMAPs (D~i)k~o, r = EB1!l r(i) and 1r = ®:!l1r(i)

such that F(x), the stationary cumulative distribution of the aggregate input rate process is completely known from the cumulative distribution of the individual D-BMAPs. In order to match F(x) and Fc(x), which must be a cumulative distribution function that jumps by -J:t at each value x E "Y (since the stationary distribution of a circulant is 1rc = -J:teT ) , the range of x is partitioned into a set of N equal probability rates. The matching problem is then again identical to the matching of the rate distribution for a CMPP in (Hwang et al. 1995), which is solved as a minimisation problem, in which the components of a are the parameters that can be tuned, and that is solved by using the NeIder Meade simplex search method (NeIder et al. 1965).

A problem which can pop up by implementing the method as described above is the calculation of the powerspectrum of a D-BMAP (D k) k>O. As can be seen from (5), the complete eigenstructure (eigenvalues )., + corresponding right and left eigenvectors g, and h, such that h,g, = 1) of D needs to be known. Calculating the eigenvectors can for relatively large periodic matrices give unsatisfactory results. In that case, it is also possible to calculate the powerspectrum directly from the autocorrelation sequence by using the fact

Circulant matching method/or multiplexing ATM traffic 241

that appropriate subsequences of the autocorrelation sequence converge to limits which are known in closed form: Property. If (Dk)k?O is a D-BMAP of period d, and 1f'i, (E~o kDk) i and

ei are parts of 1f', E~o kDk and e corresponding to a permutation of the states of a periodic D which can always be made (Qinlar 1975), then

d-l 00

R[md + I] m--=r liml = d 2: 1f'i (2: kDk) oe(i+1)modd i=O k=O '

00 (11)

1f'(HI)modd (2: kDk) (0) e(HI+1)modd· k=O ,+1 modd

This property is proven in an analog way as the proof in (Geerts 1997) of the property that appropriate subsequences of the covariance sequence of the number of arrivals in a time slot of a periodic D-MAP (this is a D-BMAP with Dk = 0 if k 2: 2) converge. By replacing R[dk+l] by its limit as soon as IR[dk + l]-limll < f, an approximation for P(w) can be calculated directly from the autocorrelation sequence.

3 APPLICATION OF THE CIRCULANT MATCHING METHOD TO VIDEO SOURCES

The circulant matching method for D-BMAPs of subsection 2.3 needs now of course some validation. For this, the method is applied to an MPEG source type model developed in (Helvic 1996). This model was used in a series of Connection Admission Control (CAC) experiments (Aarstad et al. 1998) performed in the EXPERT project of the European Telecommunications research programme ACTS at the ATM testbed in Basle, Switzerland.

In MPEG encoding of a video sequence, three different compression levels are used. Thereby, three types of frames, namely 1-, P- and B-frames are generated. After encoding, the frames are arranged in a periodic deterministic sequence (group of pictures) usually of length 12 in the pattern IBBPBBPBBPBB.

In (Helvic 1996) and (Conti et al. 1996), a Markov model for an MPEG source is presented. The model used here is the one of (Helvic 1996). It is level oriented (see Figure 1), where level i models the activity of the MPEG source when the generated load of the B- and P-frames between two I-frames is between li and lHl. Within a level, the B- and P-frame activities are modelled by single states, the I-frame load by an approximate distribution given the level. Parameters in the model are the transition probabilities between the different states of the model and a load for each state (expressed in bits per frame) which is generated while being in that state. The state sojourntime is 45 msec for all states (a frame duration).


Two examples of MPEG sources are used in the experiments and also modelled as D-BMAPs. They are based on a 24 minutes trace from the Bond movie "Goldfinger" and a 24 minutes trace from an Asterix cartoon. Both traces have been made available by O.Rose at the Institute of Computer Science at the University of Wiirzburg. The source based on the Bond movie is modelled with 5 load levels and two I-frames at each level (and thus 65 states) while the Asterix cartoon is modelled with 4 load levels and also 2 I-frames at each level (52 states). In the sequel of this paper, these sources will be refered to as "Bond" and "Asterix" .

...... 10 .. 11

..... " ......

...... _. Figure 1 Structure of the artificial Markovian MPEG source

A D-BMAP (Dkh>o can be constructed from the data generated by the method of (Helvic 1996) by using the given transition matrix as the transition matrix D for the D-BMAP and by transforming the load given for each state into number of cells per frame. If this results in n cells per frame for state i, define Vj : (Dnkj := (D)i,j, (Dmkj := 0, "1m f:. n.

Application of the circulant matching method to D-BMAPs based on the MPEG model for the superposition of Bond sources, Asterix sources or a combination of those two, gives a new D-BMAP (a, ,) which is an approximation for the superposition. Since D has periodicity 12 (see Figure 1) and dimension 52 for the Asterix source, a search for a circulant Q which has as required eigenvalues the 4 eigenvalues of D which are different from zero and have their argument in [0, H is performed. By imposing Q to have also period 12, as described in section 2.3, Q will have as eigenvalues among others all the eigenvalues of D. The result is a circulant of dimension 132. For the Bond source, D has 5 eigenvalues in the segment [0, ~ [ and the dimension of the resulting circulant is also 132. For the combination of Bond and Asterix there are 8 eigenvalues with argument in [0, H: 4 come from the Asterix source and 5 from the Bond source, but of course they have Ao = 1 in common. The result is a circulant of dimension 276. These dimensions will stay the same irrespective of the number of sources that is multiplexed. The difference will be in ,. For Bond and Asterix sources this means thus that as soon as two sources are multiplexed, the dimensions of the approximation are smaller than those of the exact superposition.


The underlying time unit for the circulant D-BMAPs (a,"Y) is still a frame length of 45 msec. Since this D-BMAP will be used as input for a single server queue with a constant service time which equals the time needed to transmit one cell onto the outgoing link (= 1 slot), (a, "Y) has to be transformed into a D-BMAP (a, i) with one slot as the underlying time unit. If it is supposed that the number of slots of being in a state is geometrically distributed with mean x, where x is the number of slots in a frame duration, p = 1 - ~ is the probability to go from a state to the same state after one slot. The D-BMAP (a, "Y) can thus be transformed to (a, i) by replacing ao by p (ao is 0 since Q is periodic) and mUltiplying all the other elements of a by (1 - pl. Further, all the elements of"Y have to be divided by x.

4 RESULTS

Experimental multiplexing results were obtained in the EXPERT ATM testbed by using a traffic generator and analyser instrument called ATM-100 which gives the possibility to generate and analyse quite general random traffic. The ATM-100 is equipped with two Synthesised Traffic Generators (STGs) that are used for generating the artificial MPEG traffic. The traffic is multiplexed on an output port of a Fore ASX-200 switch with a buffer of 100 cells. Due to hardware constraints in the traffic generators a pacing rate function has been used to limit the output port capacity to 37.44 Mbit/sec, thereby reducing the number of sources required to adequately load the system. The aggregate traffic stream is analysed in the ATM-100, permitting cell loss measurements.

Those multiplexing experiments were performed in the framework of a CAC investigation for video and data and are reported in detail in (Aarstad et al. 1998). The experiments are based on multiplexing, since the way to perform them is to change the traffic mix until a CLR below, but as close as possible to a fixed value is obtained. These experimental multiplexing results are used to validate the circulant matching method for D-BMAPs .

..... ) I~

..

10

~~-7--~~1~.--~IO--~.~-IO=-~.~~~G· -Figure 2 Comparisson of analytically and experimentally obtained results


To be able to compare results with the experimental results, the circulants obtained for multiplexing a number of Bond and Asterix sources have to be fed into a multiplexer and values for the CLR have to be calculated. This multiplexer is modelled as a discrete-time D-BMAP/D/l/K+l queueing system, where K is the buffer size and K + 1 the system size. The service time equals one time slot, i.e. the time needed to transmit one cell on the outgoing link. In (Blondia et al. 1992), the D-BMAP/D/l/K+l model is solved and a formula for calculating the CLR is derived.

All the results presented are obtained for a queue length of 100 cells and an outgoing link of capacity 37.44 Mbit/sec. This implies that one time slot equals 11.325 J.LSec. By transforming bits into number of cells, it is assumed that a cell of 53 bytes can contain 48 bytes of data. Figure 2 compares the analytically derived 10-4 CAC boundary with the experimentally obtained one. As in the experiments, for a mix of two types of sources, the admission boundary is close to linear (Aarstad et al. 1998). IT the points in Figure 2 are compared, it is seen that the analytical results are more conservative than the experimental results, with a larger deviation if the number of Asterix sources grows. For the D-BMAPs of the MPEG sources, the parameters as obtained from the method in (Helvic 1996) are used, which give rise to a mean arrival rate of 58.1212 cells/45 msec or 0.54820 Mbit/sec for the Asterix source and 63.3247 cells/45 msec or 0.59666 Mbit/sec for the Bond source. However, if the sources are implemented in the traffic generator, the parameters are automatically slightly changed to adapt them to the hardware limitations of the STGs. Depending on the number of sources generated, these slight differences may become more important. The first limitation is that the STGs can only provide transition probability values in integer multiples of 2~6' The second limitation is that the peak rate in a state must divide the link rate such that the interarrival time between cells in a given state is always the same integer number of slots. The result is that the mean arrival rate for an experimental Asterix source is 0.51318 Mbit/sec and 0.59221 Mbit/sec for a Bond source. The analytical model for the Asterix source generates thus 0.03502 Mbit/sec more than the experimental model, which means that for a certain experimental point the corresponding analytical CLR will be worse depending on the number of Asterix sources used. This explains partially why in the analytical curve the number of sources that can be accepted is smaller than in the experiments, with a larger difference if more Asterix sources are involved. Analogous observations are found by simulation (Aarstad et al. 1998).

5 CONCLUSIONS

In this paper, the circulant matching method to approximate the superposition of a number of discrete-time batch Markovian arrival processes by matching the stationary cumulative distribution and the autocorrelation sequence of the input rate process was proposed. The method was applied to the super-


position of MPEG source type models. For validation of the method, experimental results of experiments performed within the ACTS project EXPERT were used. The results confirm the accuracy of the method.

Acknowledgement. We would like to thank the partners of WP4J? of the EXPERT project together with whom the experiments were performed. Also the valuable e-mail discussions with Hao Che are gratefully appreciated.

REFERENCES

Aarstad, E., S. Blaabjerg, F. Cerdan, S. Peeters and K. Spaey (1998) CAC investigation for video and data. To appear in Proceedings of IFIP TC 6 Fourth International Conference on Broadband Communications.

Blondia, C. and O. Casals (1992) Statistical Multiplexing of VBR Sources: A Matrix-Analytic Approach. Performance Evaluation, 16, 5-20.

Blondia, C. (1993) A Discrete-Time Batch Markovian Arrival Process as BISDN Traffic Model. Belgian Journal of Operations Research, Statistics and Computer Science, 32(3,4), 3-23.

Blondia, C. and F. Panken (1995) Traffic profile of a Connection in an ATM Network with Application to Traffic Control. Proceedings of ATM hot topics on Traffic and Performance, From Race to ACTS, Milan.

Che, H. and S.Q. Li (1997) Fast algorithms for Measurement-Based Traffic Modeling. Proceedings of IEEE INFOCOM '97.

Qinlar, E. (1975) Introduction to Stochastic Processes. Prentice-Hall, Englewood Cliffs, New Jersey.

Conti, M., E. Gregori and A. Larsson (1996) Study of the Impact of MPEG-1 Correlations on Video-Sources Statistical Multiplexing. IEEE Journal on Selected Areas in Communications, 14(7), 1455-7l.

Geerts, F. (1997) A proof of the correlation decay of a periodie D-MAP. Available at http://win-www.uia.ac.be/u/fgeerts.

Helvie, B.E. (1996) MPEG source type models for the STG (Synthesized Traffic Generator). SINTEF Report STF40 A96016.

Hwang, C.L. and S.Q. Li (1995) On the Convergence of Traffic Measurement and Queueing Analysis: A Statistical MAtch Queueuing (SMAQ) Tool. Proceedings of IEEE INFOCOM '95,602-12.

Landry, R. and 1. Stavrakakis (1997) Multiplexing ATM Traffic Streams with Time-Scale-Dependent Arrival Processes. Computer Networks and ISDN Systems, 29.

Lazar, A., G. Pacifici and E. Pendarakis (1993) Modeling Video Sources for Real-Time Scheduling. IEEE GLOBECOM '99, Houston, Texas.

Li, S.Q. and C.L. Hwang (1992) Queue Response to Input Correlation Functions: Discrete Spectral Analysis. Proceedings of IEEE INFOCOM '92.

NeIder, J.A. and Mead, R. (1965) A Simplex Method for Function Minimization. Computer Journal, 7, 308-13.

PART SEVEN

Applied Queueing Theory

19 Approximate Analysis of a Dynamic Priority Queueing Method for ATM Networks

Anoop Ghanwani Internetworking Technology, IBM Corporation Box 12195, Research Triangle Park, NC 27709, USA Tel: +1-919-254-0260 Fax: +1-919-254-5483 Email: [email protected]

Erol Gelenbe Department of Electrical and Computer Engineering, Duke University Box 90291, Durham, NC 27708, USA Tel: +1-919-660-5442 Fax: +1-919-660-5293 Email: [email protected]. edu

Abstract A scheduling discipline for multiple classes of traffic in an ATM network is discussed and analyzed. The scheduler has the desirable property of providing minimum bandwidth guarantees for each class of traffic. Its simplicity makes it particularly well suited for high speed implementation. The scheme is a modification of static head-of-line priority queueing, and was originally presented in a slightly different form by Huang and Wu. We begin by considering a system with two queues which is analyzed by decoupling the system into separate MIG/1 queues. The analysis is found to provide a very good estimate for the mean response time of customers in each queue. The applicability of the analysis to a system with multiple queues is also demonstrated.

Keywords Coupled queues, ATM networks, scheduling disciplines

Perfonnance of Infonnation and Communication Systems U. Kl>mer & A. Nilsson (Eds.) ~ 1998IF1P. Published by Chapman & Hall

250 Part Seven Applied Queueing Theory

1 INTRODUCTION

In asynchronous transfer mode (ATM) networks, data are transported in fixed size 53 byte cells. The ATM Forum has standardized many classes of service for users' traffic based on the loss and delay requirements of various applications (Jain 1996). In order to meet the service requirements for each class of traffic, it is necessary to provide a scheduling algorithm to decide which class receives service when the server becomes free. Many scheduling algorithms have been proposed and analyzed, ranging from simple scheduling disciplines such as static priority and round robin, to more sophisticated algorithms such as weighted fair queueing and its variants. A discussion of scheduling disciplines for high speed networks may be found in (Zhang 1995) and the references therein.

We consider a priority queueing system with two classes of traffic. A counter is associated with the low priority queue which is incremented whenever a high priority cell is served and a low priority cell is waiting for service. The counter is reset whenever a cell from the low priority queue is served. High priority customers* have non-preemptive priority over low priority customers except when the counter has reached a predefined threshold L. In that case, the head-of-line cell of the low priority queue is served and the counter is reset. The counter may be thought of as a measure of the "impatience" of the cell waiting at the head of the low priority queue. The behavior of the scheduler is completely described as follows:

• If both queues are empty, the server remains idle until a cell arrives to the system.

• If the low priority queue is empty, and there are jobs in the high priority queue, a job from the high priority queue is scheduled for service.

• If the high priority queue is empty, and the low priority queue has cells, then a low priority cell is scheduled for service and the counter is reset.

• If both the queues have customers waiting then:

- If the value of the counter is less than L, a cell from the high priority queue is scheduled for service, and the value of the counter is incremented by l.

- If the value of the counter is equal to L, a cell from the low priority queue is scheduled for service and the counter is reset.

The instantaneous priority of a traffic class depends on the value of L and the arrival rate for each class. This yields a closely coupled queueing system where the degree of coupling depends on L. A closed form solution for the exact mean response time of this system does not exist. A generalized version

·The words "customer" and "cell" are used inter-changeably since we are analyzing an ATM system.

Approximate analysis of a dynamic priority queueing method 251

Figure 1 Priority queueing system with two classes of traffic

of this scheme was proposed in (Huang et al. 1993) for a system with n priority queues, each having a counter associated with it. When a counter reaches the threshold L j , 1 ~ i ~ n, the cell at the head of that queue is scheduled for transmission in the next slot provided no other higher priority queue's counter has exceeded the threshold. The algorithm incurs very little processing overhead; yet it avoids the problem of "starving" lower priority traffic. Our scheme is slightly different in that the first queue does not have an "impatience" counter.

Many adaptive schemes based on static priority and round-robin which attempt to overcome the drawbacks of each have been proposed. Kleinrock (Kleinrock 1976) proposes a model where the instantaneous priority depends on a variable parameter. A model with p classes is considered, each having a parameter b" associated with it (0 ~ bi ~ b2 ~ ••• ~ b,,). The priority of a class i customer, which arrived at time T, at time t is then given by (t - T)bi. Lim and Kobza (Lim et al. 1988) propose a scheme referred to as head-of-line priority with jumps (HOL-PJ). They consider a model with p classes of traffic. Class i has non-preemptive priority over class j if i < j. However, a customer has an upper limit on the amount of time it spends in a given queue. If that limit is exceeded, the customer joins the end of the next higher priority queue. Ozawa (Ozawa 1990) studied a system with two queues where the high priority queue receives exhaustive service and the service of the low priority queue is K-limited. Lee and Sengupta (Lee et al. 1993) propose and analyze a model with two classes of traffic in an ATM network. The system is serviced using the round-robin service discipline between classes. A threshold L may be defined for either class. If the queue length for the class exceeds the threshold, cells from only that class will be serviced until the queue length falls below the threshold; it then reverts back to roundrobin. The analysis of coupled queueing systems such as the ones described above typically involves transform based analysis often leading to numerical solutions. Closed form solutions hard to achieve without making simplifying approximations about the behavior of the system. Our focus is a very simple method for approximating the mean response time of the system described above.

The remainder of this paper is organized as follows. In Section 2, the system with two queues is analyzed and the results are compared with the mean response time obtained from discrete event simulation. Section 3 shows how the analysis may be extended to a multi queue system. Again results are presented


to compare the analytical approximation with simulation. The conclusions of our work are presented in Section 4.

2 NOTATION AND ANALYSIS

We use a time-slotted model where the duration of a slot is the time required to service a single cell. The arrival process at queue i is assumed to be Poisson with rate parameter Ai. Let Qi be the stationary probability that queue i is busy, i.e. that there are cells either in service or waiting to be served. Let qi be the stationary conditional probability that the head-of-line cell in queue i receives service given that both high and low priority queues have cells waiting to be served. We use the suffix 1 to denote the high priority traffic class and suffix 2 to denote the low priority traffic class. We make the following approximation to account for the behavior of the scheduler. When both queues are busy, the low priority queue will on average receive service lout of every (L + 1) slots. Therefore, we can set q2 = L~1 and q1 = 1 - q2. Then, the probability that queue i is busy is given by

(1)

where Si is a random variable which denotes the number of slots between the time a class i customer gets to the head-of-line, to the time when it leaves the system. Note that 8 i consists not only of the amount of time that the server will be kept busy by the cell, but also includes the time that the cell spends at the head of the queue waiting to access the server. In other words, 8 i is the sum of access time and service time, where access time is a random variable which accounts for the time that the cell waits before it gets access to the server, and the service time is a single slot. Let k be the number slots that a cell spends at the head-of-line position before getting service. We approximate 81 , 8 2 by geometrically distributed random variables with means:

(2)

(3)

and second moments:

(4)


(5)

Substituting (2) and (3) in (1), we can write 0:1 = ~1 >. and 0:2 = ~1 >. • -0<2Q2 -O<lQl

These equations may be solved simultaneously to yield a quadratic equation in either 0:1 or 0:2. The root of interest can be found by using the additional criterion Ai ~ O:i ~ 1. Note that since the service time of a customer is a single slot, it is required that Al + A2 < 1 for stability.

This approximate analysis allows us to decouple the system into separate queues, each with its own arrival rate and service time. To compute the mean waiting time, we apply standard results for an MIGl1 queueing system (Gelenbe et al. 1980) separately to each queue as follows:

The mean response time is then Ri = Wi + E[Sil. From comparison with simulation, we find that using these results, an accurate estimate of the mean response time for the high priority traffic class is obtained. However, the results are not as good for the low priority traffic class. We therefore make use of the conservation law applicable to MIGl1 queues when the service discipline is work-conserving. The law states that (Kleinrock 1976):

Wo 1- p'

(6)

'" >"E[S~l • where Wo = L..Ji~' In our case, the RHS of EquatIon (6) becomes >'1 +>'2 . W2 is then computed as: 1->'1->'2

where Wt = Rl - 1. The mean response time for the low priority queue is then R2 = W2 + 1.

The mean response times using the analytical approximation are compared with results from discrete event simulation in Figures 2-7. In each case, the traffic load on the high priority queue is a constant value (either 30% or 50% of the server capacity); the load on the low priority queue is varied from very light until a value which saturates the system.

The figures indicate that the approximation yields very accurate response times for most of the cases tested. In most instances, the error between the analytical and simulation results is less than 10%. It performs especially well when the system is light to moderately loaded (up to 60-70% load). The


12

10

~ ; 8

i ~ 8 .

~

~~--~O.~I---70.2~--~O.3~--~~~--~--~--~O.7 I.,

Figure 2 Results for A1 = 0.3, L = 1

16'r---'---~--~---'---'--~==~c=~

14

12

.10 . E

18

i E 8

2 ."

8.~~~0~.I--~0~.15~-70.2~~02~5--~0~~--~~~~~O.C5 i.,

Figure 3 Results for >'1 = 0.5, L = 1

approximation tends to produce less accurate results in cases where the L is very small and the load is high (Figure 3). This is likely due to the fact that in this instance, the queues are highly coupled, and the approximation based on decoupling yields inaccurate results. In fact, a system with L = 1 is essentially equivalent to a polling system.

3 ANALYZING A SYSTEM WITH MULTIPLE QUEUES

The queueing analysis presented in Section 2 may be used for analyzing systems with more than two queues. The procedure is as follows. Consider a


15r----r----r---~----~--~====~==~

10

~L----~~,----0~.2----0~.3----~~.----~~5~--~0 .• ~--~OJ

Figure 4 Results for Al = 0.3, L = 3


system of n queues. Queues 2 through n each have a threshold Li E Z+. In order to be able to guarantee a minimum bandwidth of Li~l for class i, it is required that E:"2 Li~l < 1. We assume that the arrival process at queue i is Poisson with rate parameter 'Yi. For a stable system, we also require E~=l 'Yi ~ 1.

First, the system is solved by reducing it to a two queue system - the first queue and all the others put together. For this case, using the notation defined in the previous sections, the arrival rates for the two queues are given by: Al = 'Yl, A2 = E~=2 'Yi. For this system with two queues, the value of L for the second queue is given by L = E:=: rl+r - 1. The two queue system is


15r----r----.----r----~--~====~~~

o

10


18 .

16

1 • . . ~ 12 .

j ~'0

~ 8


then solved using the method outlined in Section 2 to yield the mean response times for the first queue, and the mean response time for all the other queues. Next, we go through the same procedure described above with the first two queues corresponding to one queue and all the others corresponding to the the second queue. This will yield the mean response time for the first two queues combined, and the mean response time for the rest of the queues. Then, using the law of conservation, we can compute the mean response time for the second queue by itself. In this way, the 2 queue system must be solved n - 1 for an n queue system yielding the mean response time each class. The following steps summarize the procedure for solving a system with n queues.


16

,. 12

i r i 8 E

g~OO--~~I--~O.I~5~O~.2--~O.2~5~O~.3~O~.~~~~~'~O~.'5~~O.5~~~55 Ia-. Figure 8 Results for 71 = 0.2, 72 = 0.2, L2 = 4, L3 = 4

• Step 1. Set m f- O. • Step 2. m f- m + 1. • Step 3. Create a two queue system with parameters:

• Step 4. Use the analysis of Section 2 to compute the mean response time R1 and R2 for the two queue system.

• Step 5. The mean response time for queue m is:

• Step 6. If m < n - 1, go to Step 2, else the mean response time for the nth queue is given by R~ = R2 •

Results of this method for a system with three queues is presented in Figures 8 and 11. Again, we see that the approximation is very good except when the equivalent value for L is small and the load on the system is high. In the scenario of Figure 9, the value of L in the first iteration is T:j:T1 - 1 = 1.5.

g 5

4 CONCLUSIONS

An adaptive queueing discipline for ATM network nodes with two classes of traffic is analyzed. An approximation is used in which the two queues are

258

30

25

E20

I i 15 E

10

Part Seven Applied Queueing Theory

O~~--~--~--~~---L---L--~--L-~ 0." 0.1 0.15 0.2 0.25 0.3 0.35 0.4' 0.45 0.5 0."

1,

Figure 9 Results for 'Y1 = 0.2, 'Y3 = 0.2, L2 = 4, L3 = 4

18

14

12

,'0 ii 8 E

g"~~~'~~~~'5--~0.2~~0~.~~~0.3~~0~.35~~M--~0~A5~~0~.5~~" Ia-. Figure 10 Results for 'Y1 = 0.2, 'Y2 = 0.2, L2 = 4, L3 = 6

decoupled for the purpose of analysis. We also demonstrate how this approach may be used to analyze systems with more than two queues. The analytical approximation is compared with results from discrete event simulation and is found to work very well under a variety of traffic conditions for systems with two and three queues.

REFERENCES

Gelenbe, E. and Mitrani, I. (1980) Analysis and Synthesis 0/ Computer Systems. Academic Press.


30

25

10

8.0~5--0~.1--~0.1~5~0~.2--0~.2~5~07.3~0~.~~70.~4~0~.45~~05~~O.55 Y,

Figure 11 Results for '/'1 = 0.2, '/'3 = 0.2, L2 = 4, L3 = 6

Huang, T.-Y and Wu, J.-L. C. (1993) Performance analysis of a dynamic priority scheduling method in ATM networks. lEE Proceedings-I, 140, 285-290.

Jain, R. (1996) Congestion control and traffic management in ATM networks: Recent advances and a survey. Computer Networks and ISDN Systems, 28, 1723-1738.

Kleinrock, L. (1976) Queueing systems, Volume II: Computer applications. John Wiley and Sons.

Lee, D.-S. and Sengupta, B. (1993) Queueing analysis of a threshold based priority scheme for ATM networks. IEEE/ACM Transactions on Networking, 1, 709-717.

Lim, Y. and Kobza, J. (1988) Analysis of a delay-dependent priority discipline in a multiclass traffic packet switching node. in Proc. IEEE INFOCOM.

Ozawa, T. (1990) Alternating service queues with mixed exhaustive and Klimited service. Performance Evaluation, 11, 165-175.

Zhang, H. (1995) Service disciplines for guaranteed performance service in packet-switching networks. Proceedings of the IEEE, 83, 1374-1396.

5 BIOGRAPHY

Anoop Ghanwani received the Bachelor of Engineering in Electronics and Telecommunications Engineering from the Govt. College of Engineering, Pune, India in 1992. He received the Master of Science in Electrical Engineering from Duke University in 1995, and is presently enrolled in the doctoral program. Since August 1996, he has been working as Staff Engineer with the Internetworking Technology department at IBM in the Research Triangle Park, NC, USA. His research interests include routing, scheduling and bandwidth man-


agement in high speed networks.

Erol Gelenbe is the Nello L. Teer Jr. Professor of Electrical and Computer Engineering at Duke University, and is also Professor of Computer Science and of Psychology-Experimental. He has authored four books on queueing systems and computer and communication system performance, and some 100 journal papers. His former doctoral students are active in academic and industrial research in Europe and the US. His honors include Fellow of the IEEE (1986), Chevalier de l'Ordre du Merite (France, 1992), Dott. Ing. "Honoris Causa" of the University of Rome (Italy, 1996), Grand Prix France Telecom (French Academy of Sciences, 1996), Science Award of the Parlar Foundation (Turkey, 1995). Erol's interests cover computer-communication networks and distributed systems, computer performance analysis, artificial neural networks and image processing. In the area of networks, recent work has included CAC in ATM, as well new product form queueing networks. His applied work since 1993 includes designing search algorithms in probabilistic environments, novel algorithms for explosive mines, automatic target recognition, brain imaging and video compression. Currenty his research is funded by the Computational Neurosciences Program of the Office of Naval Research, the U.S. Army Research Office, the Multidisciplinary University Research Initiative on Demining (MURI-ARO), and IBM. Erol is an Associate Editor of several journals including Acta Informatica, Proceedings of the IEEE, Telecommunication Systems, Performance Evaluation, Journal de Recherche Operationnelle, Information Sciences, Simulation Practice and Theory, and RESIM: Reseaux et Systemes Multimedia.

20 Using Gibbs Sampler in Simulating Multiservice Loss Systems Pasi Lassila*, Jorma Virtamo** Laboratory of Telecommunications Technology, Helsinki University of Technology P.O.Box 3000, FIN-02015 HUT, Finland, Tel: +358-9-451 2439*, +358-9-451 4783**, e-mail: {Pasi.Lassila.Jorma.Virtamo}@hut.fi

Abstract In this article we consider the problem of calculating the blocking probabilities of calls in a multiservice network by using simulation. Traditional simulation methods become computationally intensive as the state space grows. We develop a method that alleviates this problem. The method is based on using the so called Gibbs sampler to generate a Markov chain with the desired stationary distribution. In particular, by making an additional 'virtual' step from each state and calculating the expected contribution from this step analytically, we are able to collect information from a subset of the state space for each generated sample. This leads to a smaller variance of the estimate for a given computational effort.

Keywords loss systems, simulation, Gibbs sampler, variance reduction

1 INTRODUCTION

Modern broadband networks have been designed to integrate several service types into the same network. On the call scale, the process describing the number of calls present in the network can be modelled by a loss system. Associated with each call is the route through the network and the bandwidth requirements on the links. When the call is offered but there is not enough bandwidth on all the links along the requested route, the call is blocked and lost. We are interested in calculating the blocking probabilities for each call.

The steady state distribution of the system has the well known product form. A problem with the exact solution is, however, that it requires the calculation of a so called normalization constant, which entails the calculation of a sum over the complete allowed state space of the system. In a network of realistic size the state space very rapidly becomes astronomical.

Performance of Information and Communication Systems U. Korner & A. Nilsson (Eds.) © 1998 IFIP. Published by Chapman & Hall


In such a situation we have two alternatives: to use analytical approximations or to simulate the problem to a desired level of accuracy. In this paper we will be dealing with an efficient method for doing the simulation. Traditionally the simulation approaches have focused on either Monte Carlo (MC) summation techniques or the Markov chain simulation techniques. MC summation has been extensively studied by e.g. Ross (Ross 1995, chap. 6). Markov chain simulation methods include the regenerative method (Crane et at. 1975, Crane et al. 1977), which has been lately used in the context of rare event simulation in loss networks by Heegaard (Heegaard 1997).

The problem with the aforementioned methods is that they become computationally intensive as the state space grows. The reason is that they collect information about the state space on a state-per-state basis. What is actually needed is a method that can collect more information with each sample than that represented by the sample itself.

In this article, we will present a method that is based on a family of simulation methods called Markov Chain Monte Carlo (MCMC) methods using the Gibbs sampler (Tierney 1994). This method enables us to exploit the product form solution of the system, and we are able to calculate part of the problem analytically while the simulation is being carried out. In practice, this means that with each generated sample we can collect information of not just the current sample state, but a large number of other surrounding states.

The rest of the paper is organized as follows. Chapter 2 introduces the basic stochastic model of the problem. Chapter 3 describes the Gibbs sampling method for loss networks. Chapter 4 contains the main results of this paper with methods for improving the performance of the Gibbs sampler. Numerical results are presented in chapter 5 and the conclusions in chapter 6.

2 MODEL DESCRIPTION

Consider a network consisting of J links, indexed with j = 1, ... , J, each having a capacity of Cj resource units. The network supports K classes of calls. Associated with a class-k call, k = 1, ... , K, is an offered load Pk and a bandwidth requirement of bj,k units on link j. Note that bj,k = 0 when class-k call does not use link j. Let the vector h j = (bj,l, ... , bj,K) denote the required bandwidths of different classes on link j. Also, we assume that a call is always accepted if there is enough capacity left and that the blocked calls are cleared. The state of the system is described by the vector x = (Xl,"" XK), where element Xk is the number of class-k calls in progress.

The set of allowed states S can be described as S = {x: h j . x ::; Cj ,

Using Gibbs sampler in simulating multiservice loss systems 263

j = 1, ... ,J}, where the scalar product is defined as b j . x = LA: bj,A:Xk. This system has the well known product form stationary distribution

1 K x" 1 K f( ) 1r(x) = G IT ::! = G IT fA:(xA:) = ; , with G = L f(x) , (1)

A:=1 A:=1 xES

where fA:(xA:) = p%" jXA:!, and f(x) denotes the unnormalized state probability. G is the normalization constant.

The set of blocking states for a class-k call, BA:, is

BA: = {x E S : b j . (x + eA:) > Cj for some j} ,

where eA: is a K-component vector with 1 in the kth component and zeros elsewhere. The blocking probability of a class-k call, BA:, is then

BA: = L 1r(x) = L 1r(x)lxEB" . (2) xEB" xES

In the remainder of this paper we will be dealing with an efficient simulation method for calculating the blocking probabilities.

3 GIBBS SAMPLING FOR LOSS SYSTEMS

Our problem is now of the following type. We want to evaluate some quantity H defined as the sum of a function h(·) over the allowed state space S,

H= Lh(X). (3) xES

In general, the Me method solves the problem by generating identically distributed samples Xn E S from some distribution p(x) = Pr[Xn = x] such that p(x) ::I 0, 't/x E S. With respect to this distribution H can be written as an expectation

H = L h((:)) p(x) = Ep [h(X)jp(X)] xES P

The estimator for H when N samples have been drawn is

(4)


Estimator (4) has the correct expectation when each Xn has the distribution p, irrespective of whether the Xn are independent or not. Positive correlation between the samples, however, would make the estimator less efficient from the point of view of its variance.

In our case we are interested in calculating the blocking probabilities as given by eq. (2) with hex) = 1I"{X)1xEBk. Then a natural choice is to let p{x) = 1I"{x), and we get the estimator

(5)

One approach for generating the samples is by Markov chain simulation. This relies on the fact that, assuming the holding times are exponentially distributed, our system itself is defined by a Markov chain, e.g. the embedded discrete time Markov chain (jump chain) associated with the arrival and departure epochs. The points in the full jump chain, when weighted with the expected life time of each state, have the stationary distribution 11" and, as noted above, can be used as samples in the summation of eq. (5) despite the fact that they are not independent.

In MCMC methods the idea is the same - to simulate some Markov chain for constructing the distribution 11". The question is only: are there other Markov chains that have the same steady state distribution 11"? The answer is yes and, in fact, many of them (Tierney 1994). The Gibbs sampler introduced later in this chapter is just one of them, but its properties allow us to exploit the product form of the steady state distribution to gain significant simulation efficiency increases, as will be discussed in chapter 4.

3.1 General Theory

Let X = (Xl, ... , X K) E S denote the vector random variable with the distribution 1I"(x) as in (1). We are now interested in ways of constructing a Markov chain X~ having the invariant distribution 11". One way is to use transition probabilities based on conditioning, as defined in the following theorem {taken with slight modification from (Tierney 1994)).

Theorem 1: Let sets At. ... , AI form a partition of the state space Sand let A(x) denote the set which a state x in S belongs to. Let X be a random variable with distribution 11". Then the Markov chain X~ with the transition probability

Pr [X~+1 = Y I X~ = x] = Pr [X = y I X E A{x)] (6)

has the invariant distribution 11".


Proof:

L Pr [X~+l = Y I X~ = x] Pr [X~ = xl xES

= L L Pr [X~+l = Y I X E A(x)] Pr [X~ = xl i xEAi

L Pr [X = Y I X E Ail L Pr [X~ = xl xEAi

= L Pr [X = Y I X E Al Pr [X; E Al

Now, if X~ has the distribution 71", so does X~+l because then

Pr [X;+l = Y] = L Pr [X = Y I X E Ail Pr [X E Al = Pr [X = yl = 7I"(Y) 0

i

Let pel) denote the transition probability matrix with the components given by eq. (6). The Markov chain generated by this transition matrix is not irreducible, because there are no transitions between different sets. However, by defining several partitions 1, ... , M we can construct an irreducible Markov chain X~. Let p(rn), m = 1, ... , M, denote the corresponding transition ma-trices. Then, with a suitable choice of the partitions, the Markov chain X~ corresponding to the compound transition matrix P = pel) ... p(M) will be irreducible. Since each p(rn) has the invariant distribution 71" also the compound matrix P will have the invariant distribution 71", and because X~ is now irreducible, 71" is also its unique stationary distribution.

3.2 Gibbs Sampler and its Application to Loss Networks

In our case we have a product form solution 71" and it is natural to define the sets in a partition to consist of points in coordinate directions. This leads to the so called Gibbs sampler.

We define K partitions and denote the particular set in partition k to which a state x belongs by Ak(x). This set consists of the states

where I is the set of non-negative integers. For the sequel, we denote by Lk (x) the largest value of the component k (variable I) in the above set Ak(x).

To illustrate the concept consider the simple network of Fig. 1, with the state space depicted in the same figure. In this case we have two traffic classes,


• • • C3 PI • • • • P2

• • • • • nl

Figure 1 Example network and its state space.

K = 2, and we use two different partitions with the 'rows' corresponding to partition 1 and the 'columns' to partition 2 (see Fig. 2).

n2

{\ {\ {\ {\ , , ,., ,., ,., -.-.-.--.;5 , I , \ '.' '.' c_ -------- I , ,., , , I ,

C" ~~~~~~~~~. I I., '.' I., I I , I , I , ------

<' \ \ \ \

-------- nl nl

Figure 2 The state space partitions 1 and 2 (left and right).

Associated with each partition, there is a transition matrix p(k) with the transition probabilities (6). Then we construct a compound transition matrix p = p(l) ... p(K). The corresponding Markov chain X~ is irreducible since it is possible to move from any state x in the coordinate convex state space S to any other state y with at most K transitions.

The simulation of the Markov chain X~ consists of making transitions with the transition matrices p(k) in cyclical order, see Fig. 3. In transitions generated with p(k), the state remains in one of the sets Ak(x), i.e. only the component Xk changes. Starting from the state X~ the value of Xk of the next state is obtained by drawing it from the distribution /k(Xk)/Gk(Lk(X~)) in the range 0, ... , Lk(X~), where the normalizing function Gk(·) is defined by

L

Gk(L) = 2: /k(l) . 1=0


• • •

Figure 3 Gibbs sampler example.

Along the generated path, we collect information about the number of visits to the blocking states of class-k calls in order to form the estimator (5), i.e.

The Gibbs sampler provides a way of generating Monte Carlo samples from the state space S, which is simple requiring only the generation of random variables from univariate truncated Poisson distributions for each transition. The advantage it has is that it manages to eliminate the problem of generating 'misses' from the state space S, as happens with the traditional MC summation techniques. On the other hand, the generation of transitions from the Markov chain of the Gibbs sampler is almost as easy as for generating them from the embedded Markov chain associated with the process. The samples generated with the Gibbs sampler are, however, much less correlated than the samples from the embedded Markov chain.

3.3 Uniform Sampling with Gibbs Sampler

This idea of partitioning the state space can also be used to generate a Markov chain with a uniform distribution over the complete allowed state space S. In general, if we want to use uniformly distributed samples from the state space we will have p( x) = 1/ S in estimator (4), where S denotes the size of the state space S. The uniform distribution is trivially of the product form and the Gibbs sampler is applicable. Now, starting from the state X~ the transitions generated with p(k) are obtained by drawing Xk of the next state


from the uniform distribution in the range 0, ... ,Lk(X~). The estimator from (4) for the blocking probability of a class-k call is then

, S N S N

Bk = N L 1I'(X~)lX:'EBk = NG L f(X~)lx:'EBk . n=l n=l

(7)

G is unknown in (7), but similarly from (1) and (4) we can estimate G by

(8)

Using this in (7) we get another estimator

(9)

where Of is the estimator for Gf = LXEBk f(x). The uniform sampling may not be a very effective way to do the sampling,

because it often 'wastes' time on sampling every part of the state space with equal probability, when some parts of the state space are actually more important than the others. In particular, in our case when the distribution 1I'(x) is concentrated in a small part of the state space S, the uniform sampling does not necessarily produce very good results.

4 IMPROVED GIBBS SAMPLING METHOD

The method as described in the previous chapter does not yet give any significant improvement over the known techniques. We can, however, improve the efficiency of the method considerably by utilizing prior knowledge about the conditional distributions of the sets.

4.1 Improved Poisson Sampling

The idea is simple: At each step of the chain, starting from the current state X~, we make a 'virtual' transition with transition matrix pCk) to the state Y~. Since in stationary state X~ has the distribution 11' and pCk) has the invariance


property, the state y~ after the virtual transition also has the distribution 7t. We can then use y~ as a sample point instead of X~ and get the estimator

(10)

Now it is possible to take into account the effect of the extra step analytically by calculating the expectation of (10) conditioned on the X~ (see Appendix for a formal explanation on this step). This is easy to do since

where L~ = Lk(X~) is the largest value of Xk in the set Ak(x) and B(n,p) is the well known Erlang loss function (B-formula). Then our estimator becomes

(11)

In effect, by this method we have included transitions to all states in Ak(x). In particular, a contribution from a blocking state is obtained for every point X~ in the Markov chain. It is easy to see that the variance of estimator (11) is smaller than that of (5). They are both unbiased estimators with the same expectation. In case of (5), the sample values are either 0 or 1, while in (11) the samples belong to the range (0,1].

Note that the function fk(·)/Gk(-) = B(·,Pk) can be precomputed for all k and all required values of the argument. It is also worth noting that our improvement method does not require the use of the Gibbs sampler to generate the samples X~. Actually, they can be generated by any means provided that the X~ have the distribution 7r. Thus using traditional Me summation techniques to generate the X~ is also possible.

4.2 Improved Uniform Sampling

The improvements described in the previous chapter can also be used when the state space is sampled with a uniform distribution. Again, let y~ denote the state after making a virtual transition from the state X~ having the stationary distribution and consider using y~ for the estimator


Calculating the expectation of this extra virtual step conditioned on X~ gives

E [f(Y~)lY~E8k I X~] = ;k f(k)(X~)fk(L~) , n

where f(k)(X) = I11# fl(XI), and, as before, L~ = Lk(X~) is the largest value of Xk in the set Ak(x). The estimator then becomes

(12)

where the unknown G can similarly be estimated using the extra 'virtual' step,

N ~ N

{; = ~ L ;k f(k)(X~) L fk(l) = ~ L ;k f(k)(X~)Gk(L~) . (13) n=1 n 1=0 n=1 n

Combining (12) and (13) gives the following ratio estimator for the blocking probabilities

Bk = 2:::-1 f(k)(X~)/k(L~)/ L~ 2:::=1 f(k)(X~)Gk(L~)/ L~

(14)

Again, the functions fk(·) and Gk(·) can be separately precalculated and stored into arrays before the actual simulation run.

5 NUMERlCAL RESULTS

Our numerical example consists of the star network with 12 traffic classes studied by Ross (Ross 1995, p. 240) for the moderate traffic case. We compare our results with the results obtained using the importance sampling heuristics in (Ross 1995, chap. 6). Table 1 shows the results we obtained from using the improved Poisson sampling and uniform sampling (MCMC*) and the results of Ross (Ross 1995, p. 243). However, Ross obtained his results by generating 100000 LLd. MC samples and we used 50 independent runs of simulations with 50000 cycles (each roughly corresponding to one MC sample). In order to make the results comparable, we have scaled our results by multiplying the confidence intervals by .;25. As expected, the uniform sampling method does not give particularly good results, but the Poisson sampling method gives confidence intervals almost one third of those of Ross' indicating clear variance reduction.


Table 1 Blocking probabilities (%) with confidence intervals

Class Ross

1 0.336 ± 0.024 2 0.283 ± 0.022 3 0.275 ± 0.022 4 0.072 ± 0.009 5 0.064 ± 0.009 6 0.011 ± 0.003 7 2.270 ± 0.070 8 1.935 ± 0.065 9 1.885 ± 0.065 10 0.488 ± 0.Q25 11 0.438 ± 0.024 12 0.073 ± 0.008

MCMC* (Poisson)

0.349 ± 0.008 0.299 ± 0.008 0.291 ± 0.008 0.069 ± 0.003 0.061 ± 0.003 0.011 ± 0.001 2.291 ± 0.025 1.965 ± 0.022 1.911 ± 0.026 0.493 ± 0.009 0.433 ± 0.009 0.081 ± 0.003

MCMC* (Uniform)

0.347 ± 0.067 0.303 ± 0.077 0.283 ± 0.502 0.070 ± 0.015 0.064 ± 0.017 0.011 ± 0.003 2.256 ± 0.330 1.973 ± 0.332 1.919 ± 0.320 0.502 ± 0.092 0.452 ± 0.087 0.084 ± 0.016

We also made tests on the rare event example of Heegaard (Heegaard 1997), but noticed a tendency to underestimate the probabilities. The reason is that when performing rare event simulation the Markov chain of the Gibbs sampler is confined to move only within a very small part of the whole state space. Then it does not necessarily sample the most important blocking states for all traffic classes. Therefore, when dealing with rare event simulation our improved method needs to be combined with importance sampling methods to shift the probability mass closer to the state space boundaries.

6 CONCLUSIONS

In this article we have presented an efficient simulation method for calculating the blocking probabilities for calls in a multiservice loss system. The method is based on the use of the Gibbs sampler with an appropriate partition of the state space. We are then able to exploit the product form solution by calculating analytically the effect of using as samples not the current state X~ of the simulation of the Markov chain, but states after a 'virtual' step from the current state generated with the transition matrix p{k). It is then possible to calculate analytically the probability of this new sample hitting the blocking state of a class-k call. Thus for each state X~ in the chain we get a contribution from the blocking state for class-k call leading to clear reduction in the variance over the traditional Me summation techniques as shown by our numerical results. Also, it was shown that the improved method does not lead to excessive computational complexity.

ACKNOWLEDGEMENT

The authors wish to thank Samuli Aalto for many useful discussions during the course of the work.


REFERENCES

Crane, M.A. and Iglehart, D.L. (1975) Simulating Stable Stochastic Systems: III. Regenerative Processes and Discrete Event Simulations. Operations Research, vol. 23, no. 1, 33-45.

Crane, M.A. and Lemoine, A.J. (1977) An Introduction to the Regenerative Method for Simulation Analysis. Springer-Verlag, Berlin.

Heegaard P.E. (1997) Efficient Simulation of Network Performance by Importance Sampling. Teletraffic Contributions for the Information Age. Proceedings of ITC-15, vol. 2a, Elsevier, Netherlands, 623-632.

Ross K.W. (1995) Multiservice Loss Models for Broadband Telecommunication Networks. Springer-Verlag, Berlin.

Tierney L. (1994) Markov Chains for Exploring Posterior Distributions. The Annals of Statistics, vol. 22, No.4, 1701-1762.

APPENDIX

Consider the sum

H = L h(x)p(x) = E [h(X)] , xES

where X is a random variable with the distribution p(x), and the corresponding estimator

A 1 N

H= N Lh(Xn) ' n=l

where Xn are samples of the random variable X. Let P be any transition matrix with invariant distribution p(x). Then Y

which is obtained from X with this matrix also has the distribution p(x). H may then be written as

H = E [h(Y)] = E [E [h(Y) I Xll

Assume now that E[h(Y) I X] can be calculated analytically. Then a new estimator for H can be written

N

if = ~ I: E [h(Y) I X = Xnl , n=l

which for each sample Xn includes all the points reachable from Xn with the transition matrix P.

PART EIGHT

Mobility and Wireless Networks

21 Effects of User Mobility on a TCP Transmission

Anne Fladenmuller, Ranil De Silva2

1 School of Electrical Engineering, 2 School of Computing Science University of Technology, Sydney P. a.Box 123, Broadway, NSW 2007, Australia e-mail: {anne.ranil}@eng.uta.edu.au Tel:+61 2 9514 2460 Fax:+61 2 9524 2435

Abstract This paper studies Mobile IP performance during handoffs. We have conducted experiments with TCP and mobile IP to observe the effect of handoff on transmission reliability. This paper shows that although Mobile IP may be appropriate for current applications, its long handoff periods make it unsuitable for the future.

Keywords Mobility, Handoff, Mobile IP, TCP

1 INTRODUCTION

With the increasing number of portable computers and the development of wireless networks, mobile computing has become more popular. Although there are still many technical problems to obtain seamless mobility, data can now be transparently transmitted to the host independently of the location given by its IP address. This is achieved through mobile routing protocols like Mobile IP.

With such mobile protocols, users can connect their laptop on diverse networks and receive data without changing their IP address or modifying their network configuration. They can also move between different networks without having to restart their applications. Therefore, when a mobile host switches networks, a handoff occurs to adjust the mobile routing functionality. Several protocols provide such services and all require fast handoffs.

Basing our work on the mobile IP standard, we have conducted some experiments, with varying network conditions, observing the effect of handoffs on higher layer protocols like TCP.

Performance of Infonnation and Communication Systems U. KHmer & A. Nilsson (Eels.) e 1998 IFIP. Published by Chapman & Hall

276 Part Eight Mobility and Wireless Networks

2 MOBILE COMPUTING

Mobile computing introduces a number of problems to current Internet working standards. We identify three main problems dealing with mobility in the Internet - mobile routing, wireless protocol support and mobile application support.

1. The first problem deals with the IP address which has two uses in the Internet - to provide a unique identification for a network interface and secondly to provide routing information about this interface. When a computer becomes mobile, the IP address is still used to identify the network interface but it no longer indicates the location of the mobile computer. This causes normal Internet routing to fail. A number of different techniques have been proposed to solve this problem - one such solution is the Mobile IP standard.

2. The second problem involves protocol support for wireless networking technologies which have been integral in the development of mobile computing. Wireless network technologies have different network characteristics to fixed networks and traditional protocols result in poor performance when operating over wireless networks.

3. The third problem identified with mobile computing is support for mobile applications. Mobile computers currently are likely to be disconnected from the network for large periods. This could be the result of power saving measures on power-limited computers or due to a lack of network connectivity when moving. Mobile applications must be able to survive this and to maximise time when connected on the Internet. In addition, with mobility, applications will evolve and will have to support new services like location dependent behaviour. For this to occur there must be proper services present to aid application development.

This paper is focused on the first problem of mobile routing and in particular one facet of it - the handoff that occurs when a mobile computer moves between different networks.

3 MOBILE ROUTING PROTOCOLS

The aim of mobile routing protocols is to hide the movement of the mobile host to the upper layer protocols and applications. A number of solutions have been proposed all based on the principles of relaying packets from the home network to a foreign network before passing the packets to the mobile host. Routing in the opposite direction is assumed to take the normal routing path.

Mobile IP (IETF 1996) achieves the re-routing through encapsulation of IP headers. If the mobile host is at its home network, then packets can be routed

Effects of user mobility on a rep transmission 277

to it using normal routing. If the mobile host moves to a foreign network, the mobile host registers with its home agent to forward any packets addressed to the mobile host via the foreign agent. The packets arriving are encapsulated in a new IP header and sent to the foreign agent. The packet is routed through the network using this new header. At the foreign agent, the new header is removed and the packet is sent to the mobile host. When the mobile host returns to its original network, it deregisters with the home agent and packets are again routed to its normal location.

Many of the alternate solutions also attempt to solve wireless networking problems at the same time. For example 1-TCP (Bakre et al. 1995) uses a non standard Mobile IP implementation developed at Columbia University to solve mobile routing and at the same time uses two separate TCP links to provide different services for varying wireless and fixed environments.

A different solution for handling mobile routing is Snoop (Balakrishnan et al. 1995) which attempts to use multicast addresses to hide the location of mobile computer.

4 NETWORK SWITCHINGS

When the mobile computer moves into a new network, mobile routing services will have to change to reflect this. These changes generally require an exchange of packets called a handoff and during this period, normal transmissions to the mobile host are disrupted. We are interested in the effects of mobile routing handoffs on transport protocols.

Handoffs take place at two levels. The first is the low level handoff that involves the mobile host moving to a new network. In terms of a fixed network, this may consist of plugging the mobile computer onto the network while in an wireless network environment it may simply consist of moving into a new cell. The second level involves the mobile routing handoff, that detects the mobile host has moved into a new network and handles changes to redirect traffic to the mobile host.

It has been shown in (Caceres et al. 1994) that handoffs· have a negative effect on TCP performance over wireless networks. Packets get lost during the switching of networks and that triggers the TCP congestion control algortihm. As a result the transmission throughput is decreased and the performances drops.

In order to determine whether this degradation of performance is due to the wireless link or more generally to a special network configuration, we compare the effects of mobile IP handoffs under different conditions. In the next section we describe the results of our experiments to show the effect of handoffs over wireless and fixed networks. Thus we intend to show that it is not possible to improve the performances without modifying TCP, mobile IP or both.

"the non-standard Columbia implementation of Mobile IP was used


Mobile Host

Figure 1 Testbed configuration

5 EXPERIMENTS

5.1 Network configuration

Our experimental testbed consists of a mobile host, two foreign agents and a home agent deployed in a normal office environment as shown in Figure 1. The PCs (486s and pentiums) used for these tests were running Linux (version 2.0.30) and the Mobile IP vl.O developed at the State University of New York, Binghampton (Dixit et al. 1996). We have chosen this implementation as it complies with the IETF Mobile IP draft (revision 16). Tcpdump is used to observe the data transmission during the Mobile IP handoff.

The home and foreign agents and the corresponding host are all connected through fixed LANs (Ethernet lOMbps). The mobile host can be connected to the foreign agent using wireless links (WaveLan 2Mbps) or fixed networks (Ethernet lOMbps).

5.2 Wireless vs Fixed Network Handoft's

The experiment done with wireless links between the mobile and the foreign agents is shown in figure 2. This graph presents the packets sent and the acknowledgments exchanged during the transmission. The dotted line corresponds to the registration phase occurring between the foreign and the home agent. Similarly the figure 3 represents the experiment done in a fully wired environments.

In both cases, it takes about 3 seconds for the transmission to be normally reactivated although the registration phase between the home and the foreign agent takes only 0.5 seconds. This difference can easily be explained as the handoff period consists of several operations of which one is the registration. The low-level handoff during which the mobile host is disconnected from both networks lasts nearly 1 second for both cases. The discovery period for the mobile host to detect that it has moved into a new network can take up to a second as this is how often advertisements are sent by foreign agents.

Adding the disconnection, the discovery and the registration times, we ob-

Effects of user mobility on a rep transmission 279

woo.--------.-------,--------,--------.------~

1800 Packets sent • Packets ac:know1edsed +

Registration between HA and FA ..... . 1600

1400

.. . ...... .

4 10 TIme (seconds)

Figure 2 Handoff in wireless environment

tain a handoff period of 2 to 3 seconds for both experiments. But once the handoff is finished we can notice the transmission does not immediatly recover. This delay, of nearly one second, is the result of TCP's congestion control mechanisms : the exponential backofi" and slow start algorithms.

In TCP (Stevens 1994), each packet has to be acknowledged to guarantee the reliability. If after a certain time* the acknowledgment has not been received, the packet is retransmitted. To prevent network congestion, the timeout value is doubled for each unsuccessful retransmission. This behaviour is called the exponential backofi" and can be observed on both figures just after the disconnection at T=2.5s. After the disconnection, it is necessary for a data packet to be correctly received to resuscitate the connection. Due to successive timeouts occurring during the handofi" period, the exponential backoff algorithm results in long delays before retransmitting a data packet. Therefore after the registration, there can be a period of no activity until a retransmission occurs.

Furthermore the slow start algorithm is designed to prevent TCP from transmitting its full window size when the underlying network is congested. It is based on the assumption that if a packet is lost during transmission, it is due to congestion and as a result TCP immediates reduces its current window size. It can be observed from the curves on both graphs that rate of transmission is slower after the handofi".

As a conclusion of these experiments, we have shown that the use of a wireless link does not increase the handoff time. However, if one of the mobile IP

*RTO: Retransmission TimeOut value is approximately 3 x roundtrip time


4~.-----~-------r------.-------~-----.------~

/ , 3000

O. 0 ........ / 4 6 10 12

TIme (seconds)

Figure 3 Handoff in wired environment

registration message is lost due to the poor link quality· then the handoff for a wireless link might be longer. The only difference between the experimental results shown is the throughput of the transmission.

An important issue to raise is the poor performances of TCP. One third of the handoff time is due to the unsuitable congestion control algorithm of TCP. In order to avoid slow start, it is necessary that the sender receives an acknowledgment before the timeout occurs. In local area networks, due to the short roundtrip delays and given the handoff period, it is unlikely to prevent timeouts from occurring. It is then important to check if the roundtrip time can in some circumstances be greater than the handoff time.

5.3 Increasing the roundtrip time

We have conducted similar experiments as in section 5.2, but we have chosen the corresponding host in order to increase the roundtrip time and hence the retransmission timeout value to help avoid TCP's slow start. For our experiments, the corresponding host was in France while the rest of the computers remained in Australia.

The results obtained in figure 4 show that the throughput is 100 times lower than the one obtained in figure 3. In this configuration, we had a timeout time of roughly 1.5 seconds, where as the handoff period remained at 3 seconds. Since the timeout time was less the handoff period it was not possible to avoid

-This occured only once during our experiments.

Effects of user mobility on a rep transmission

40r------,-------r------.-------.------.--~~_,

35

30

25

20

15

10

Packets sent ¢

Packets acknowledged + Registration between HA and FA .....

+ + 0

o + +

• o + 0 o o

+ 0 o o

+ 0 o

+ 0

o o

+0 ... o

+0 o

+0

• o -10 o

+0 o o

+0 o

+0 +0 o

+0 o

-10 o

+0

O~~+_~------~------~------~----~------~ o 6 10 12

Time (seconds)

Figure 4 andoff when transmitting in a wide area network

281

the slow start. We believe that our choice of network configuration is about the worst that can be achieved currently on the Internet. This suggests that it may not possible to avoid slow start during a Mobile IP handoff in any realistic network.

6 CONCLUSION

The work presented in (Caceres et al. 1994) shows that Mobile IP handoffs degrade transmission over wireless links. We have extended this conclusion to wired links and we have shown the congestion control algorithm would in any case be triggered. Buffering packets at the foreign or home agent may appear as a good solution to reduce loss during handoff but it can not prevent timeouts occurring thus triggering the slow start algorithm.

Although current applications may not be adversely affected by Mobile IP handoffs, the problem will become more significant in the future. As users become more mobile, the frequency of handoffs will increase. In a pico-cell environment, if handoff takes too long, user may reach the next cell before its completion. Therefore it will be necessary in the future to improve handoff performances which will require the modification of both Mobile IP and TCP.


REFERENCES

Bakre, A. and Badrinath, B. (1995) Indirect TCP for mobile hosts. In Proc. of 15th Intemation Conf. on Distributed Computing Systems, May.

Balakrishnan H. Seshan S. Amib E. and Kratz R. (1995) Improving TCP lIP performance over wireless networks. In Proc. of 1st Inti. ACM Con/. on Mobile Computing and Networking (MOBICOM), November.

Caceres R. and Iftode L. (1994) Improving the performance of reliable transport protocols in mobile computing environments. In JSAC, special issue on Mobile Computing Networks, 1994.

Dixit A. and Gupta V. Mobile IP for Linux (version 1.00). Technical Report, Dept. of Computer Science, State University of New York, Binghampton.

Internet Engineering Task Force IP Mobility Support. Technical Report, April.

Stevens W. R. TCP lIP Illustrated Volume 1, Addison-Wesley, 1994.

7 BIOGRAPHY

Anne Fladenmuller received her Ph.D. from University Pierre et Marie Curie in 1996. She then completed a post doctorate at the School of Electrical Engineering, University of Technology, Sydney where she has since taken up the position of Lecturer. Her research interests include mobile communications, network protocols and QoS Management.

Ranil De Silva received his B.CompSci(Hons) from Bond University in 1993 and has just submitted his Ph.D. thesis at the School of Electrical Engineering, University of Technology, Sydney (UTS). He is currently employed by the School of Computing Science, UTS as a Research Assistant. His main research interests are in adaptive protocols and mobile computing environments.

22 Achievable QoS in an Interference /Resource-Limited Shared Wireless Channel

Jeffrey M. Capone Department of Electrical Engineering Arizona State University, Tempe, AZ 85287-7206 jcapone<Oasu.edu

Ioannis Stavrakakis Department of Electrical and Computer Engineering Northeastern University, Boston, MA 02115 ioannis<ocdsp.neu.edu

Abstract In this work, the region of achievable QoS - which is central to the development of a call admission control mechanism - is precisely described for a system of heterogeneous VBR sources with real-time service constraints. The QoS for each application is defined in terms of a packet dropping probability. Packets may be dropped due to delay violations and channel induced errors. The shared transmission resources are defined to be the slots (packet transmission times) of a TDMA frame. The region of achievable QoS is precisely described for a interference/resource-limited network by considering the underlying TDMA-MAC structure and the physical channel. A simple DLC protocol that combats the effects of the wireless channel while satisfying the real-time requirements is proposed and its impact on the region of achievable QoS is evaluated. The results presented here clearly illustrate the negative impact of a poor channel and the positive impact of the employed DLC protocol on the achievable QoS.

Keywords Quality of Service (QoS), TDMA, Scheduling, DLC.

1 INTRODUCTION

In integrated services wireless networks transmission resources are shared among geographically dispersed applications with diverse traffic characteristics and quality of service (QoS) requirements. In this work, the shared transmission resources are defined to be the slots (packet transmission times)

Perfonnance of Infonnation and Communication Systems U. Komer & A. Nilsson (Eds.) © 1998 IFIP. Published by Chapman & Hall


of a TDMA frame. This resource structure has been widely considered in both cellular personal communication networks (PCN) [1] and wireless LANs, as well as in recent work toward the development of wireless ATM networks [2]. The QoS requirements for each application are defined in terms of a maximum tolerable packet delay and dropping probability. To provide QoS guarantees and use the bandwidth efficiently, call admission and scheduling functions are necessary.

A variety of scheduling policies have been proposed to support real-time traffic in a shared wireless environment [3, 4, 5, 6, 7]. In [3, 4], the performance of the scheduling policies are evaluated for different combinations of variable bit rate (VBR) sources, while in [5, 6, 7], the scheduling policies are designed to meet (if achievable) the QoS required by the set of heterogeneous VBR applications. In [5], the authors determine a very conservative scheme and provide only sufficient conditions to ensure that the scheduling policy can deliver service satisfying the delay constraints of the VBR sources and meet their deterministic QoS guarantees. Probabilistic QoS guarantees are considered in [6, 7] and in this paper. For example, packets from a particular source (such as voice or video) might only need to meet their delay constraint 99% of the time, and can tolerate being dropped otherwise. In this work, necessary and sufficient conditions in order for the probabilistic QoS to be achieved are presented, leading to bandwidth efficient call admission control and scheduling algorithms.

In a wireless network, achievable QoS is shaped not only by the amount of available resources and the employed transmission scheduling, but also by the channel quality (interference). As a consequence, the region of achievable QoS vectors is shaped by the packet discarding process at both the transmitter and the receiver due to resource and interference limitations, respectively. In addition, the performance - and therefore the region of achievable QoS -can be enhanced by considering a properly designed DLC protocol for this environment. Such a protocol is also considered in this paper.

2 DESCRIPTION OF THE SYSTEM MODEL

Consider a system where N heterogeneous VBR sources compete for T slots of an up-link TDMA channel. At the beginning of each frame n each source i requests a random number of slots denoted by .Ai (n). If the aggregate demand in frame n, L:~1 .Ai(n), exceeds the number of slots available to the VBR traffic - referred to as an overloaded frame - then decisions must be made regarding the amount of service that will be provided to each source. The number of slots, a{ (n), under scheduling policy f allocated to source i may be less than what is required by that source, .Ai(n), due to resource limitation. Packets from a source which do not receive service over a frame following their arrival are considered to have excess delay and are dropped at the source.

Achievable QoS in a shared wireless channel 285

The effects of the wireless channel are modeled as in [8], where a Gaussian noise channel with random bit erasure interference is considered. The erasure process might be produced by a burst noise process which produces bursts of erasures. However, in [8], an interleaver/deinterleaver is employed to turn the erasure bursts into statistically independent bit erasures. Therefore, in this system, packet erasures are considered to be statically independent and occur when the interference in the channel is such that the packet is corrupted in manner that it can not be corrected. The corrupted transmitted packets are discarded (dropped) at the receiver.

The event that the packet is corrupted and therefore dropped is a function of interference in the channel, the transmitted power, the coding scheme, and the packet length. Let Z be an indicator function of a packet erasure. That is,

Z={ 1 if the packet is corrupted o otherwise (1)

Therefore, the expected value of Z, E[Z] = {3, is the probability that a packet is corrupted by the channel and dropped.

Considering the combined impact of scheduling policy f and the physical channel, the number of packets from source i dropped in frame n due to the above competition for the resources and the interference in the channel is given by,

{ ,,>'i(n) Z

f( ) L.",m=l m d,. n = .() f() "a{(n) A, n - ai n + L.",m=l Zm

if L:f=l Aj(n) ::; T

if L:f=l Aj(n) > T (2)

Zm is an indicator function associated with the transmission of the mth packet

from source i. Let d{ = E [d{ (n) ] , a{ = E [a{ (n)] and Ai = E [Ai ( n )] be the

(assumed time invariant) expected values of the associated quantities. Suppose that the QoS requirement of application i is defined in terms of a

maximum tolerable average per frame packet dropping rate di , 1 ::; i ::; N. Then the QoS vector associated with these applications can be defined in terms of the (performance) packet dropping rate vector d = (d1, d2 , ••• , dN ).

When the QoS requirement of the application i is defined in terms of a maximum tolerable packet dropping probability Pi, the corresponding packet dropping rate di is easily determined by di = Ai Pi.

The first question addressed in Section 3.1 is whether (under the given channel conditions) a given QoS vector d is achievable under some policy f. The results from Section 3.1 are modified to reflect the impact of the proposed real-time DLC protocol and are presented in Section 3.2. The second question, addressed in Section 4, is concerned with the design of scheduling policies that deliver an achievable target QoS vector d.


3 DETERMINATION OF THE REGION OF ACHIEVABLE QOS VECTORS

The establishment of the region of achievable QoS vectors is based on a set of inequalities and an equality constraint derived by employing work-conserving arguments. The superscript / is used to denote the employed packet scheduling policy. It is assumed that the scheduling polices are work-conserving (that is, non-idling) and induce a performance vector d! .

3.1 Achievable QoS Provided by the Underlying MAC and Physical Channel

Let S = {I, 2, ... , N} be the set of all sources and d~ denote the average system packet dropping rate under scheduling policy /, denoted by,

(3)

Let Ag(n) denote the aggregate arrival rate from sources in set g, 9 ~ S. That is, Ag(n) = :LiE9 Ai(n).

Summing (2) over all sources i E S and by considering the expected value of the associated quantity, the average system packet dropping rate under work-conserving scheduling policy / is derived and it is given by,

d~ = { E [As (n) I As (n) > T] - T (1 - /3) } P (As (n) > T)

+/3 {E [As(n) I As(n) ~ T]} P (As(n) ~ T).

(4)

As it can be seen from (4), d~ is independent from the policy /; it only depends on the aggregate arrival process, the number of resources T, and the channel characteristics /3. Therefore, the system dropping rate, d~, is conserved under any work-conserving policies / and is denoted as bs.

Let d~ denote the average subsystem 9 packet dropping rate under policy

/, defined by, d~ ~ E [:LiEgd{(n)] = :LiEgE [d{(n)] = LiEgd{, 9 C S. That is, d~ is equal to the aggregate packet dropping rate associated with sources in group 9 only, under policy /; all N sources in S are assumed to be present and served under policy /.

Let bg denote the lower bound on the aggregate packet dropping rate for sources in g. This bound is equal to the packet dropping rate of a system in which only sources in 9 are present and served under a work-conserving


policy; sources in set {S - 9} are considered to be removed. It is given by,

bg = {E [Ag(n) I Ag(n) > T] - T (1 - (3) } P (Ag(n) > T)

+f3 {E [Ag(n) I Ag(n) ~ T]} P (Ag(n) ~ T).

(5)

It is apparent that no policy can deliver a lower dropping rate than bg to sources in set 9, when all sources in S are present. It can be seen that this lower bound is attained by all policies f which give service priority to packets from sources in set 9 over those in the complement set {S - 9}. It has been shown in [6] that in an error-free channel, the following conditions,

dg > bg "19 ~ S

ds bs ,

(6) (7)

are necessary and sufficient in order for a QoS vector d = (d1, d2 , ... , d N) to be achieved by some scheduling policy f. This result can be extended to account for the channel quality provided that bg , given in (5), is a super-modular set function; a detailed proof can be found in [9].

Let V denote the collection of all vectors d satisfying (6) and (7). Then by definition V is a convex polytope. Using results from convex polytopes, any vector in the set V can be expressed as a convex combination of extreme points (vertices) of V; that is, V may be expressed as the convex hull of its extreme points, V =conv[exp(V)].

In addition, from the polytope structure and the super-modularity property of the set function bg , it can be shown (see [6]) that d* is a vertex ofthe set V iff d* is a dropping rate vector resulting from an Ordered HoL (O-HoL) priority service policy 1r= (11'1,11'2, ... , 1I'N); 1I'j E {I, 2, ... , N}, 1I'j =I 1I'j, 1 ~ i, j ~ N. The index of 1I'j indicates the order of the priority given to the 1I'j source. None of the 1I'j sources, j > i, may be served as long as packets from sources 1I'k,

k ~ i, are present. Fig. 1 provides a graphical illustration of the region V for the case of N = 2

and N = 3 sources. The extreme points correspond to QoS vectors d induced by the N! ordered HoL priority policies 1r= (11'1,11'2, ... , 1I'N)'

The region of achievable QoS is shaped by both the amount of available resources and the level of interference in the wireless channel. To illustrate this, consider the following example of two sources competing for T slots in a TDMA frame. The source packet arrival processes are assumed to be mutually independent. Each arrival process is embedded at the frame boundaries. The number of packets generated (and requesting service) by a source in the current frame boundary is (probabilistically) determined by the present state of the underlying arrival process. The region of achievable QoS is only dependent on the state probability distribution, thus, correlation in the source packet ar-


i-~II

". " . : (1.2)

[)roPPinll'lle. sou"," I

Figure 1 The region (polytope) 1) for a system with two and three sources under channel conditions 13 = 0.02.

Lower Bound for System Packet Dropping Probabllity 10' '""""'"___r-__r_-..---___r-__r_~..______r-__r_-.._____,

, , , ,

~ Error-Free Chlnnel -:- Wireless Channel

Intert.renOl-Llmit.d

1O-30~----7-~-~----78 --'"10:--'----,1':-2 -"-:14--'"16,-----,1':-8 --!20

T (oIo1slfrome)

Figure 2 System packet dropping probability for in an error-free channel and a (non-ideal) wireless channel with channel conditions 13 = 0.02.

rival process may be considered without affecting the region of achievable QoS or the analysis presented in this paper.

In this example, each VBR source is modeled by discrete-time batch Markov arrival process embedded at frame boundaries, with mean rate of 3.6 and 3.2 packets per frame, and variance of 2.04 and 3.36 packets per frame, respectively. In Fig. 2, the conserved system packet dropping probability Ps = E[Abss(n)] is plotted as a function of available resources T (time slots) for an error-free channel (f3 = 0) and a wireless channel with channel quality, 13 = 0.02.

As it can be seen in this figure, there are three distinct regions of operations:


Resource-Limited, Interference/Resource-Limited and Interference-Limited. In the resource-limited region, the performance is primarily determined by the amount of available resources. This result is evident since the packet dropping probability for the system with the error-free channel and the (non-ideal) wireless channel are almost identical. In the interference-limited region, the dropping probability in the error-free channel is zero, while the performance in the wireless system is limited by the interference and given by f3 = 0.02. The performance in the interference/resource-limited region is determined by both, the available resources and the level of interference in the channel. In this example, the system packet dropping probability in this region ranges from 10-1 - 10-2 , an operation region of interest for real-time applications. It is important to note (as shown earlier) that, in general, satisfying the system packet dropping rate (probability) is only necessary and not sufficient to guarantee that the target QoS vector is achievable*.

3.2 Impact of Real-Time Data Link Control

A Data Link Control Layer (DLC) can be added to combat the effects of the wireless channel in an interference/resource-limited or interference-limited system. Due to the real-time constraints of the supported applications', traditional automatic repeat request (ARQ) strategies are not possible. In this section, a real-time DLC protocol is proposed and the impact that this layer has on the region of achievable QoS is evaluated.

To combat the effects of interference, the real-time DLC protocol considered in this work will generate multiple copies of certain packets for transmission over the current frame. This strategy will improve the probability of correct reception (or reduce the probability of packet dropping at the receiver) while meeting the real-time service constraint. Copies are transmitted only during underloaded frames utilizing the remaining resources* . Transmitting a copy from a set 9 during an overloaded frame would reduce the probability of packet dropping at the receiver for the set g, but would force an original packet from the complement set {S - g} to be dropped at the source. As a result, the overall system dropping rate to increase. In view of the above discussion, if the objective of the real-time DLC protocol is to minimize the system packet dropping probability (or equivalently packet dropping rate), and therefore maximize system throughput, then multiple copies of packets can be sent only during underloaded frames - utilizing the remaining resources.

During underloaded frames, the number of copies generated by the the DLC is a function of the scheduling policy and the amount of remaining resources.

°In the special case of a homogeneous system, such as a cellular voice system, satisfying system performance is sufficient to guarantee that the target QoS vector is achievable. This result has been established in [6). °The remaining resources in frame n are defined to be (T - .xs(n».

290 Pan Eight Mobility and Wireless Networks

A policy that attempts to "fairly" allocate the remaining resources among sources will result in the minimum system dropping rate. This result can be seen by letting kf = (k{, k~, ... , k{s(n»)' 1 ::; kin ::; T, 1 ::; m ::; As(n), be a vector which determines the number of transmissions of each packet m E {I, 2, ... , As(n)}. For a given As(n), the expected number of packets arriving at the receiver in error under this policy is equal to,

As(n) L pic!,., (8) m=1

where,2:~s~~) kin = T, 1 ::; kin ::; T, 'tim E {I, 2, ... , As(n)}. Since p:& is a convex function of :1:, that is, 'Ypa + (1 - 'Y)Pb 2:,8"Ya+(1--y)b for 0 ::; 'Y ::; 1, then,

(9) m=1

Since (9) is minimum when kin = As1n) = k, (9) is minimized when each

sources i receives Ai(n)k = ~~~~)T slots for transmission of the Ai(n) packets and its copies. In this sense the policy is "fair".

However, due to the granularity in the system (that is, resources can be allocated only in integer multiples), the following is considered. During un-

derloaded frames, let each packet be transmitted R ~ l As~n) J, R 2: 1, number

of times, where l.J denotes the integer part, and let X ~ (T - As(n)R) be the number of packets that can be transmitted one additional time, (R + 1). The system dropping rate is then conserved regardless of which set of sources the packets that are transmitted one additional time belong to. Allocating the additional retransmission during underloaded frames according to a policy allows for further diversification of the resulting QoS vector delivered, while still satisfying the requirement of minimum system dropping rate. Therefore, under any fair-work-conserving policy, the system dropping.rate (given below) is minimum and also conserved.

The results from Section 3.1 can be modified to account for th~ impact of the DLC protocol. Considering the effects of the physical channel, the scheduling policy and the real-time DLC protocol, the number of packets from source i dropped in frame n is given by,

{ "Ai(n) nR+1!,. zq

d{ (n) = L..J(m=) 1 r( 1) ;a[ (n) Ai n - ai n + L..Jm=1 Zm

if As(n) ::; T ,0 ::; i::; N. if As(n) > T

(10)


1!n E {O, I} and indicates the dependency of the additional transmission of a copy of packet m on the fair policy f, where L~J~) 1!n = X, \:If. z;? is an indicator function associated with the qth transmission of the mth packet from source i. In this case, E[d{ (n)] = d{ (mean per frame packet dropping rate) is the QoS provided to the network layer by the underlying DLC, MAC and physical channel.

The region of achievable QoS vectors when the above DLC layer is present can be derived by modifying the lower bounds given by (4) and (5), to account for the impact of the real-time DLC protocol. As previously stated the system dropping rate under all fair-work-conserving polices f is conserved, it is given by,

bs = {E [As{n) I As{n) > T] - T (1- f3)} P (As(n) > T)

+E [Xf3R+l I As(n) :S T] P (As(n) :S T)

+E [(As(n) - X) f3R I As(n) :S T] P (As(n) :S T) .

(11)

With the addition of this DLC protocol, the lower bound bg for the aggregate packet dropping rate for sources in 9 under any fair-work-conserving policy f is determined to be,

bg = { E [Ag (n) I Ag (n) > T] - T (1 - ,8) } P (Ag (n) > T)

+E [min[Ag(n),X]f3R+1 I Ag(n):S T] P(Ag(n):S T)

+E [max[O, Ag(n) - X]f3R I Ag(n) :S T] P (Ag(n) :S T).

(12)

The expected value in (12) is with respect to {Ag(n), As(n)}, which is easily computed since P(Ag(n) = i, As(n) = j) = P(Ag(n) = i)P(A{S_g}(n) = j-i). The expressions in (11) and (12) reduce to (4) and (5) respectively, for R fixed and equal to 0. The extreme points in this case correspond to FairOrdered-HoL (F-O-HoL) priority service policies. A F-O-HoL service policy is an O-HoL service policy 7r= (1rl' 1r2, .. " 1rN) in which the additional retransmissions are also allocated according to 7r.

With the addition of the real-time DLC protocol, the region of achievable QoS for an interference/resources or interference-limited system can be improved compared to the system not employing the DLC protocol. The impact the real-time DLC protocol has on the system packet dropping probability for the example described in Section 3.1 is shown in Fig. 3.

In this figure, the performance of the two systems is compared to that in an error-free environment. As it can be seen in this figure, the system employing the real-time DLC protocol induces a lower packet dropping probability than the system without. The impact is most significant in the interference/resource-


Lower Bound for System Packet Dropping ProbabiNty 10' =---r--'--~--r--.--~--r--.--~--.

-.:... Error-Free Channel

-.; NoDLC

- .~. Ole Improvements

Figure 3 The impact of the real-time DLC protocol on the system packet dropping probability in a wireless channel with channel conditions (3 = 0.02.

Region 01 Achievable CoS 'Of fnledOl8llC8lRuoulC8-UmHod System O.2r---'--~--r--r--r-r---r--r----'-----'--r----,

0.18

0.16

'. '. '.

0.04

0.02

- Error-Free Charnel

- - NoDLC . -. - OLe Improvements

'. '.

, '---------

~~~0~.02~0~.04~~o.=re~o~~~~0.~1~0.=12~O~.14~0~.1~6~O.=18~0.2 DroppIng Rate. Soun:e 1

Figure 4 The impact of the real-time DLC protocol on the system packet dropping probability in a wireless channel with channel conditions (3 = 0.02.

limited and interference-limited regions. In these regions the system with the real-time DLC takes advantage of the remaining resources and can reduce the packet dropping probability.

The impact that the real-time DLC has on the region of achievable QoS V is illustrated in Fig. 4. In this figure, V is derived for the system of sources given in Section 3.1 and with T = 10 slots. Thus, according to Fig. 2, the system is interference/resource-limited. As it can be seen, a larger collection of QoS vectors can be accommodated.

Achievable QoS in a shared wireless channel

4 A CLASS OF POLICIES DELIVERING ANY ACHIEVABLE QOS VECTOR IN 1)

293

In this work, the region of achievable QoS 'D leads to a class of scheduling polices capable of delivering any achievable performance. The result follows from that fact that'D can be written as a convex combination of the extreme points (vertices) d ext- i of 'D. That is if d E 'D, then d = E~l aidext-i for some

0:= (aI, a2,··., aN!) where ai ~ 0, 1 ~ i ~ N!, E~l ai = 1. Therefore, by selecting the F-O-HoL priority policy that induces the extreme point d ext- i of'D with probability ai, any QoS vector in 'D can be delivered. This class of policies is referred to as a mixing F-O-HoL priority policy. Typically, several mixing priority polices exist that can deliver the target dropping rate vector. This allows for the incorporation of additional constraints representing other desirable qualities of the policies. Functions of interest may be minimized subject to the constraints presented to guarantee the delivery of the target QoS vector. For instance, among all the mixing policies inducing d, the one which minimizes the variance of the service provided to certain sources may be identified.

5 CONCLUSION

In this work*, the region of achievable QoS has been precisely described for a system of heterogeneous real-time VBR sources competing for an unreliable wireless channel. The QoS has been defined in terms of a packet dropping probability (or equivalently packet dropping rate). Packets from sources in the system were dropped as a result of delay violations and channel induced errors. As a consequence, it has been shown that the region of achievable QoS is shaped by both the interference in the physical channel and the amount of available resources. In addition, a simple DLC protocol has been proposed to combat the effects of the wireless channel while still satisfying the realtime service constraints of the associated applications. The results presented in this paper illustrate the positive impact of the employed DLC protocol on the region of achievable QoS.

REFERENCES

[1] N.D. Newman, R. Ganesh, K. Joseph, and D. Raychaudhuri. Packet CDMA Versus Dynamic TDMA for Multiple Access in an Integrated Voice/Data PCN. IEEE Journal on Selected Areas in Communications, 11(6):870-884, August 1993.

• Research supported in part by the National Science Foundation under Grant NCR 9628116.


[2] D. Raychaudhuri and N. Wilson. ATM-Based Transport Architecture for Multiservices Wireless Personal Communication Networks. IEEE Journal of Selected Areas Communications, 12(8):1401-1414, October 1994.

[3] B. Walke, D. Petras, et al. Wireless ATM: Air Interface and Network Protocols of the Mobile Broadband System. to appear in IEEE Personal Communication Magazine.

[4] G. Anastasi, D. Grillo, and L. Lenzini. An Access Protocol for Speech/Data/Video Integration in TDMA-Based Advanced Mobile Systems. IEEE Journal of Selected Areas in Communications, 15(1), January 1997.

[5] C. Chang, K. Chen, M. You, and J. Chang. Guaranteed Quality-of-Service Wireless Access to ATM Networks. IEEE Journal of Selected Areas in Communications, 15(1), January 1997.

[6] J. Capone and I. Stavrakakis. Achievable QoS and scheduling Policies in Integrated Services Wireless Networks. Performance Evaluation, 26 and 27(1), October 1996.

[7] J. Capone and I. Stavrakakis. Delivering Diverse Delay/Dropping QoS Requirements in a TDMA Environment. In Proceedings of ACM MobiCom, Budapest, Hungary, Sept. 1997.

[8] J. Bibb Cain and D. McGregor. A Recommended Error Control Architecture for ATM Networks with Wireless Links. IEEE Journal of Selected Areas in Communications, 15(1), January 1997.

[9] J. Capone and I. Stavrakakis. Achievable QoS In an Interference/Resource-Limited Shared Wireless Channel. submit-ted to IEEE Journal of Selected Areas on Communications.

6 BIOGRAPHY

Jeffrey M. Capone received the B.S.E.E. degree from the University of Vermont, Burlington, VT, in 1992, the M.S.E.E. and Ph.D. degree from Northeastern University, Boston, MA, in 1995 and 1997, respectively. In 1997, he joined the faculty of Electrical Engineering at Arizona State University. His primary research interest is in the design and analysis of controlling policies for bandwidth management in wireless communication networks. Ioannis Stavrakalcis received the Diploma in Electrical Engineering from the Aristotelian University of Thessaloniki, Thessaloniki, Greece, 1983, and the Ph.D. degree in Electrical Engineering from the University of Virginia, 1988. In 1988, he joined the faculty of Computer Science and Electrical Engineering at the University of Vermont as an assistant and then associate professor. Since 1994, he has been an associate professor of Electrical and Computer Engineering at Northeastern University, Boston. His research interests are in stochastic system modeling, teletraffic analysis and discrete-time queueing theory.

23 Call Connection Control in CDMABased Mobile Networks with Multiple Frequency Assignments

Sang-Ho Lee*, Sung-Hee Kim*, and Sung-Woo Park** * Mobile Network Service Section, ETRI, Korea ** Dept. of Information & Communication Eng., Hannam Univ., Korea shlee @nice.etri.re.kr

Abstract CDMA-based mobile networks with multiple FAs (Frequency Assignments) can inherently provide soft handoff as well as hard handoff. Then, there naturally arises a trade-off between soft handoff and hard handoff. To deal with this problem, this paper proposes an efficient call connection control scheme that is capable of handling the handoff requests in a flexible way. The performance of the proposed scheme is analyzed using the Markov chain and some numerical results are provided.

Keywords Handoff, CDMA, Mobile Networks, Connection Control, Wireless ATM

Performance of Information and Communication Systems U. Korner & A. Nilsson (Eds.) © 1998 IFIP. Published-by Chapman & Hall


1 INTRODUCTION

Mobile communication systems eventually aim at providing mobile end users (stations) with seamless multimedia service. To this end, wireless ATM (Asynchronous Transfer Mode) is being considered as one of the most promising technologies that enable mobile stations to communicate in a high-speed asynchronous mode [1]. However, it seems practically impossible to adopt ATM on the air interface in the current PCS (Personal Communication System) or the upcoming IMT-2000 (International Mobile Telecommunications for the 2000's). The IMT-2000 system shall be deployed in conjunction with ATM, but its wireless access still relies on the wide-band COMA (Code Oivision Multiple Access) which extends the transmission bandwidth of the existing COMA. Thus, for the time being, the COMA is expected to play an important role in the operation of mobile communication systems.

The main advantage of COMA is that the so-called soft handoff is allowed during the mobile's handoff. Compared with the hard handoff, the soft handoff inherently offers mobile stations the better QoS (Quality of Service) by providing the seamless communication service. From the system's point of view, it also provides the better performance in terms of cell coverage area and reverse link capacity [2]. Soft handoff can be supported only when the same FAs (Frequency Assignment) are available between two adjacent cells. Let us suppose that base stations are equipped with multiple F As. If the target base station can provide the same FA as the one currently used by the mobile station, soft handoff can be activated. Otherwise, the handoff request must be rejected or can still be accepted as being the hard handoff. Rather than rejecting the handoff request, it may be desirable to switch it to hard handoff.

From the above statements, we see that there exists a trade-off between soft handoff and hard handoff. If soft handoff is emphasized, the QoS of the individual connection will be improved. However, the handoff blocking probability will increase due to the low utilization of wireless channels. On the contrary, if hard handoff is emphasized, the handoff blocking probability will be lowered at the expense of the QoS of each connection. Thus, by carefully controlling the amount of hard handoff, the overall network performance may be improved. For this purpose, this paper proposes an efficient call connection control scheme for the COMAbased mobile networks where multiple FAs are available at base stations. The main purpose of the proposed scheme is to obtain the satisfied network performance by adjusting the ratio of soft handoff and hard handoff.

This paper is organized as follows. Section 2 introduces an example of the COMA-based mobile networks with their wireless FAs. In Section 3, we review the general handoff procedure of the mobile system. In Section 3, the proposed call connection control scheme is also described. In Section 4, the performance of the proposed scheme is analyzed using the Markov chain and some numerical results are provided. Finally, we conclude this paper in Section 5.

Call connection control in CDMA-based mobile networks 297

2 SYSTEM MODEL

2.1 Network architecture

The general architecture of the CDMA-based networks for IMT-2OOO is shown in Figure 1. The whole network is hierarchically constructed and consists of two parts: the core network and the radio access network.

As shown in the Figure 1, switching entities such as MSC (Mobile Switching Center) are physically interconnected with each other on apoint-to-point link and comprises a core network. A series of BSCs (Base Station Controllers) and BTSs (Base Transceiver Systems) are connected to the MSCs through the radio access networks. Both user traffics and control information are exchanged between MSC and BTSIBSC using the A TM-based transport layer. On the other hand, only control information is transferred between the HLR (Home Location Register) and SCP (Service Control Point) based on the ATM. HLR and SCP manage the location information of mobile stations and the control information of intelligent service, respectively.

Radio Access Networks Core Networks

d ---I ~ MS

COMA (W·CDMA)

0 ~ MS : Mobile Station BTS : Base Transceiver System sse : Base Station Controller MSC : Mobile Switching Center HLR : Home Location Register SCP: SelVice Control Point

Figure 1 Example architecture ofIMT-2OOO network.

The wide-band CDMA is being considered for wireless access protocol of the IMT-2OOO systems. In the IMT-2OOO, the base stations would support a various sizes of cell (e.g. macro cells, micro cells, and pico cells) depending on traffic conditions. The size of cells tends to be smaller to attain higher capacity in emerging wireless mobile networks. With the smaller size of cells. handoff would occur more frequently than ever and must be carefully handled to avoid the performance degradation due to itself. Moreover, the QoS required by some multimedia connections may put more strict restrictions on the performance of handoff process.


2.2 Wireless channels

The 2 GHz (1.885-2.025 GHz, 2.110-2.200 GHz) frequency bands are assigned for the IMT-2000. In the IMT-2000, the maximum transmission speed may vary from a few hundred kbps to Mbps (pico cell: 2 Mbps, micro cell: 384 Kbps, macro cell: 144 Kbps) depending on the current situation of mobile stations (e.g., location, moving speed, type of service, etc.). To cope with these varieties, the system will be implemented with several different frequency bands (1.2515/20 MHz). As of this writing, the detailed layout of frequency allocations for the IMT-2000 has not been available. Instead, we show the channel structure of CDMA-based PCS that are already implemented in Korea. Basically, one FA is allocated to each cell. However, in an urban area, multiple FAs (e.g. 2FA, 3FA) can be given to accommodate high volumes of user traffics.

Down-link channels of PCS can be divided into two: broadcast channels for control information and traffic channels for user information. The broadcast channel is composed of pilot channel, sync channel, and paging channel. Since the system is based on the CDMA, mobile stations are able to differentiate between logical channels with the unique code assigned to each channel. These codes are known as the Walsh code and have orthogonal properties among themselves.

1750 1840

A-band

1760 18 0

B-band

1770 1860

1750 MHz 1840MHz

C-Band

1 2 3 4 5 6 7 8 9 1011 1213 14 15 16 17 18 1920 21

11FA=1.23MHzI

Figure 2 Frequency assignment of PCS in Korea.

2.3 Handoff process

The conventional handoff requires the mobile station to break the ongoing connection with the currently communicating base station before establishing a new connection with the target base station (break before make). This hard handoff is widely used in the existing analog/digital cellular systems. On the other hand, with the soft handoff, the mobile station can commence its communication with the target base station without interrupting the ongoing connection (make before break).

In the CDMA-based mobile networks with multiple FAs, soft handoff as well as hard handoff may exist to enhance the utilization of wireless access channels. The generalized inter-BTS handoffprocess can be summarized as follows; 1) If a mobile station detects the strength of the pilot signal received from the


adjacent base station beyond a certain threshold while communicating, it notifies this information to BSC via BTS.

2) The BSC then sends to the target BTS the soft handoff request that the same FAs be assigned as the one used by the origin BTS.

3) The target BTS makes the reservation of the requested FA and acknowledges the soft handoffrequests back to the BSC. If the channel in the same FA is not available, hard handoff is invoked by reserving a channel on the different FA.

4) The BSC sends back the results to the mobile station and the mobile station takes a proper action according to this response. That is, for the soft handoff, the mobile station adds another wireless channel with the target BTS and communicates simultaneously with the two BTSs. For the hard handoff, the mobile station disconnects the current connection and establishes a new connection with the target BTS.

3 CALL CONNECTION CONTROL

From the step (3) of the handoff process described in the previous section, we know that the soft handoff is preferably invoked over hard handoff. The handoff request is switched to hard handoff only when there are no available channels on the requested FA. Suppose that only soft handoffs are allowed to exist. Then, the handoff blocking probability will be adversely affected due to the asymmetrical occupancy of calls on different FAs. On the other hand, if the hard handoff is allowed, the corresponding connection must be disconnected and the retransmission of data is unavoidable. In this case, the handoff blocking probability can be smaller at the expense of the deteriorated QoS of individual connection.

To deal with the above-mentioned trade-off between soft handoff and hard handoff, this paper proposes a new call connection control scheme that provides more flexible handling of the handoff process. The main purpose of the proposed scheme is to let the system fully exploit the advantages of soft handoff while retaining the occurrence of hard handoff within the acceptable level. To do this, the proposed scheme keeps the occupancy of each FAs balanced among themselves by maintaining the difference of ongoing calls among the FAs below the given threshold. Of course, this threshold directly affects the system performance (e.g. handoff blocking probability and call blocking probability etc.) and should be carefully chosen.

For the sake of convenience, we restrict our focus on the case that there are only two FAs available for each base station. In addition, two different cases can be considered depending on the existence of handoff queues: with queues and without queues. Figure 3 illustrates the proposed scheme using pseudo code. In the Figure 3, ni and n2 represent the number of active calls in each FA, respectively, and qi and q2 the number of waiting handoff calls in each FA's queue, respectively. T is the threshold that determines the execution of hard handoff and is called the hard handoff threshold hereafter.


1* Handoff without Queue *1

if (NEW CALL) then if (nl<n2)

admit call to FAI else if(nl>n2)

admit call to FA2 else

admit call randomly to FAlor FA2

else if (HANDOFF CALL) if (Inrn21<1')

soft handoff else

hard handoff

1* Handoff with Queue *1

if (NEW CALL) then if (Empty Queue)

if (nl<n2) admit call to FA I

else if (n 1>n2)

else

else reject call

else if (HANDOFF CALL)

if (lQrQ2' < 1')

admit call to FA2

admit call randomly to FAlor FA2

soft handoff else

hard handoff

Figure 3 Call connection control scheme.


4 PERFORMANCE ANALYSIS

4.1 Queuing model

We investigate the perfonnance of the proposed call connection control scheme. Here, we only describe an analysis for the one with handoff queues. To simplify our analysis, we assume that the mobile network operates under the homogeneous traffic conditions [3]. That is, all cells have the same total number of channels. Each mobile station in the network has the same new call rate, handoff rate, and call holding time, all of which are independent each other. The new call arrivals follow an independent Poisson process with the mean rate A. in each cell. The handoff call arrivals also follow an independent Poisson process with the mean rate Tin each FA. The call holding time is distributed exponentially with the mean l/JL The sojourn time of every mobile station in a cell is also assumed to be exponentially distributed with mean 1/ r. Note that r represents the handoff rate of each mobile station.

Based on the above assumptions, the proposed call control scheme can be modeled as a queuing system as shown in Figure 4. All the servers in the system are partitioned into two groups according to the number of FAs and handoff queues are provided for each FA.

FAI FA2 ..................................................... · . . . · . . . · . . . · . . . · . . . · . . . · . . . · . . . ~ ~YI ~YI ~YI ~ ~ ~Y2 ~Y2 ~Y2 ~ · . . . ........................................................

Figure 4 System model with queue.

Now we start our analysis with the birth-death process. Then channel occupancy of each FA can be described in a 4-dimensional space as follows;

where c is the total number of wireless channels in each cell, b is the size of queue in each FA, nl is the number of occupied channels in FAt, n2 is the number of

occupied channels in FA2, ql is the number of handoff requests waiting in FAt's

queue, and q2 is the number of handoff requests waiting in FA2's queue. However,

302 Pan Eight Mobility and Wireless Networks

making use of the operational relationships between wireless channels and handoff queues, the above 4-dimensional state space can be reduced to the 2-dimensional one.

Aa=.:t/2+r, Ba=1; Da= .1.+r; E=i(Jl+Y,) B'=I; + I; Ab = .1. 12 + r, Bb =T; Db - '+ r c'( ) -'" , =/Jl+Y,

Figure 5 A Markov chain for a particular cell

Figure 5 describes an example of state transition diagram in a particular cell

with T=l, c=2, and b=2. Let 1t'(npn2 ,Qpq2) denote the steady-state probability

of the state (n) ,n2 ,Q) ,Q2) in the Markov chain. Then there exists a flow

equilibrium equation for each state. In words, the total rate of flowing into a state will be equal to that of flowing out from it. Since the total number of states is

(b + c + 1)2 , we obtain (b + c + 1)2 -1 linearly independent flow equations. By

solving the above 2-dimensional birth-death process from the chosen linearly independent equations combined with the normalization condition (the sum of all steady state probabilities must be equal to one), the steady state probabilities can be obtained.

After finding the steady-state probabilities, we can determine some important

parameters that affect the network performance: new call blocking probability PN ,

handoff blocking probability PH ' and hard handoff probability PHD'

PN = L1r(nI,n2,QI,Q2) "j="2=C


PH = L7r(n1,n2,ql,q2 )/2+ L7r(n1,n2,Ql,Q2 )/2+7r(c,c,b,b)

{ql (bnq2 =bnlql-q21(T} {q2 (bnql=bnlql-q21(T}

PHD = L7r(n1,n2,Ql,Q2 )/2 + L7r(n1,n2,Ql,Q2 )/2

{ql(q2=bnlql-q21~T} {ql )q2=bnlql-q21~T}

4.2 Numerical examples

Some numerical examples are provided in this subsection. Throughout the analysis,

we assume that c=5, A.=60 [calls/min], ~ = T2 =10 [calls/min], J.l=O.2 [calls/min],

and rl =r2=1O[calls/min].

Figure 6 plots new call blocking probability, handoff call blocking probability, and hard handoff probability against various values of hard handoff threshold. No handoff queues are assumed here. From the Figure 6, it is observed that, as the hard handoff threshold increases, the new call blocking probability and the handoff call blocking probability do not show any remarkable changes while the hard handoff probability decreases drastically.

0.1

0.01

0.001

0.0001

2 3 4 5

:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: ........................................................................................ ........................................................................................

.......... ::: ..... ':"::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: ....................

:: 0 New Call Blocking Prob. :: 0 Hand-Off Blocking Prob . .. I:::. Hard Hand-Off Prob.

Hard Hand-Off Threshold

Figure 6 Call blocking and hard handoff probabilities vs. hard handoff threshold (without handoff queue).

In Figure 7, the same probabilities as in the Figure 6 are shown, but handoff queues are provided. Compared with the previous results with no handoff queues, the new call blocking probability is slightly increased due to the effects of handoff queueing. On the contrary, the handoff blocking probability and the hard handoff probability are prominently decreased. Moreover, we notice that, as the hard


handoff threshold increases, the handoff blocking probability increases while hard handoff probability decreases. Compared to the results in the Figure 6, it can be said that the handoff blocking probability is more affected by the hard handoff threshold when there are handoff queues.

1.00E+OO

1.00E-Ol

1.00E-02

1.00E-03

1.00E-04

1.00E-OS

1.00E-06

1.00E-O?

1.00E-OB

1.00E-09

2 3 4 S

lllllllllll!ll!!l!!l!!! !! .. ~::::::::::::::::!lH!l!H!!!!!!!l!!!!!ll!!!!!l!!!l!!!!

Hard Hand-Off Threshold

Figure 7 Call blocking probabilities vs. hard handoff threshold (with handoff queue).

1.00E+OO

1.00E-Ol

1.00E-02

1.00E-03

1.00E-04

1.00E-OS

1.00E-06

1.00E-O?

1.00E-OB

1.00E-09

2 3 4 S

1::1::1::.:::.1:.:::::::::.:::::.:::::::::::::.1::::::::::::::I:::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! n!!!!!!!!!!!!!!!!!!!!:::::: ~ ~!!!!!!!!!!!!!!!!!!!!!!!!!

New Cali Blocking Prob. 10 Hand-Off Blocking Prob. ~ ~ Hard Hand-Off Prob.

Queue Size

Figure 8 The performance evaluation probability versus queue size


Figure 8 plots the same probabilities again, but against various queue sizes. Handoff queues are provided and the hard handoff threshold is given T=l. As seen from the Figure 8, the handoff blocking probability considerably decreases as the size of queue increases. Hence, we believe that the waiting queues are very helpful for the efficient handoff process. On the other hand, we also observe that the size of handoff queues does not affect noticeably both the handoff blocking probability and the hard handoff probability.

5 CONCLUSION

We proposed the call connection control scheme for more efficient handoff in the CDMA-based mobile networks where multiple FAs exist in each base station. Based on the assumptions of homogeneous traffic conditions, the performance of the proposed scheme has been investigated using the Markov chain for the two cases: with queue and without queue. For the performance measures, three different kinds of probabilities are chosen: new call blocking, handoff call blocking, and hard handoff. From the analysis, we obtained the following conclusions. • When no handoff queues are used, the hard handoff threshold affects directly

the hard handoff probability. Thus, it is desirable to have larger value of hard handoff threshold to reduce the occurrence of hard handoff.

• When handoff queues are used, the hard handoff threshold affects both handoff blocking probability and hard handoff probability. Thus, proper trade-off between them is necessary to guarantee a certain level of QoS.

• As long as the hard handoff threshold is fixed, the size of handoff queues mainly affects the handoff blocking probability without affecting the other two probabilities. Thus, larger size of queues is preferred to obtain the lower handoff blocking probability.

6 REFERENCE

[1] D. Raychaudhuri and N. Wilson, "ATM-Based Transport Architecture for Multiservices Wireless Personal Communication Networks", IEEE JSAC, pp.1401-1414, Oct., 1994.

[2] AJ.Viterbi, A.M.Viterbi, K.S.Gilhousen, and E.Zehavi, "Soft hand-off extends CDMA cell coverage and increases reverse link capacity", IEEE Journal on selected areas in Communications. vol. 12. no.8, pp. 1281-1288, Oct., 1994.

[3] Kwan L. Yeung and Tak-Shing P. Yum, "Optimal prioritized handoffin linear microcellular radio systems", Proc. IEEE GLOBECOM, pp. 494-498,1995.

PART NINE

Multimedia Applications

24 Authoring and E-LOTOS conception of interactive networked multimedia applications in MUSE environment

L. P. Gaspary and M. J. Almeida Universidade Federal do Rio Grande do Sui Campus do Vale - Bloeo N, Porto Alegre, Brazil Phone: ++55 (51) 316-6161, Fax: ++55 (51) 319-1576 E-mail: {pasehoal.janilee}@inf.ufrgs.br

Abstract This work presents MUSE, a graphical environment for modeling interactive networked multimedia applications. Through an advanced graphic interface and a new high-level authoring model, it is possible to create complex systems in a fast and intuitive way. The authoring model proposed in this work and adopted by the tool deals with media objects distributed in a computer network, allowing the definition of acceptable delay thresholds and alternative media objects. Due to the large expressiveness of the model, however, specifications with logical and temporal inconsistencies may be generated. For this reason, the tool also provides E-LOTOS specifications used with the purpose of analyzing and verifying the applications aiming at validating the temporal requirements defined by the author.

Keywords Multimedia, synchronization, formal conception, E-LOTOS, validation

Perfonnance of Infonnation and Communication Systems U. Korner & A. Nilsson (Eds.) © 19981FIP. Published by Chapman & Hall

3 IO Part Nine Multimedia Applications

1 INTRODUCTION

The advance of the utilization of multimedia applications in several fields of human activity is remarkable. Independent of the area, whether education or entertainment, the possibility to aggregate dynamic resources like audio and video to the ones already widely used like text and image results in benefits to the users of such applications. Besides, with the popularization of the Internet, there is an increasing demand for their execution in distributed environments.

The possibility of having an application with its media objects dispersed in a network influences the creation and modeling of such applications. Users must provide the authoring tools with information like temporal restrictions, defining acceptable delay thresholds to the presentation of the elements that compose the system and establishing the presentation of alternative media objects.

The definition of these restrictions is accomplished based on a synchronization model, which dictates the rules about how the media objects of an application can be related in time. Several synchronization models have been proposed (Blakowski, 1996). Most of them are both flexible and very expressive. That is the reason why the resulting specifications can be source of incoherences where the logical and temporal consistency of the involved media objects can not be assured. An alternative would be to use directly a formal description technique (PDT) to describe the applications, making its analysis possible and so guaranteeing its consistency. The disadvantage of this direct use, however, is the high complexity inherent to PDTs. So, the need of having a structured high-level model to specify interactive networked multimedia applications becomes evident. The resulting specifications shall then be translated to a PDT so that verification and simulation methods can be applied to them.

In this context, an interactive networked multimedia applications authoring model was created. MUSE (MUltimedia Applications Specification Bnvironment) was developed to support this model, allowing the user to easily define a multimedia presentation according to the MHEG-5 standard (ISO, 1995). The adoption of MHEG-5 allows multimedia information to be shared without worrying about the platform or operating system used, providing specification and development of portable applications. To make the validation process of the specifications possible, the environment automatically generates E-LOTOS specifications. The results obtained from the validation are presented to the author in a quite readable way in the own environment. Mter the elimination of the incoherences, MHEG-5 applications are generated and can be executed by a MHEG engine. This work is part of DAMD project (Distributed Multimedia Applications Design), sponsored by the Brazilian research council.

This paper is organized as follows: section 2 presents important aspects to be considered in the applications authoring process, relating them to some multimedia synchronization models pointed by the literature. This section also presents the proposed authoring model. In section 3 basic aspects of E-LOTOS PDT as well as a mechanism to represent in this language, specifications generated by the authoring model are presented. Section 4 illustrates the functionality of the environment and in section 5, one can read the final considerations.

Authoring and E-LOTOS conception of multi-media applications 311

2 PROPOSED AUTHORING MODEL

The specification of multimedia applications is accomplished with base in three fundamental aspects: logical structuring, establishment of temporal relationships and spatial definition among the elements belonging to the application. The logical structuring is concerned to offer abstraction mechanisms, providing a wide and structural view of the application. The specification of the temporal behavior involves the definition of synchronization relations among media objects. The spatial synchronization cares about adjusting the positioning of the visible media objects according to the output devices (video).

The temporal relations are established according to a synchronization model, which imposes rules on how these elements can relate to each other. Several models have been proposed in the literature. One of the most adopted by existent authoring tools is the time-line based one (Hirzalla, 1995). However it presents many limitations such as the difficulty both to modularize the application and to establish relations among elements with variable or unknown duration like user interaction for example (Soares, 1997). Models based on restrictions like HTSPN (Hierarchical Time Stream Petri Nets) (Senac, 1995) and object-oriented models do not present these problems. On the other hand, these models have not been widely used in commercial tools because of the difficulty in understanding the specifications resulting from them.

In this work, an authoring model that joins mechanisms for logical structuring the applications to a synchronization model similar to HTSPN is proposed. The logical structuring level is based on the concept of scenes and groups, providing a broad view of the application. The definition of temporal synchronizations is done in each scene by means of a simplified graph. The spatial synchronization allows media objects to be positioned considering the output device.

2.1 Logical structuring

The complexity of multimedia applications increase according to the growth of involved media objects and, consequently, to the several temporal relationships established among them. This is the fundamental reason why the specification of these applications in only one plane is inappropriate. To solve this problem, the concept of scenes was incorporated into the model considering the MHEG-5 standard. Multimedia applications can be organized as a group of scenes related by events, which provide the navigation among them. Each of these scenes can be seen as a black box with an internal behavior that, under certain conditions, enables the presentation of other scenes. In figure 1, one can see an application structured in three scenes: Scenel, Scene2 and Scene3.

The use of this concept, however, does not solve the problem of complexity at all, since a specification with many scenes will be hardly understood. Trying to make the understanding of so large applications easier, a hierarchy mechanism was added to the model by means of the concept of group of scenes.

312 Part Nine Multimedia Applications

I nltlalGroup Scene 1 Scene2 Scene:!

Scene3 AudlO2

P'I (2,3) End

;-D

Figure 1 Representation of a simple example.

2.2 Temporal synchronization

The temporal synchronization of an application, as mentioned previously, refers to the ordering of the presentation of its media objects in time. Each media object has a presentation duration that mayor may not be foreseen, depending on its nature. The following topics present how the synchronization relationships can be established.

Basic synchronization Media objects can be presented sequentially or simultaneously. In the sequential presentation, the playout of a media object depends on the end of the presentation of another media object. Scene2 (see figure 1) models the sequential presentation of a recorded interaction (RI) and three images (PI, P2 and P3). The parallelism, on the other hand, considers that media objects start to be presented from a same instant. This is modeled in Scene3, where the animation fragment ANCPI is presented in parallel with a button (Interaction).

Duration of the presentation of media objects and acceptable delay thresholds A minimum and a maximum duration of presentation are associated to each media object. In the case of an image or a text, these values are equivalent because they are time-independent media objects. When one deal with media objects like audio and video, however, it is important to determine both a minimum and a maximum


presentation duration, since these media objects will be hardly presented at the nominal rate due to problems like network traffic (see figure I). The representation of these durations is given by an interval.

Interaction mechanisms and scene transition User interaction corresponds, for instance, to a button click or an object selection. It is represented in this model as a constructor whose presentation duration is uncertain, varying between the minimum and maximum values associated to it. When the maximum threshold is reached, the scene continues with its presentation. It is still possible to specify a button without maximum duration; in this case, its evolution will only happen after the interaction. Scene3 (figure 1) shows a button (Interaction) with duration of [0,20]. It means that the user will have 20 seconds to select it. When this time elapses, P4 will be presented.

The user interference is normally associated to a scene transition. Transition is the constructor that makes the navigation among scenes possible. Its execution involves both the immediate suspension of the presentation of all the media objects belonging to the current scene and the beginning of a new scene presentation. In Scenel (see figure 1), one can see the transition to Scene2. The transitions are also modeled in both Scene2 and Scene3.

Synchronization points Synchronization points allow the beginning of the presentation of one or more media objects to be associated to different policies related to the end of the presentation of other media objects that converge for these points. To improve the specification power, the model has adopted some widely commented firing rules in the literature. They allow the association of different behaviors to the synchronization points (Senac, 1994). The rules supported by the model are the following: • Master: a synchronization point is fired when the presentation of a master

media object is finished, interrupting all the other ones. The master media object is identified by the presence of the character m or the word master close to it. This is the rule adopted by the synchronization points of Scenel (figure I).

• Earliest: the synchronization point is fired when the presentation of the first media object is finished, interrupting all the media objects that are running simultaneously. Graphically, this policy is represented by the presence of the character e or the word earliest close to the synchronization point.

• Latest: the absence of an indication close to the media object or to the synchronization point means that all the media objects that precede this point will be executed (or they will conclude due to the elapsing of their maximum presentation duration) before the synchronization point is fired.

Synchronization instants In MUSE, the synchronization among components in other instants than the beginning and end of their presentations requires the division of these components in parts, creating a group of segments. The granularity of this division is directly


associated to the precision degree wished for the synchronization. Scene 1 (figure 1) shows such synchronization between a video (VD) and an audio (AU). Both of them were fragmented in three segments.

2.3 Spatial synchronization

The spatial synchronization allows the author to organize the positioning of the visible components of a scene. It is not possible to accomplish the spatial synchronization considering a certain elapsed time after the beginning of the scene presentation. It is so, because in each execution, due to the acceptable temporal variations, the components can be presented in different instants. For this reason, the spatial synchronization is always accomplished with base in the presentation of a component. The spatial disposition of the components of Scene2 (figure 1) during the presentation of PI, for example, will allow to organize only the component PI. If in the definition of this scene there were other components defined to be simultaneously presented with PI, these components would also appear in this view.

3 REPRESENTING MULTIMEDIA APPLICATIONS IN E-LOTOS

The formalization of specifications is important for the process of their validation. The proposed authoring model, due to its high flexibility and expressiveness, allows both temporally and logically incoherent specifications to be defined. The analysis process detects, for example, conflicts in resources usage and tests if the application end can be reached from all the possible navigation paths. Thus, specifications described by an author according to the model presented in the previous section are translated to a formal representation, analyzed and the obtained results are presented to the user, who will make the necessary adjustments.

The formal description technique E-LOTOS (Enhancements to LOTOS) (ISO, 1997) is an enhanced version of LOTOS and is in standardization process. The main innovation of the language is the incorporation of quantitative time notion, allowing the definition of instants in which actions or events may happen. This is a fundamental feature for representing multimedia applications and for this reason, E-LOTOS was chosen to formally represent them.

The representation of multimedia applications is hierarchical and considers the four essential elements of the authoring model: application, group, scene and media object. All these elements are modeled as processes that evolve according to previously established synchronization relationships. The way of formally represent multimedia applications commented in this section is based on the approach presented in (Courtiat, 1996). Further details are presented in the following topics.

Authoring and E-LOTOS conception o/multi-media applications 315

3.1 Data representation and root process instantiation

Data representation is done by means of a library called classes, which define data types for all possible media objects. There are types like BitmapClass, StreamClass and SwitchButtonClass, whose definition is based on their respective MHEG-5 classes. For example, the fields of BitmapClass are the media object, its position in the output device and its dimensions. The application is started from the instantiation of the root group process (Initial Group ). After that, the application is indeed able to evolve.

3.2 Group representation

In the representation of groups, the hiding operator is used. Taking the example of figure 2, one can see that some internal events like the beginning of both Scene2 (s_Scene2) and Scene3 (s_Scene3) are not visible outside the process (1).

InlUalGroup ~nel

Data

'J"-~r~ lu'~~w' proceu lnidalGrolC)llsJniUalGrolCl,e..lnlUalGrclCl,lrUr"actlcn,Data)

( .. ,R1:SlreamClass.dl :Tlme.d2:TIme,PI :BltmapClass. eSPl :T1me, P2: BltmapClass.dP2:T1 me,P3: BitmapCIass. dP):T1me, .. ):exit II hide s_Scene.s_Scene2,s_Scene3,rect.End in (I)

SJ nlUalGrolCl; p .. s_Scene2n,s_Scene3'2 (2)

(s_~ne2)4Sc_lls_Scene,a_Sc.ne2,Da!ll,rflCLEnd]( ... ) (3) Is_~ne2,s_SceneJ) .... Scene2(. _Scene2.._Scene3,lnteractfc",Data. (4)

rflCLEndJ (R1,dIRI,d2RI,PI,eSPI.P2.dP2,P3,dP3) Is_~l .... SceneJI. _Scene3,e_lnlU.lGroup.Data,rect.End]( ... ) (5)

endp.r [>rect.End;exit (6)

endhlde endD<CC

Figure 2 InitialGroup modeling in E-LOTOS.

These events are used to synchronize the presentation of the scenes belonging to InitialGroup. The synchronization is modeled with the par operator (2). For instance, the beginning of Scene2 is associated with the end of Scenel (s_Scene2) (3 and 4). The same occurs with Scene2 and Scene3: the beginning of the later is synchronized with the end of Scene2 (s_Scene3) (4 and 5).

The disabling operator must also be mentioned (6). As one can observe, the req_End event reaches all the processes of the group; it is used to model the end of the application. When generated (by a transition to end), groups and scenes are terminated with exit.


3.3 Scene representation

Scene modeling differs in many aspects from group representation. One of the differences is that scene processes instantiate media objects and restrictions instead of groups and scenes. The presence of the loop operator in the representation is another important difference (1). It is used to allow a scene to be presented more than once, which may happen when the application is logically organized as a net. Figure 3 shows Scene2 previously instantiated in figure 2.

proce .. Sanfl [._San.2.~_Scene2.Data,rI!<l,Erd) CRI :Sb'umCIa5s,dl :Tlm~,<l2 :TIm~.Pl :8itmapCla5',dPI :Tim~,

P2:8rtmapCia5s.dP2:Tlme,Pl:BitmapClaSs,dPl:Time) hide . _Scene,._Pl,s_P2,s_Pl,s_T'an5,rI!<l,Res In

loop 'o",vu In (I) s_Sceno2; p., s_PI'2,s_P2'2,s_Pl'2. s_Trans'2

[._Pl) .... R1 (._Scene, ' _Pl,Dal3,rI!<l,Erd,rI!<l,Res) CRI,dl,d2) [._Pl,._P2) .... P1[._PI,._P2,DaI3,r«LErd/«LResl(Pl,dPI» [s_P2,. _Pl) .... P2[s_P2, s_Pl,llata,reQ..End,r«LResl(P2.dP2» [s_Pl,.Jrans) .... P3[s_Pl,s_Trans,Data,r«LEnd,reQ..Res)(Pl,dP3» (s_Trans] .... TrallSltlon(sJrans,e.,Sanfl,rI!<l,Erd.rI!<l,Res)()

endp., endloop [> I«LEn:I;u lt

endhlde end roc

Figure 3 Representation of Scene2.

The req_Res event is responsible for restarting the media objects of the current scene when a transition to another scene occurs. The code that models a scene transition is composed of three events: s_Trans, reCJ-Res and CScene (see figure 4a). The former denotes the occurrence of the transition. The second invokes the media objects of the scene to be reset. The third one indicates the end of the scene presentation. As the transition is a never end process, it is also disabled by the occurrence of the req_End event. When the transition is to the end of the application, the req_Res event is replaced by the req_End event (see figure 4b).

proc_ Transition [s_Trans,CScene,rI!<l,End,reQ..Res):exIt .. proc_ Transition [s_Trans,CScene,rI!<l,Endj:exlt I. loop forever In s_Trans,reQ..End;CScene;exIt

s_Trans;reQ..Res;CScene endproc endloop [> '«LEnd;exlt

.ndproc

(a) Scene transition (b) Transition to the end of the applcation

Figure 4 Representation of transitions.


3.4 Basic objects and temporal restrictions

Basic or monolithic objects were defined by (Hirzalla,1995) and model the presentation of simple media objects. These media objects are defined by the occurrence of synchronous (beginning, end) and asynchronous (user interaction) events. Several combinations of these events can be formulated, but only eight are pointed as important in the definition of interactive multimedia scenes. This work presents three of these combinations (see table 1). The fourth object presented in this table (pSsSe - Synchronous start Synchronous end) doesn't appear in (Hirzalla, 1995). It allows time-dependent media with both minimum and maximum presentation durations to be modeled. In the definition of the processes, the Data event was used to represent the presentation of the media object.

Table 1 Representation of basic objects

process pSsSe[start,end,Oata:class] (medla:class,d:tlme):exit Is

start;Oata(!media);wait(d);end@t[t=O];exit end~roc

1f'.f4,.i.j.t.,.tI4iMI,ifJ.iQ.;i.j,t."ti .Isalp"j,';14·t• process pSsAme[ sta rt,end,user, Data: class] (media:class,dl,d2:tlme):exlt Is

start; Oata(!media);wait(dl) ; (user@t[t<=d2] [] wait(d2);exit);end@t[t=O] ;exlt

end~roc E944 .. i.j·t.'·4IiiM'·iQ,tg.'k.i,t.'·4Jg·t.

process pSsAe[start,end,user,Oata:class] (medla:class,d:tlme) : exit is

start;Oata(!medla);walt(d);user;end@t[t=O];exlt

process (medla:class,dl,d2:tlme) : exit Is

start;Oata(!media);walt(dl);end@t[tsd2];exlt end~roc

Used to model time-independent objects like Image and text with a presentation known duration.

Used to model user Interaction; If the Interaction doesn't occur during the Interval [dl,d2] the process is finished when the maximum time (d2) is reached.

Modeling of user Interaction without a maximum time to wait defined. The process finishes only once the Interaction occurs.

Used to model time-dependent media objects like audio and video, which have a minimum and a maximum duration defined.

Figure 5 shows the representation of P2, which appeared in the definition of Scene2 in figure 3. The event req_End (3) can again be observed, because media objects are also always 'being executed (1); if there is a loop in the scene definition, some media objects may be executed more than once during the presentation of the scene. In the same figure, one can also see the effect of the occurrence of the req_Res event: the restart of the media object to its initial state (2).

The authoring model and consequently the tool, to be described in the next section, provide the definition of three distinct temporal restrictions: WaitMaster, WaitLatest and WaitEarliest. Their E-LOTOS representation controls the end of the media objects that converge to the synchronization point. Restrictions are not implemented in libraries because their behaviour depends on the number of media objects that converges to the synchronization point. Figure 6 shows the representation of the WaitEarliest restriction.


process P2 [s_P2,e_P2, Oata,''''LEnd,''''LResl:exlt is (P2:BibnapClass,dP2:Time) loop fo,ever In (1)

pSsSe(s_P2, e_P2, Oatal (P2,dP2) [>''''LRes (2)

endloop [> ''''LEnd;exit (3)

endproc

proceu WaitEa~iest [e_A,e_B,e_C,e_Restrlctlon,''''LEnd,''''LResl:exlt Is loop forever in

(e_A[]e_B[]e_ C);e_Restrictio!1Ot[t=Ol [>''''LRes

endloop [>""LEnd;exit

endproc

Figure 5 Representation of P2 media object. Figure 6 WaitEarliest restriction.

4 THE AUTHORING ENVIRONMENT

The authoring environment is divided in two units: media repository and specification area. At any moment, the user may insert media objects into the repository. This is done by browsing a local media object or referencing a remote one. The specification area is composed of the scenes and groups of an application. Each scene is represented by two different views: the temporal and the spatial one. The temporal view allows the user to insert icons and to establish their relationship using arches. The visible elements, used in the temporal synchronization, can be adjusted in the spatial view.

Figure 7 shows the basic functionality of the authoring environment. The toolbar has shortcuts to its main functions (1). Two support windows can be observed: Specification Hierarchy (2) and Icons Palette (3). The former provides the user a general view of the application, presenting all the scenes and groups in a tree and providing a structured view of the relationships among them. In this case, the modeled application was the example presented in section 2 and is composed, therefore, of three scenes: SceneI, Scene2 and Scene3 (4). The later, in its turn, provides mechanisms to visualize and edit the properties of the icons. In the same figure, the bitmap icon (PI) of Scene2 is selected and its specific properties are presented in the mentioned window. Icons that have an associated media object (audio, text, image, and video) present a special property called media. This property must be filled with a media object existing in the repository. In this example, icon PI is associated to the media object Rio Bonito.

In figure 7, one can also observe the specification of Scene2 (5). It is composed of video (RI) followed by the sequential presentation of three images (PI, P2 and P3). By the end of the presentation of the last media object, a transition to Scene3 occurs. These information are presented by the temporal view. At the same time, the spatial view of Scene2 taking the icon PI as reference is showed (6). It is possible to move or resize the visible media objects. Their properties related to coordinates and dimensions are automatically updated.


-"-1-1 - " ~ ... .,- • -.,- • - ""-- ",. "" .... '00 .. -- 1915

0

Figure 7 Graphic interface of the authoring environment.

Time-dependent media objects, like video, can be divided in smaller segments, allowing the synchronization of other media objects with specific points of them. The environment provides mechanisms that make the process of fragmentation of these media objects easy. MUSE also provides means to reuse scenes and groups. It can be done by browsing the group or scene to be retrieved. It is necessary just to redefine the transitions, defining where the application should evolve to after its presentation. Finally, it is also important to highlight the functionality of E-LOTOS code generation. This is obtained through the special saving option Save as ELOTOS.

5 CONCLUSIONS

This work initially proposed a new model for specifying interactive networked multimedia application. Besides, mechanisms for mapping this model to the ELOTOS language were presented. Finally, the developed environment was described. The main contribution of this work is, therefore, the construction of a tool turned on both ease of use and good expressiveness. At the same time, means to provide the formal representation of applications aiming at its analysis is also a great contribution.

The model proposed distinguishes intentionally the concepts of logical structuring and temporal synchronization. The logical structure of the applications facilitates its organization in chapters, sections or in any other unit. For this reason, the application becomes modular, which contributes to lessen the complexity of the scenes and to avoid the occurrence of the state explosion problem.


The future works include the creation of mechanisms that allow the user to define in the own tool parameters of quality of service, which will be used during the execution of the application. The possibility to define alternative media objects is also an important future task.

It's important to highlight that the use of this environment integrated to the other tools being developed in the project provides a complete framework covering all the steps involved in distributed multimedia applications design: specification, verification and presentation. The easiness of the authoring model presented to the user and the use of a formal description technique to validate the applications created by him tum the environment attractive and easy to use without restricting the expressiveness of the tool.

6 REFERENCES

Blakowski, G. and Steinmetz, R (1996) A Media Synchronization Survey: Reference Model, Specification, and Case Studies. IEEE Journal on Selected Areas in Communications, 14,5-35.

Courtiat, J. P. and de Oliveira, RC. (1996) Proving Temporal Consistency in a New Multimedia Synchronization Model. ACM Multimedia, Boston, November 1996.

Hirzalla, N.; Falchuk, B. and Karmouch, A. (1995) A Temporal Model for Interactive Multimedia Scenarios. IEEE Multimedia, Fall 1995, 24-31.

ISO/IEC DIS 13522-5. (1995) Information Technology - Coding of Multimedia and Hypermedia Information, Part 5: Support for Base-Level Interactive Applications.

ISOIIEC JTCl/SC21IWG7. (1997) Enhancements to LOTOS. Revised Working Drafts on Enhancements to LOTOS (V4), Project WI 1.21.20.2.3.

Senac, P.; Diaz, M. and de Saqui-Sannes, P. (1994) Toward a formal specification of multimedia synchronization scenarios. Ann. Telecommun., 49, 297-314.

Senac, P.; Willrich, R and de Saqui-Sannes, P. (1995) Hierarchical Time Stream Petri Nets: A Model for Hypermedia Systems. Lecture Notes in Computer Science, 935, 451-470.

Soares, L. e Rodrigues, R (1997) Autoria e Formata~lio Estruturada de Documentos Hipermfdia com Restri~6es Temporais. In Proc. of III Workshop sobre Sistemas Multimidia e Hipermidia, 183-197. (In Portuguese)

25 Simple integrated media access - a comprehensive service for future internet

J. Ruutu a and K. Kilkki b

Nokia Research Center

a P. 0. Box 422, FIN-00045 NOKIA GROUP, Finland tel: +358 9 4376 6188, fax: +358943766851 e-mail: [email protected] b 3 Burlington Woods Drive, Suite 260, Burlington, MA 01803, USA, tel: + 1 781 564 9609, fax: + 1 781 564 9696 e-mail: [email protected]

Abstract The basic objectives offuture Internet are to increase the network capacity, to offer a practical real-time service, and to develop a feasible charging scheme.

These objectives introduce very strict requirements for the traffic control system. This paper presents a new simple approach for traffic management:

Simple Integrated Media Access (SIMA). The strength of SIMA lies in its wide area of applications. There is no need to build complex systems with several

service classes each appropriate to only certain applications.

Keywords SIMA, Internet, Charging, Quality of Service, ATM

Perfonnance of Infonnation and Communication Systems U. Kl>mer & A. Nilsson (Eds.) © 1998 IFIP. Published by Chapman & Hall


1 INTRODUCTION

The Internet is at a phase of great changes. There are several stringent new requirements because of two reasons: the invasion of new users, and the rapid development of new applications. These requirements mean that network capacity must rapidly be increased, real-time service has to be fundamentally improved, and a feasible charging scheme must be introduced. There is not too much time for the development as the penetration is growing fast (Snyder, 1997).

The current Internet approach for meeting these requirements consists of several service specifications, Resource Reservation Protocol, QoS routing, etc. We can make an interpretation that the basic philosophy of Internet development is to define different services for different basic communication needs. The supposed advantage of this approach is that by dividing the service specification task into several smaller parts the specification process is easier than if the all the service types were included in a single specification. However, this advantage is somewhat questionable because the whole service concept (with all the different service types) is what the network operator should manage and sell to customers and what the customer should buy and use.

The charging problem must also be solved before there is a real possibility to offer Internet with real quality and reasonable bandwidth. As stated in (eukier, 1997) the developing of billing has not been a high priority for Internet engineers who prefer flat-rate charging for its simplicity. A lot of carriers would prefer to throw bandwidth at the problem of managing QoS as J. McQuillan has expressed the situation (McQuillan, 1996). This type of approach, adopted for instance by Telecom Finland (Greenfield, 1997), means that even a pure best-effort type of service is capable to meet most of the current service demand.

However, there are different kind of views as well, for instance, usage-sensitive pricing, priority-based pricing, additional value-added services and Intranet tolls are possible charging schemes (Firdmand, 1997). Especially, the priority-based pricing is a promising approach as it is based on premise that customers who want better service should pay more. The best approach is the one which can flexible combine different properties but at the same time allows a very straightforward network management and charging. We believe that the Simple Integrated Media Access (SIMA) concept is able to reach this ambitious target (SIMA, 1998).

2 SERVICE SPESIFICA TION

The SIMA specification covers the whole Internet service including charging, QoS and performance aspects, and traffic control functions in the network. The primary idea of the SIMA service is to maximize the exploitation of network resources with a simple control scheme while keeping the ratios of QoS levels offered to different flows unchanged under changeable traffic conditions. The maximization is based on three key features: all flows with different QoS requirements share the total

Simple integrated media access 323

capacity of every link, the network attempts to avoid any unnecessary packet discarding, and flow level blocking can be totally avoided. The approximate constancy of QoS ratios and simplicity are achieved by using eight drop preference levels which make possible a fair packet discarding scheme inside the network without keeping track on every flow (see Chapter 4).

2.1 Nominal Bit Rate

When the network operator offers the SIMA service, a customer first pays for some Nominal Bit Rate (NBR, kbitls) and then he/she can trade the speed for QoS. Let us assume that a user pays X $/month. This charge is translated to a NBR using an arbitrary function. The function NBR = F(X) could be linear, but there is no reason to specify the relationship between NBR and charging. If NBR is permanent, it is probably related to an interface. The next level of NBR

is the NBR assigned to a user (or IP-address). The bottom level is the NBR of a flow (determined, for example, by a pair of IP address and port number). Both interface based and user based approaches have the drawback that they do not separate different applications properly: a high-speed file transfer may disturb other flows, although the user may consider the file transfer a background process which uses only the capacity left by other more demanding applications. Therefore, as regards the performance and QoS of the SIMA service the most useful approach is the one where every flow has its own NBR.

2.2 Real-time vs. Non-real-time

The other part of the SIMA service concept is the possibility to request a real-time service. The user is entitled to himlherself determine whether the flow is a real-time (rt) or non-real-time (nrt) one. In practice, this decision can be made usually at the application level: a real-time service is requested only for interactive audio or video applications. If a real-time service is requested, the SIMA network attempts to offer as short delay and small delay variation as possible by using small buffers reserved only for real-time connections. The measurement for the drop preference determination shall be more sensitive for traffic variations in case of real-time service than with non-real-time service.

If the user changes a VBR connection from nrt-service to rt-service without changing NBR or traffic process, the delay will decrease, but the cell loss ratio may increase because real-time measurement gives worse drop preferences during peak rates. If the user wants to obtain the same quality, this impairment of loss ratio should be compensated by increasing NBR. Real-time-service could, in this respect, be more expensive than non-real-time service although there is no difference in the actual tariffs. In consequence, if the application is a real-time one, it is advantageous for the user to select the real-time class, because it is the only way to attain small delay and delay variation.


2.3 Quality of Service expectations

The total SIMA service requested by a user consists of a nominal bit rate and of a possible real-time service request. This half of the service is as clear and reasonable as possible. The other half of the service is the expected QoS of the flow, or actually, the expected QoS of the application that the customer uses over the SIMA network. An essential issue for the success of the SIMA service is how reasonable and acceptable this part of the service concept will be.

In a circuit switched network a busy period means that the call blocking probability increases. In packet networks the packet loss ratio increases during busy periods, and effectively, the available capacity for a flow decreases if a TCP/IP type of protocol is used. In a SIMA environment, when a user buys a NBR for a flow and then sends traffic into a SIMA network, there is usually no flow level blocking. The quality of the flow depends on two issues: the NBR to actual bit rate ratio, and total load in the network. Therefore, a potential difficulty is that the customer cannot precisely know what the QoS of a flow will be because rapid traffic variations may bring about unexpected changes of QoS (however, even in the case of services using resource reservation the actual quality of flows using certain quality class may vary significantly).

Because the quality of existing flows is not in the same way predictable as with services using complicated resource reservation mechanism, the SIMA network shall be implemented in a way that the users can rely on the fairness of the service. The fairness of the SIMA service is based on the fact that all flows with the same actual bit rate to NBR ratio perceives similar QoS. Thus, a home user with 10 kbitls NBR receives the same QoS as a large company with NBR of 100 Mbitls provided that both are transmitting at their own NBR.

Another aspect of fairness is the possibility to obtain more quality with higher price or lower price with less quality by changing the actual bit rate or NBR. This means that each customer is entitled to change the NBR to actual bit rate ratio and by that means to optimize his/her quality to charge ratio. If the ratio increases, the quality of the flow is enhanced. If the user sends traffic by using a constant bit rate, the SIMA service offers 7 different quality. Although the absolute quality of each drop preference depends on the network dimensioning and on actual traffic process, the quality levels can be described approximately as follows:

7 = reserved for non-SIMA services with resource reservation 6 = excellent quality: negligible packet loss ratio 5 = high quality: packet losses only during exceptional traffic peaks 4 = good quality: small packet loss ratio even during busy hour 3 = moderate quality: usually small packet loss ratio except during busy hours 2 = satisfactory quality: from time to time very high packet loss ratio 1 = suitable for best-effort traffic during busy hour 0= suitable for best-effort traffic during non-busy hours

The charge of drop preference j will be X * 2)-4 , if the charge of level 4 is X, and if the charging is proportional to NBR. However, quality level 0 can be in practice


obtained free of charge, and the operator may use different charging scheme with level 7. The network operator may try to dimension the network in a way that the traffic of the three lowest levels is able to fill the network during busy hour. Now, as the charge of level 6 service is 16 times higher than that of level 2, we can assume that there will be much more traffic offered to the lowest drop preferences. It is reasonable to assume that the most intense traffic variations occur at the lowest quality levels, whereas the charging may dampen the variations at the highest quality levels. Note that even very high load of the low quality levels has no significant effect on the packet loss ratio of the highest levels.

2.4 SIMA service chain

The total service chain of SIMA is outlined in Figure 1.

User Charging

C --+ XEcu +

tariff

Input to network

function -+ NBR for the flow I.·· .... ····, + T ~ actual offered

traffic of the flow

+

Traffic control

P------~~ rtlnrt ---. SIMA packets + SIMA traffic control + aggregate traffic process +

Performance

network capacity -+ network

Q~~~------------------ performance

Figure 1 Service chain of SIMA. C is the user's readiness to pay, I is information given by the network, T is actual traffic sent into the network, P is the parameters needed to control the flow, and Q is the quality experienced by the user.

The user input to the SIMA network consists of charge (C ~ X $), actual traffic sent into the network (T), and rtlnrt selection (the only pre-defined traffic or quality parameter used with SIMA). The network may inform the user of the offered service tariffs by announcing the NBR or as the user may know the charging function, he can select directly a proper NBR. The main output of the network is the actual QoS of the flow, which depends directly on the network performance. Note that there is a (one-way) connection from the charge of the flow to the actual QoS of the flow via NBR, the SIMA control and network performance. Therefore,


although there is no pre-defined exact relation between charging and QoS, the user may optimize the charging of the flow by trying firstly a low charge, and then doubling the charge until the quality level is sufficient. Another important feature is that the traffic control information is conveyed purely by the SIMA packets or cells, which means that there is no need to have any traffic control information transported between different network nodes. Finally, as there is no packet or cell discarding based on a separate traffic flow, packets or cells are discarded only if the total load exceeds the link capacity.

3 COMPARISON OF SIMA AND OTHER SERVICE APPROACHES

3.1 Current service schemes

The starting point of the development of Internet services is the current best-effort service model. The well-known problems of best-effort service are that there is no relation between quality and charging, and that there is no way to offer high quality (small packet loss or small delay) for those flows that need these features. The prevalent approach to solve this problem is to design guaranteed service classes, each of which has certain quality features. A simplified service chain of this approach is presented in Figure 2.

The user input to a network with a guaranteed service consists of requested traffic and quality parameters (P), and actual traffic sent into the network (T). Actually, this is quite a big difference between SIMA and guaranteed service. With SIMA a customer mainly informs how much he/she is willing to pay. With guaranteed service the customer must first predict the parameters of hislher flow, something that is not easy even for an expert. The network informs users of the charge of the flow by using a complicated tariff table including all possible combinations of traffic and quality parameters.

The guaranteed service approach means that the network attempts to give a statistical prediction of the actual quality of the flow: certain service class will generate certain average quality (it is assumed that each user is willing to understand the meaning of the parameters). However, the connection between requested quality and actual quality is more complicated than can be concluded directly from service specifications due to variations in aggregate traffic process.

The output of the network is the actual QoS of the flow, but in this case the quality (or rather, quality impairments) consists oftwo parts: first one (Ql in Figure 2) contains the possible packet loss ratio due to the control of each flow (UPC in ATM networks), and the other one (Q2) contains the effects of control functions directed to the aggregate traffic load. In order to improve quality, these effects have to be discerned since either the traffic parameters or service class should be changed. This optimization needs quite profound understanding of the properties of services, network and traffic.

Simple integrated media access

User Input to network

c : P -+ requested

traffic +

+ tariff table

Traffic control

charging X Ecu

quality -+ service class parameters

Performance

+ traffic --+ ·flow control· + other control

functions

T

01

descript. +

offered . ----------... traffic -+

disctded traffic

+ accepted traffic

+ aggregate traffic process

+ network--+ network

02 capacity performance ~4~-----------------------~--~-

Figure 2 Service chain of a guaranteed service.

3.2 Service comparison

327

As C. Heckart has expressed it in (Heckart, 1995) gone are the days when carriers could be content to provide one small component of larger picture; carriers must now offer comprehensive service packages that increase their value to users and make it difficult for customers to find another provider to supply the same end-toend solutions. This real need may induce a serious problem with services using guaranteed quality: how to build a reasonable service package offered to ordinary customers not familiar with technical details. The principal question is whether the SIMA service can in this respect be better than the other approaches for integrated services. It is important to note that it is not reasonable to only compare individual services realized by SIMA, or some other service models, but the whole service package offered to customers.

The prevalent approaches are service specifications developed at IETF's Integrated Service working group (IntServ), and ATM specifications. The two main services needed in future Internet are a real-time service with high quality, and a file transfer service with loose requirements for packet loss ratio and delay. In addition, some customers may benefit from a service which guarantees a small packet loss ratio but does not provide small delay. If the network operator attempts to satisfy all these requirements by using the current specifications, he must


implement several dissimilar services. Possible combinations are: guaranteed service, controlled load service and best-effort service if IETF's specifications are used (IETF, 1994), and CBR+rt-VBR, ABR and UBR if ATM is used (ATM Forum, 1996) (ITU-T, 1996). Table 1 provides a brief summary.

Table 1 Comparison of network services.

IntServ ATM SIMA Guaran Contr. Best CBR+ ABR UBR SIMA . servo Load effort rt-VBR

Charging ? - flat rate based on ? flat rate based on traffic, QoS (+usage) NBR parameters

Traffic Many Many - PCR, SCR, - - (NBR) parameters BT Pre-defined yes yes no yes yes no no

J20S par. Small delay yes no no yes no no yes or no Loss ratio small small high small small high small-

high Controlled no yes no no yes no possible service

One of the main problems with the current approaches is different charging principles of different services. The charging of any service relying on resource reservations is likely to be based on the traffic and QoS parameters used at the reservation phase. Best-effort service uses, instead, flat rate or usage based charging schemes. The charging of controlled load services may combine these two schemes (and be quite complicated). In total, if we take into account the need of different charging levels for busy and idle hours, the charging structure tends to be very complicated due to the large amount of parameters. On the contrary, the charging of the SIMA service can be based purely on one parameter, NBR.

When a customer requests a service shelhe shall inform the network what kind of service is needed. This information consists usually of some traffic parameters and quality parameters and perhaps service class. In order to successfully use a service, the customer shall understand the meaning of these parameters (if they cannot be totally hidden from end-users), and even to make proper guess for their values. Taking into account the reluctance of many Internet users to learn technical details, the current service concepts seem to be unsatisfactory in this respect. With SIMA there is only NBR and the selection between real-time and non-real-time service. The latter selection can be usually left for the application.

The next question is whether a SIMA network can offer all the necessary service types. SIMA can provide efficient real-time service, different packet loss ratios from negligible to high, and a free combination of these two categories (delay, packet loss ratio). The most unclear service class is the controlled load service with small packet loss ratio. However, it should be stressed that if there is no strict delay requirement, a small packet loss ratio can be always attained by using efficient


upper layer protocols. Therefore, when using TCPIIP or a similar protocol, there is no urgent need for a controlled load service as an end-user service, rather the objective of the controlled load service is to optimize the use of network resources. A SIMA network offers good possibilities for an application using TCPIIP or similar protocols, because the packet loss ratio decreases rapidly when the transmission rate goes down enough (say, to a level of 3*NBR). In this respect SIMA service is essentially better than a pure best-effort service.

Because traffic and network management is one of major costs of telecommunication network, it is very important to keep management functions as simple and efficient as possible. The realization of a guaranteed service requires traffic parameters for every flow, controlling of these parameters, resource reservation at every network node, complicated signaling for the transfer of parameters, dimensioning of complicated buffer and switching structures, etc. It will be very difficult to implement and manage this type of network. In contrast, the SIMA service may work without such ordinary management functions as Traffic Descriptor, QoS parameters, Connection Admission Control (CAC), or Usage Parameter Control (UPC), etc. All these functions are replaced by the measuring unit at access nodes and the scheduling and buffering unit (SBU).

The SIMA service is able to meet the simplicity requirement essentially better than a network with several service classes, and it can satisfy the basic service needs of most customers. The remaining questions are related to the performance and QoS of SIMA networks. As to the throughput, the main advantage of SIMA is that there is no need to fragment the network capacity, instead, all services and all flows divide the whole capacity of every link. In this respect SIMA is very efficient. In a SIMA network, sufficient quality can be obtained by proper network dimensioning. The operator may offer satisfactory QoS to nominal connections (i.e., to those connections in which actual bit rate is equal to NBR). In practice, this may mean that the operator measures the average packet loss ratio of packets with drop preference 4. This ratio should remain on a reasonable level. If this packet loss ratio is exceeded continuously, the operator shall firstly identify the bottlenecks in the network and then increase the network capacity in those points. The network operator simply throws bandwidth, and the SIMA service manages QoS. This network dimensioning scheme provided by SIMA is a natural extension of the prevalent way of managing Internet.

4 IMPLEMENTATION OF SIMA SERVICE

The implementation of the SIMA service consists of two main parts: access nodes and core network nodes presented in Figure 3. There is a fundamental difference between these node types: the traffic measurement of every flow is performed at access nodes whereas at the core network nodes the traffic control functions do not need to know anything about the properties of separate flows.


CE1 CE2

Figure 3 Customer equipment (CEl) connected to an other customer equipment (CE2) through a SIMA network with access nodes (A) and core nodes (C).

4.1. Access node functions

Let us suppose that there is an IP flow (i) at an access node. A nominal bit rate, NBR(i), is associated to the flow and the user is transmitting IP packets (which may be converted into ATM cells) into the network according to an arbitrary traffic process. At the user/network interface there is a measuring device which measures the momentary bit rate of the flow at the arrival of the j:th packet (or cell). This rate is denoted by MBR(i,j). The device gives every packet a drop preference, DP(i,j), based on the MBR(i,j) to NBR(i) ratio:

x = 4.5 -In( MBR(i, j) )lln(2) NBR(i)

{ 6 ifx~6

DP(i, j) = Int(x) if 0 < x < 6

o ifx:50

(1)

where Int(x) is the integer part of x. Consequently, if MBR(i,j) = NBR(i) the packet (or cell) gets drop preference 4, if MBR(i,j) > 5.66 NBR(i) the packet gets the lowest drop preference (0), and if MBR(i,j) < 0.17 NBR(i) the packet gets the highest preference (6). Drop preference 7 is reserved for those connections that use a network service with guaranteed bandwidth and quality. The accepting and discarding of packets inside SIMA network is only based on the drop preferences.

The proper value for time constant of actual bit rate measurement depends on the buffer capacity reserved for the service class used by the connection. With realtime services the buffer should be small, and thus the measurement period must be short. When using a non-real-time service the user may want to send bursts of packets without high packet loss ratio. As a consequence the averaging period should be much longer.


4.2. Scheduling and buffering unit

The key issue in the implementation of the SIMA service in a high capacity core network is the packet discarding system before the actual buffering shown in Figure 4. At any instant there is an accepted level of drop preference (DPa): if an incoming packet has the same or higher drop preference, it is accepted, otherwise it is discarded. The calculation of DPa is based on the buffer occupancy levels of the real-time buffer (MrJ and non-real-time buffer (Mnrt).

M",

DDDDDDDDD Figure 4 A packet scheduling and buffering unit (SBU).

All the packets which have been accepted in the scheduling unit are situated either in the real-time or non-real-time buffer. Both buffers may apply the First In First Out (FIFO) principle. In order to obtain a small delay and delay variation, the real-time buffer should be relatively small (e.g., 10 kbyte). All packets (or cells) in the real-time buffer shall be transmitted before any packet in the non-real-time buffer. It should be emphasized that the delay priority of real-time flows has no effect on the packet loss ratios. The non-real-time buffer should be much larger (e.g., 1 Mbytes) because of the packet scale fluctuations in typical non-real-time traffic processes. Moreover, large buffers make it possible to offer reasonable service for those flows that are capable of adjusting their bit rate.

It should be emphasized that the function of each scheduling and buffering unit (SBU) is independent of all other SBU's; all the tasks of SBU are performed based on the information of incoming packets, and moreover, all the necessary functions for the implementation are described in Figure 4. Thus, the management of the SIMA network is very straightforward.

5 CONCLUSIONS

The current specifications fail to adequately address the need of simple management and feasible charging for future Internet and other networks with high capacity and quality requirements. Accordingly, there is a need in the communications industry for a network management architecture that is simple in concept and in its implementation, yet adequately addresses the quality of service

332 Pan Nine Multimedia Applications

requirements to support a variety of network services, including real-time and nonreal-time services. There exists a further need for a system and methodology that provides for the implementation of a simple and effective charging capability that accounts for the use of network services. The present SIMA service introduced in this document is capable to fulfill these and other needs which remain unaddressed by current traffic management approaches.

The SIMA service is technically based on three key ideas: the use of nominal bit rate concept, the use of eight drop preference levels for every packet, and separation of real-time and non-real-time connections at the buffer level. If a user needs a connection over an IP or A TM network, he should select a nominal bit rate which could be even a constant proportional to a monthly fee. The user shall select also either a real-time or a non-real-time service class. In addition to these two parameters the user does not need to give any information about the properties of the connection like required bit rate or quality of service. After the connection establishment the capacity division among different connections is based on a drop preference which is determined using a ratio of the measured bit rate and the nominal bit rate. Drop preference in addition to the real-time/non-real-time separation is sufficient for every network node to properly manage the traffic.

Because there is no need for various traffic classes, traffic parameters and network services, the SIMA service makes possible a simple and efficient implementation of network nodes, a simple and fair charging scheme, and very simple traffic management in the core network. The SIMA concept is a very promising scheme for solving the most acute traffic control problems in Internet.

6 REFERENCES

ATM Forum (1996) Traffic Management Specifications v.4.0, af-tm-0056.000. Cukier, K. (1997) ... Net tariffing lags behind, Communications International, 7

April, p. 4. Firdmand, E. (1997) Rx for the Internet: Usage-Based Pricing, Data

Communications, Jan., pp. 27-28. Greenfield, D. (1997) Euro-ATM Get Ready for the Rollouts, Data

Communications, Feb., pp. 48A-48G. Heckart, C. (1995) ATM Services, The Truth, Telephony, Sept. 18. IETF (1994) RFC1633 Integrated services in the Internet architecture: an overview. ITU-T (1996) Recommendation 1.371, Traffic control and congestion control in B-

ISON. International Telecommunication Union, 90 p. McQuillan, J. (1996) Internet poised for great change, Broadband Networking

News, Nov. 26, p. 7. SIMA (1998), SIMA information is available at http://www-nrc.nokia.com/sima/. Snyder, B. (1997) California crunch, Pacific Telesis documents woes of Internet

traffic, Telephony, March 31, 1997, p. 6.

26 Performance Evaluation of an Inter-Stream Adaptation Algorithm for Multimedia Communications

AZaa Youssef, Hussein Abdel- Wahab, and Kurt MaZy Department of Computer Science Old Dominion University Norfolk, VA 23529, USA {youssef, wahab,maly)@cs.odu.edu

Abstract Controlling the quality of a collaborative multimedia session, which employs multiple streams, is a challenging problem. In this paper, we present and analyze the performance of an inter-stream adaptation algorithm, which dynamically allocates the shared resources reserved for a session among the streams belonging to it. The objective of this dynamic allocation is to optimize the overall session quality. The traffic characteristics of the streams are specified using the M-LBAP (Modified Linear Bounded Arrival Processes) model. The M-LBAP model provides tight characterization for the traffic while maintaining the simplicity and linearity of the LBAP model. Delay bounds for streams sharing a group reservation are analytically derived using the M-LBAP model. Degradation paths specified using the M-LBAP model are used as the basis for a dynamic rate based algorithm for inter-stream adaptation (RISA). The performance of RISA is contrasted to static resource allocation policies, and it is shown that higher utilization and acceptance ratios are achievable by RISA. These achievable results are reflected on and summarized by a proposed metric for judging the effectiveness of resource allocation on the overall quality of session.

Keywords Inter-stream adaptation, Quality of Session, Quality of Service, resource allocation, traffic characterization.

1 INTRODUCTION

Continuous media streams represent a major component of new distributed collaborative systems, that is as equally important as the conventional data streams, for providing effective collaboration. These continuous media streams have some inherent characteristics that are not found in other data streams: they have timing and throughput requirements that must be met. In order to

Perfonnance of Infonnation and Communication Systems U. Korner & A. Nilsson (Eds.) © 1998 IFIP. Published by Chapman & Hall


meet those requirements, several quality of service (QoS) architectures, that rely on reservation of resources, such as buffers and transmission bandwidth, were proposed. Examples can be found in (Campbell et al. 1994, Ferrari et al. 1990, Zhang et al. 1993).

These collaborative multimedia systems typically rely on a multi-point to multi-point communication pattern, in which multiple sources, which change over time, generate a group of streams that are multicasted to all members of the session. This group of streams cooperate to present an integrated view to the users. These streams have two main dynamic characteristics: they are activated and deactivated at any instant in time throughout the lifetime of the session; and their relative priorities with respect to each other change over the session lifetime. The first characteristic implies that traditional resource reservation techniques, which treat different streams independently, may either over-allocate resources or allow for potential rejection of connections requested on-the-fly during a session. This motivated several researchers to propose resource sharing through group reservations by which an application can reserve collective amounts of resources to be dynamically shared by its streams (Gupta et al. 1995, Zhang et al. 1993).

The above mentioned characteristics, together with the fact that most multimedia encoders can provide multiple grades of service, suggest that there is a need for overall control, beyond the level of QoS as pertaining to individual streams in isolation of others, for a particular application. For this purpose, we proposed the concept of Quality 0/ Session (QoSess) (Youssef et al. 1997). The quality of the session as perceived by the end user, can best be determined by the end application. At every instant in time, the quality of the session depends on the priorities of the on going streams, from the application's perspective, as well as on the QoS offered for each of these streams. A QoSess control layer controls the allocation of the resources reserved for the application among the streams belonging to it, in a way that stems from the application semantics.

In this paper, we focus on the inter-stream adaptation (ISA) techniques used by the QoSess control layer to allocate the reserved bandwidth among the cooperating streams belonging to an application. This allocation is changed over time to match the dynamic nature of the streams. We use the M-LBAP traffic characterization model to specify the characteristics of the streams. The M-LBAP model is a variation of the LBAP model (Anderson 1993) that gives tighter characterization for the traffic of individual streams.

The rest of this paper is organized as follows. In section 2, the M-LBAP traffic characterization model is described. In section 3, delay bounds for streams sharing the same group reservation are derived analytically. A framework for controlling the quality of a multimedia session is described in Section 4, and a strategy for allocating resources among a group of cooperating streams is presented in Section 5. A unified metric for measuring the quality of a session and comparing the effectiveness of resource allocation strategies is proposed

Evaluation of an inter-stream adaptation algorithm

b(t) (bit)

B·S

S

Xmin

__ LBAP

__ M-LBAP _ _ _ _ _ Discrete

t (sec)

335

Figure 1 Bounding functions of 3 traffic characterization models

in section 6, and simulation results are discussed in section 7. Finally, our conclusions and future work are discussed in Section 8.

2 TRAFFIC CHARACTERIZATION MODEL

A key issue for providing QoS guarantees is the ability to characterize the traffic of the stream for which guarantees are being provided. A traffic characterization model must be tight enough to avoid excessive allocation of resources, and simple enough for the application to use in its specification and for the network to be able to support, as well as for the analysis to be tractable. In addition, the model should allow for the aggregate characterization of the traffic of a group of streams sharing the same resources which are reserved for the group.

In (Cruz 1991) bounding techniques, based on a fluid traffic model (0', p), were developed. Central to the analysis is the concept of traffic constraint function b(t). b(t) is defined to be the maximum number of bits that can arrive during any interval of length t. For the (O',p) model, b(t) = 0' + pt.

The linear bounded arrival processes (LBAP) model (Anderson 1993), characterizes the traffic using three parameters (R, B, S), where R is the average rate in bits/sec, B is the maximum burst size is packets, and S is the maximum packet size in bits. It can be easily shown that the LBAP model is simply a (0', p) model with 0' = BS and p = R. The LBAP model has the advantage of being simple for the application to use in its specification as well as for the network to use in its implementation in order to support the specified characteristics for the streams.

In (Ferrari et al. 1990), the discrete model (Xmin, Xave, I, S) is described, where X min is the minimum packet inter-arrival time, X ave is the average packet inter-arrival time, I is the averaging interval, and S is the maximum packet size. In (Zhang et al. 1994), the bounding function b(t) for the discrete


model is given by (min (r t .;,;:t/ 1 , r x ~ve 1 + r j 1 r x ~ve 1)) S. The discrete model is tighter in characterizing streams but lacks a lot of the simplicity of the LBAP model. Also, determining the optimum value of I is not a trivial task and may be impossible for real-time traffic.

The Modified-LBAP (M-LBAP) model, which we use, is derived from the LBAP model. It strikes a balance between the simplicity of specification and analysis of the LBAP model and the accuracy of representation of the discrete model. In M-LBAP, a stream is characterized by four parameters (R, B, S, PAR), where the first three parameters are the same as the LBAP original parameters, and PAR is the peak-to-average-rate ratio or the burst ratio. Figure 1 shows a graphical representation for the bounding functions of the different models. It can be easily shown that for M-LBAP, the bounding function b(t) is given by BS (1 - P~R (1 - iJ)) + Rt M-LBAP, is also a (0", p) model with 0" = BS (1 - P ~R (1 - iJ)) and P = R. This model provides a tighter characterization for the burstiness of a stream than the LBAP model and hence avoids the excessive allocation of resources.

One of the main advantages of having a linear model derived from the (0", p) model is the ability to characterize a group of streams, as a single aggregate stream. It can be easily shown that the aggregate traffic of K streams, each satisfying (O"k,Pk), k = 1,2, .. ,K, satisfies (Ef=lO"k,E!:lPk). This characteristic of the M-LBAP model makes it adequate for characterizing the streams sharing a group reservation, and regarded by the underlying network as a single aggregate stream.

3 BOUNDING DELAYS

In a packet-switching network, the end-to-end delay of a packet consists of: (1) link delay, which includes the propagation delay and other delays incurred in intermediate subnetworks if some of the links are subnetworks; (2) switching delay, which depends on the implementation of the switches; (3) transmission delay, which is a function of the packet length and link speed; and (4) queuing delay at each switch.

Under the assumption that there are no intermediate subnetworks, or alternatively that all intermediate nodes have reservation capabilities, the link delay is constant and equal to the propagation delay. The switching delay is fixed. Knowing the link speed and the maximum packet length makes the transmission delay fixed as well. The queuing delay is the component that can be affected by controlling the load or using an appropriate service discipline, and hence is the major concern.

Evaluation of an inter-stream adaptation algorithm

3.1 Bounding Delays in a FCFS Scheduler

The following theorem was stated and proven in (Zhang et al. 1994). Theorem 1:

337

Let there be n channels multiplexed on a link with a FCFS scheduler and link speed l. If for j = 1, ... , n, the traffic on channel j is bounded by b(.}, then the delays of packets on all the channels are bounded by d, where d is defined by

1 {~ } Smax d = I maxvu~o ~bj(u} -lu + -l-.1=1

where, Smax is the maximum packet size that can be transmitted over the link.

Including 8n;az accounts for the fact that a lower priority, non-real time, packet may be in transmission and cannot be preempted.

In (Youssef et al. 1997), we prove the following theorem, which defines the delay bounds for a FCFS scheduler and a group of streams whose traffic obey the M-LBAP model. Theorem 2: Let there be n channels multiplexed on a link with a FCFS scheduler and link speed l. If for j = 1, ... ,n, the traffic on channel j obeys the M-LBAP traffic specification (Rj,Bj,Sj,PARj ), and if E.i=1 Rj $ l, then the delays of packets on all the channels are bounded by d, where d is defined by

d= ~ {t BjSj (1- _1 . (1- ~))} + Smax 1 j=1 PAR) B) 1

where, Smax is the maximum packet size that can be transmitted over the link.

Based on Theorem 2, we show in (Youssef et al. 1997) that for n channels sharing a group reservation at the rate of Rtot, on a link with speed l. If for j = 1, ... , n, the traffic on channel j obeys the M-LBAP traffic specification (Rj, B j , Sj, PARj), and if Ej=1 R j $ Rtot , then the delays of packets on all the channels are bounded by d, where d is defined by

d = _1 {t BjSj (1- _1 (1- ~))} + Smax Rtot j=1 P ARj Bj 1

338 Pan Nine Multimedia Applications

FlowSPCCI FIo_, Flow...,. u"'I.IO 0 .- b •. 1

i ,specl,26 6 J u",,)6 t 6 ..

"'" 6 .A

upcc 2.56 Application

Semantic

Degradation Paths Requirements

Capacity of

Group

Reservation

Selecled Operating Points

Figure 2 Using degradation paths in inter-stream adaptation

4 A FRAMEWORK FOR SESSION QUALITY CONTROL

In a networking environment where group reservation is provided to applications to support sharing of resources, the QoSess control layer must allocate fractions of the total amount of reserved resources to each stream. As shown in Figure 2, an inter-stream adaptation (ISA) module uses its knowledge of the degradation paths of the streams, the semantic requirements of the application, and the amount of resources reserved for the application to dynamically determine the operating point of each stream, and informs the application for enforcement.

Each operating point for a continuous media stream can be mapped from encoder specific parameters, e.g., frame rate or size, number of quantization levels, encoding technique, ... etc., into traffic specific parameters. Arranging more than one operating point for a stream in the form of a degradation path, as shown in Figure 2, gives flexibility for the ISA module in adapting to availability of resources or changes in application requirements. The flow specification (FlowSpec) for a stream is composed of a traffic specification (TSpec) and a QoS requirements specification (RSpec). TSpec represents an ordered list of operating points. Using the M-LBAP model parameters, TSpec = {(R1,B1,Sl, PARd, ... , (Rm,Bm, Sm, PARm)). RSpec represents the delay, jitter, and loss constraints for the stream as well as the relative importance of each of these factors. RSpec = {D, J, L, WR, WD, WJ, Wd, where, D, J, and L are the maximum allowed delay, jitter, and loss ratio, respectively, and Wx is the weight of factor x.

In a collaborative multimedia application, the group of streams belonging to the application have a highly dynamic nature. A stream may be started/stopped at any instant. Moreover, the relative priority of a stream with respect to the other streams varies with time. In addition to priorities, other types of relation-ships between groups of streams may be implied by the semantics of the application. For example, a pair of streams, e.g., audio and video from

Evaluation of an inter-stream adaptation algorithm 339

the same source, may be required to be always in the same active/inactive state. More complex relation-ships include inter-stream synchronization and synchronization of multiple views of the same stream.

5 RATE BASED INTER-STREAM ADAPTATION

The degradation paths of n streams belonging to an application represent an n-dimensional space. A valid point in this space represents an operating point for each of the n streams. Knowing the FlowSpec of each stream allows for computing the total resources required for the selected point. The rate based approach we introduce here assumes continuous values in the range [Rmin, Rmax] for the parameter R of the M-LBAP model, while the other parameters are fixed. This is equivalent to changing only the sampling rate or alternatively the frame rate of the encoder while keeping all other precision and quality parameters of the encoder constant. For RSpec, we consider a delay bound constraint that must be respected, with no losses, and jitter is ignored. The RISA (Rate-based Inter-Stream Adaptation) algorithm is run whenever a change in priority occurs or a stream is activated/deactivated. It uses the above information to select an optimal point in the n-dimensional space of degradation paths. This is done in two phases: 1. Selection Phase: All streams are scanned in descending order of priority, granting each its requested minimum rate if the available bandwidth permits and the delay bound constraints for all selected streams are not violated, based on Theorem 2. 2. Enhancement Phase: The remaining non-allocated bandwidth is divided among the selected streams. The objective is to make the share of each active stream as close as possible to its specified Rmax, while maximizing the overall benefit gained by the session from this allocation. This resource allocation problem is formulated as an optimization problem that reduces to the well known knapsack problem (Coreman et al. 1990).

Maximize ~?=1 (Pi * Ii) Subject to: ~?=1 [fi(Rmaxi - Rmini)] ~ Rtot - ~?=1 Rmini o ~ Ii ~ 1 far i = 1,2, .... , n

where n is the number of streams selected in phase 1, Pi is the priority of stream i, and Ii is the computed fraction of (Rmaxi - Rmini) which should be granted to stream i.

The knapsack problem is a special linear optimization problem for which an optimal solution can be obtained by traversing the list of streams in the order of Pi/ (Rmaxi - Rmini) and giving each stream its maximum need until all resources are exhausted (Coreman et al. 1990).


... _----------

o~ ______ ~ __ ~------~----~----~ 10 12

Peak-ro-Average Ratio (PAR)

Figure 3 Effect of Peak-to-average ratio on Acceptance ratio

6 A METRIC FOR COMPARING RESOURCE ALLOCATION STRATEGIES

To compare the behavior of the system under the application of different resource allocation strategies, we propose to use a unified metric that reflects the overall performance of the system for a given allocation. At a certain instant in time, t, we define Qi as the degree of satisfaction of stream i. The QoSess metric is the weighted arithmetic mean of these.

QoSess =

{ Ri/Rmaxi -1

L~=l (Pi * Qi)

L7=l Pj

if i is active } if i is not active

where, Ri is the current level of resource allocation to i. The system is penalized by -1 for each inactive stream. The value of QoSess lies in the interval [-1,1]. Since the QoSess is intended for comparing different strategies, the best attainable QoSess may be below one sometimes.


7 SIMULATION STUDY

In this section we present results from simulation experiments conducted for a single node (switch). The purpose of this simulation was to investigate the effect of the M-LBAP model parameters on the performance of RISA, and to evaluate the benefits obtained from using degradation paths over static resource allocation policies, for traffic characterized by M-LBAP. In each experiment, the session was composed of identical streams with operating rate in the range from 100 to 500 Kbps. The number of streams requested to be activated was set to the maximum number that can be admitted based on the rate constraint alone (i.e. 2:~=1 Rmini = Rtot for the requested streams),

Figure 3 shows the effect of the PAR parameter on the Acceptance ratio for the RISA approach. The Acceptance ratio is defined in (Gupta et al. 1995) as the number of accepted (activated) streams divided by the number of streams requested to be activated. It is clear from the figure that the effect of the PAR parameter stabilizes for values roughly above 5. This relaxes the requirement for exact calculation of PAR, which is an advantage for using PAR instead of the peak rate as the fourth parameter for the M-LBAP model.

In order to evaluate the benefits of employing degradation paths in interstream adaptation, the RISA approach is compared to three static resource allocation strategies that do not employ the concept of degradation paths in inter-stream adaptation. These three cases cover all the extremes. The first case (Fixed-Min) represents a conservative system that is designed for worst case scenarios, where Ri = Rmini always, for each stream i. The second case (Fixed-Max) represents an aggressive design where Ri = Rmaxi. In between lies the average case (Fixed-Avg), with ~ = Rma"'iiRmini.

Figures 4 and 5 show that while some of the static strategies achieve high utilization and others achieve high acceptance ratios, RISA strikes the balance of achieving both goals. This is summarized by the QoSess metric in Figure 6. Since the number of streams requested to be activated is equal to the maximum number that can be admitted based on the rate constraint only, the QoSess values for Fixed-Min are close to those for RISA. Typically, during a session there will be periods where the number of requested streams is smaller and hence significantly higher QoSess values will be obtained using RISA relative to Fixed-Min.

8 CONCLUSION AND FUTURE WORK

The need for controlling the quality of collaborative multimedia sessions that employ multiple streams, by means of inter-stream adaptation decisions, has been recently established (Youssef et al. 1997). In this paper we focused on sessions that operate in the presence of a reservation protocol which allows for a group reservation of a collective amount of bandwidth to be shared by the streams of a session. Degradation paths defining the possible operating levels


o~~~~~~~~~~~~~~~~~~~~~~ w = ~ ~ ~ ~ ~ ~ ~ ~

Delay bound (D) in nose<::

Figure 4 Effect of Delay bound on Acceptance ratio

o~~~~~~~~~~~~~~~~~~~~~~ w = ~ ~ ~ ~ ~ ~ ~ ~

Delay bound (D) in nose<::

Figure 5 Effect of Delay bound on Utilization


Flxed-Avg

i 0

30 40 50 60 70 80 90 100

Delay bound (D) in ntsec

Figure 6 Effect of Delay bound on QoSess

of each stream were used as the basis for a dynamic rate based algorithm for inter-stream adaptation, RISA. Simulation results showed that higher utilization and acceptance ratios are achievable by RISA over typical fixed static policies. These results were reflected on and summarized by the introduced quality of session (QoSess) metric.

Currently, we are implementing the inter-stream adaptation (ISA) schemes, for more intensive experimental investigation, using the IRI (Interactive Remote Instruction) system (Maly et al. 1997) as a testbed. Also, we are investigating ISA policies that are based on discrete degradation paths, and situations where no group reservation is provided by the underlying network, but rather capacity estimation and resource usage monitoring techniques are used to estimate the resources available to the application.

REFERENCES

Anderson, D.P.(1993) Meta-scheduling for distributed continuous media. ACM Transactions on Computer Systems, 11(3), August 1993.

Campbell, A., Coulson, G. and Hutchinson, D.(1994) A Quality of Service Architecture. Internal Report MPG-94-0B, Lancaster University, 1994.

Coreman, T., Leiserson, C. and Rivest, R.(1990) Introduction to Algorithms. McGraw-Hill and MIT Press, 1990.

Cruz, R.(1991) A Calculus for Network Delay, Part I: Network Elements in Isolation. IEEE Transactions on Information Theory, 37(1), 1991.


Ferrari, D. and Verma, D.(1990) A Scheme for Real-Time Channel Establishment in Wide-Area Networks. IEEE Journal on Selected Areas in Communications, 8(3), 1990.

Gupta, A., Howe, W., Moran, M. and Nguyen, Q.(1995) Resource Sharing for Multi-Party Real-Time Communication. Proceedings of INFOCOM'95.

Maly, K., Abdel-Wahab, H., Overstreet, C.M., Wild, C., Gupta, A., Youssef, A., Stoica, E. and AI-Shaer, E.(1997) Interactive Distance Learning over Intranets. IEEE Internet Computing, 1(1), January 1997.

Youssef, A., Abdel-Wahab, H. and Maly, K.(1997) Inter-Stream Adaptation over Group Reservations. TR_97_37, Old Dominion University, April 1997.

Youssef, A., Abdel-Wahab, H., Maly, K. and Gouda, M.(1997) Inter-Stream Adaptation for Collaborative Multimedia Applications. Proceedings of the Second IEEE Symposium on Computers and Communications (ISCC'97), Alexandria, Egypt, July 1997.

Zhang, H. and Ferrari, D.(1994) Improving Utilization for Deterministic Service in Multimedia Communication. Proceedings of IEEE International Conference on Multimedia Computing and Systems, 1994.

Zhang, L, Deering, S., Estrin, D., Shenker, S. and Zappala, D.(1993) RSVP: A New Resource ReSerVation Protocol. IEEE Network Magazine, September 1993.

9 BIOGRAPHY

Alaa Youssef is a PhD candidate and research assistant in computer science at Old Dominion University. His research interests include networking support for multimedia systems, resource management in heterogeneous distributed systems, and multimedia collaborative and tele-teaching systems. Youssef received an MSc in computer science from Alexandria University.

Hussein Abdel-Wahab is a professor of computer science at Old Dominion University, an adjunct professor of computer science at the University of North Carolina at Chapel Hill, and a faculty member at the Information Technology Lab of the National Institute of Standards and Technology. His main research interests are collaborative desktop multimedia conferencing systems and real-time distributed information sharing. Abdel-Wahab received a PhD in computer communications from the University of Waterloo. He is a senior member of IEEE Computer Society and a member of the ACM.

Kurt Maly is a Kaufman professor and chair of computer science at Old Dominion University. His research interests include modeling and simulation, very high performance network protocols, reliability, interactive multimedia remote instruction, Internet resource access, and software maintenance. Maly received a PhD in computer science from the Courant Institute of Mathematical Sciences, New York University. He is a member of the IEEE Computer Society and the ACM.

Abdel-Wahab, H. 333 Alins, 1.1. 216 Almeida, M.1. 309 Aracil, J. 111

Bak,A. 189 Becker, M. 14 Beylot, A.-L. 14 Blondia, C. 177, 234 Bull, T. 3 Burakowski, W. 189

Capone, J.M. 283 Casals, O. 177

De Silva, R. 275 de la Cruz, L. 216 Dipper, R. 3

Eriksson, A. 165

Fladenmuller, A. 275

Gaspary, L.P. 309 Gelenbe, E. 249 Ghanwani, A. 249

INDEX OF CONTRmUTORS

Izal, M. 11

Karagiannis, G. 65 Karlsson, G. 205 Kilkki, K. 321 Kim, S.-H. 295

Lassila, P. 261 Lee,H. 38 Lee, S.-H. 295 Loukola, M. V. 83

Maly, K. 333 Mata,J. 216 Mild6s, G. 97 Moldov4n, I. 51 Moln4r, S. 97 Morat6, D. 111

Nicola, V.F. 65 Niemegeers,I.G.M.M. 65 Nilsson, A. 3

OI4h,A. 153 Ortiz, Z. 137

Park, S.-W. 295

Perros, H.G. 137 Perry, M. 3 Peters, B. 3 Petrovic, Z.R. 26

Reichl, P. 125 Rouskas, G.N. 137 Ruutu, J. 321

Schroeder, P. 3 Schuba, M. 125 Simon,C. 51 Skulic, V.M. 26 Skyttli,l.0. 83 Spaey, K. 234 Stavrakakis, I. 283 Sukely, S. 51

Tunbtyi, Z. 153

Van Houdt, B. 177 Veres, A. 153 Virtamo, J. 261 Vuncannon, D. 3

Youssef, A. 333

ABR service 189 Analytic models 14 ARIMA process 216 AT~ 14,177,205,321

networks 38, 189,216,249 Audits 3 Available bit rate 177

Banyan 26 Blocked call queueing 51 Blocking 26 Broadband Intelligent Networks 65 Bursty traffic 14

Call retrial 51 CD~ 295 Charging 321 Circulant matching method 234 Congestion control 177 Connection control 295 Connectionless 165 Coupled queues 249

Deterministic bitrate 205 DLC 283 Duplex 3

E-LOTOS 309 Effective bandwidth 153 Explicit rate

algorithm 189 congestion control 177

Finite capacity queue 14 Flow

control 189 handling 83

Formal conception 309

Gibbs sampler 261

Handoff 275, 295

KEYWORD INDEX

HOL 26

Integrated services 153 Inter-stream adaptation 333 Internet 165,321

service provisioning 111 IP

over AT~ 83 switching 83

Large deviation 153 Loss systems 261

Maintenance 3 Markov chain 125 Measurement based admission control 153 Mobile

IP 275 networks 295

~obility 275 MPEG video traffic 216 Multimedia 309 Multiplexing 234

Network scalability 65 Neural network 26

Outages 3

Penalty function 38 Performance

analysis 65, 125 assessment 38

Periodic sources 234

Quality of Service (QoS) 38, 165,283,321,333 Session 333

Recirculation 26 Reliability 3 Reliable multicast 125

348

Resource allocation 333 reservation 165

Round trip time delay 51

Scalability 165 Scheduling 283

disciplines 249 Self-similarity III Signalling protocol 51 SIMA 321 Simulation 261 Statistical bitrate 205 Switches 14 Switching equipment 3 Synchronization 309

Keyword index

TCP 111.275 TDMA 283 Teletraffic 205 Token bucket 153 Traffic

characterization 333 management 177 shaping 216

Validation 309 Variable bitrate 205 Variance reduction 261 Video 205

Wireless ATM 295

Performance of Information and Communication Systems: IFIP TC6 / WG6.3 Seventh International Conference on Performance of Information and Communication Systems (PICS â€™98) 25â€“28

Documents