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Chapter 8

Teletraffic Engineeringfor HSDPA and HSUPACells

Maciej Stasiak, Piotr Zwierzykowski,and Mariusz G /labowski

Contents

8.1 Introduction ................................................................................. 2988.2 System Architecture ....................................................................... 300

8.3 Model of the Full-Availability Group with Multirate BPP Traffic ........ 3038.3.1 Basic Assumptions .............................................................. 3038.3.2 Multidimensional ErlangEngset Model

at the Microstate Level ........................................................ 3048.3.3 Full-Availability Group with BPP Traffic

at the Macrostate Level ........................................................ 3058.3.4 MIM-BPP Method ............................................................. 308

8.3.4.1 Method MIM-BPP ............................................... 3088.4 Model of the Full-Availability Group with Traffic Compression .......... 309

8.4.1 Basic Model of the Full-Availability Groupwith Compression .............................................................. 310

8.4.2 Model of the Full-Availability Groupwith Uneven Compression ................................................... 314

8.5 Modeling and Dimensioning of the Radio Interface ........................... 3148.5.1 Resource Allocation in Mobile Systems with Soft Capacity ...... 315

8.5.1.1 Uplink ................................................................ 317

297

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298 Evolved Cellular Network Planning and Optimization

8.5.1.2 Downlink ............................................................ 3188.5.2 Allocation Units in the WCDMA Radio Interface .................. 319

8.5.3 Analytical Model of the WCDMA Interface ........................... 3208.5.3.1 Blocking (and Loss) Probability .............................. 3218.5.3.2 Average Throughput ............................................. 3218.5.3.3 Downlink Direction ............................................. 3228.5.3.4 Uplink Direction .................................................. 3228.5.3.5 Average Throughput Available for HSPA Users ........ 3238.5.3.6 Summary ............................................................. 323

8.6 Dimensioning of the Iub Interface with HSPA Traffic ........................ 324

8.6.1 Exemplary Architecture of the Iub Interface ........................... 3248.6.2 Analytical Model of the Iub Interface .................................... 3268.6.2.1 Blocking (and Loss) Probability .............................. 3278.6.2.2 Average Throughput ............................................. 3278.6.2.3 Average Throughput Available for HSDPA Users ..... 329

8.7 Conclusion ................................................................................... 329References .............................................................................................. 329

8.1 IntroductionThe increasing popularity of data transfer services in mobile networks of the secondand the third generations has been followed by an increasing interest in methodsfor the dimensioning and optimization of networks servicing multirate traffic. Intraffic theory, these issues are in full swing. The problems concern primarily thespecial conditions of constructing the mobile networks, and the infrastucture of theradio access networkas its development, or extension, needs a precise definitionand assessment of clients needs and is relatively time-consuming. Cellular networkoperators define, on the basis of a service level agreement (SLA), a set of key per-formance indicator (KPI) parameters that serve as determinants in the process ofnetwork dimensioning and optimization. Dimensioning can be presented as an un-ending and ongoing process of analyzing and designing the network. To make thiswork effective, it is thus necessary to work out algorithms that would, in a reliableway, model the parameters of a designed network.

The dimensioning process for the third-generation Universal Mobile Telecom-munications System (UMTS) should make it possible to determine such a capacity

of individual elements of the system that will secure, with the assumed load of thesystem, a pre-defined level of grade of service (GoS). With the dimensioning of theUMTS system servicing R99 and HSPA traffic, the most characteristic constraintsare the radio interface and the Iub interface.

Analytical modeling of radio and Iub interfaces is based on the assumption thata full-availability group carrying multirate traffic can be used as the fundamentaltraffic engineering model for those interfaces (i.e., [17]). The model of the full-availability group (FAG) is a well-known multirate model, which is characterized by

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Teletraffic Engineering for HSDPA and HSUPA Cells 299

the occupancy distribution [8]. The form of the occupancy distribution in the FAGdepends mainly on the type of multirate traffic serviced by the group (cf. [9, 10]

or [11]).Two important properties of the interface can be distinguished in the modeling

of radio interface: the level of interference and the limited number of users servicedby the interface. Several papers have been devoted to traffic modeling in cellularsystems with the WCDMA radio interface (i.e., [15,7]), but only in [12] and in [1]both properties are taken into consideration. The most general analytical model ofthe WCDMA interface is proposed in [7], where the authors model the WCDMAradio interface by the full-availability group servicing a mixture of multirate Erlang

(infinite source population) and Engset (finite source population) traffic streams [7].In the model, the dependence of mutual interference between cells on the decrease inthe theoretical flow capacity of the radio interface is taken into account on the basis ofa fixed-point methodology [13]. The characteristic feature of the developed methodis the possibility to model, unlike in the previous models, a group of cells servicingdifferent classes of users [7] as well as to take into consideration the interdependenceof service processes in the uplink and downlink directions in the case of bi-directionalservices, both symmetrical and asymmetrical. In the models hitherto discussed in

literature, it was assumed that the WCDMA interface carries only R99 traffic classes.Inthischapter,weproposetheapplicationofthismethodtomodeltheradiointerfacecarrying both R99 and HSPA traffic streams.

The relevant literature proposes only one analytical model of the Iub interface.In [6], the authors discuss the influence of the Iub organization scheme on theefficiency of the interface. The paper describes two analytical models correspondingto the static and the dynamic organization scheme of the Iub interface. In the staticscheme, it was assumed that Iub was divided into two separated links and oneof them carried a mixture of R99, whereas the other an HSDPA traffic stream.

In this scheme, each of the links was modeled by the full-availability group withmultirate traffic. The second organization scheme assumed a dynamic constraint ofthe Iub interface resources for R99 traffic, accompanied by unconstrained accessto the resources for HSDPA traffic. The dynamic organization scheme of Iub isanalyzed in a new model of the full-availability group with constraint, proposedby the authors. The analysis presented by the authors in [6] is limited only to thedownlink direction because in the uplink direction HSPA traffic is serviced basedon R99 resources [12]. In all models, the average throughput per an HSPA user was

Multirate traffic carried by the radio and Iub interfaces can be divided into the so-calledErlang multirate traffic, generated by an infinite, population of traffic sources, and the so-calledEngset multirate traffic, generated by a finite population of traffic sources.

In the chapter, we have presented models of the radio and Iub interfaces based on the mostgeneral and effective occupancy distribution [13].

In [7], the authors show that the application of Erlang multirate traffic instead of Engsetmultirate traffic leads to a higher value of blocking probabilities for all traffic streams carried bythe interface.

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not discussed. The relevant literature discusses some analytical models for multiratetraffic with compression (i.e., [1416]), which can be applied for modeling HSDPA

traffic. Models presented in [14, 15] are quite simple under the assumption thatall classes of the carried traffic are characterized by the compression property. Inany other case, when the system services classes which undergo and do not undergocompression simultaneously, the methods are characterized by a high complexity,which limits their practical application. In [16], an effective analytical model of theIub interface carrying a mixture of Release 99 and HSPA traffic classes with adoptedcompression functionality was proposed. In this chapter, we will treat this model asthe basis for modeling the HSPA traffic carried by the WCDMA and Iub interfaces.

The chapter is divided into seven sections. Section 8.2 presents the basic architec-ture of the system. In Section 8.3, we discuss the basic model (i.e., the full-availabilitygroup servicing a mixture of different multirate traffic streams), which will be usedfurther on as a model of the WCDMA and the Iub interfaces. Section 8.4 presentsa model of the full-availability group servicing multirate traffic with compressionproperty, which is used in the following sections for modeling HSPA traffic behav-ior. The application of the described analytical methods for modeling the WCDMAand Iub interface, carrying R99 and HSPA traffic, is shown in Sections 8.5 and 8.6.

Section 8.7 sums up the chapter.

8.2 System Architecture

Let us consider the structure of the UMTS network presented in Figure 8.1. Thepresented network consists of three functional blocks, designated respectively: userequipment (UE), UMTS terrestrial radio access network (UTRAN), and core net-work (CN). The following notation has been adopted in Figure 8.1: RNC is the radio

UTRAN

CN

lub

lub

lub

UE

UE

UE

NodeB

NodeB

NodeB

WCDMA

WCDMA

WCDMA

RNC

Figure 8.1 Elements of the UMTS network structure.

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network controller, WCDMA is the radio interface, and Iub is the interface con-necting NodeB and RNC.

High-speed downlink packet access (HSDPA) has been included by 3GPP intothe system specification in version 5. The aim of its introduction is to increasetransmission speed in the downlink and shorten delays in the network. An equivalentof HSDPA for the uplink is the HSUPA fast packet data transmission in the uplink,which became part of the UMTS system, in version 6 [17].

In successive versions of HSDPA, it is assumed that the users will be able totransmit data at the speed of 1.8 Mbps, 3.6 Mbps, 7.2 Mbps, and 14.4 Mbps.Therefore, new solutions have been worked out concerning the organization and

management of transport and physical channels. The following channels have beendefined in the system [17]:

High-Speed Downlink Shared Channel (HS-DSCH): A channelshared by many mobile stations, used for transmitting users data from higherlayers of the network and controlling information. The channel is an extensionof the DCH channel for high-speed data transmission.

Physical Channels: High-speed physical downlink shared channel (HS-PDSCH): Used for

data transmission with the constant spreading factor equal to 16. Shared control channel (HS-SCCH): Used to inform the mobile station

about a planned transmission in the HS-DSCH channel. High-speed dedicated physical control channel (HS-DPCCH): Used

in the uplink to confirm transmitted data and send the channel qualityindicator.

Besides the definitions of new channels, the HSDPA technology introduces the

following new mechanisms: Adaptive Modulation and AMC Coding: Apart from the QPSK mod-

ulation, HSDPA allows for the application, with a low level of interferenceand 16 quadrature amplitude modulation (16 QAM). Modulation and cod-ing schemes can be changed depending on the quality of the signal and theload of the radio link.

High-Speed Packet Transmission from the Level of NodeB: TheHS-DSCHchannelissharedbydifferentusersofthesystemtofullymakeuseof

the available resources of the radio link, depending on propagation conditionsand the level of interference. On the basis of the signal level indicator CQI inthe downlink is sent by mobile stations, the base station decides which userwill be sent appropriate data.

High-Speed Retransmission from the Level of NodeB HARQ

(hybrid automatic repeat request): HSDPA technology includes thefunction of retransmission in the physical layer. The function is located inthe base station of NodeB, and therefore the process of retransmission that

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does not get RNC involved is carried out much faster. In addition, HARQintroduces the concept of incremental redundancy. When the mobile station

receives wrong data, the data is stored and reused by the decoder to restructurethe received signal after the retransmission of redundant data to the mobilestation. The base station sends incremental redundant data if in the previoustransmission it was impossible to decode the received information.

Multicode Transmission:HSDPAallowsformulticodetransmission.Thebase station can transmit a signal to a mobile station using simultaneously upto 15 channel codes with the spreading factor of 16.

High-speed uplink packet access (HSUPA) is a counterpart to HSDPA for theuplink. It enables data transmission from the subscriber to the base station withthe speed of 5.76 Mbps. The HSUPA technology uses high-speed retransmissionfrom the HARQ level of a mobile station with incremental redundancy, allowsTTI (transmission time interval) between subsequent transmissions and introducesa new type of E-DCH (enhanced dedicated channel). The E-DCH, unlike the HS-DSCH used in the HSDPA technology, is not a shared channel but a dedicatedone. This means each mobile station sets up, with the servicing NodeB, its ownE-DCH. Additionally, HSUPA does not use the adaptive modulation(Table 8.1).

Like in the R99 version of the UMTS system, modulation BPSK is used. High-speedHARQ retransmission for HSUPA operates in a similar way for HSDPA. The basestation informs the mobile station if it has received data packets or not. When thebase station receives packets erroneously, they are immediately retransmitted by themobile station. Having received them, NodeB, also using the previously receivedsignal, tries to re-create the data sent by the mobile station. The retransmissionis then repeated until the packets sent by the mobile station have been receivedproperly, or the number of admissible retransmissions has run out. The procedure

for high-speed packet access in HSUPA is different than in HSDPA. In HSDPA, the

Table 8.1 A Comparison of the Properties of DCH Channels (R99),HS-DSCH (HSDPA), and E-DSH (HSUPA)

Feature DCH HSDPA (HS-DSCH) HSUPA (E-DCH)

Variable spreading factor Yes No Yes

Fast power control Yes No Yes

Adaptive modulation No Yes No

BTS based scheduling No Yes Yes

Fast L1 HARQ No Yes Yes

Soft handover Yes No Yes

TTI length (ms) 80, 40, 20, 10 2 10, 2

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HS-DSCH channel is shared by all participants serviced by a given cell. Due to thisreason, the base station can allocate, though for a short time, all resources to exactly

one mobile station when other mobile stations do not receive demanded data. InHSUPA, the E-DCH channel is a dedicated channel, which results in a situationwhen co-sharing is not possible. Therefore, the procedure of high-speed transmissionin HSUPA operates in a similar way as packet scheduler for the R99 traffic. RNCinforms all mobile stations about the maximum power they can use for transmission.If the interference level approaches the value that can cause instability in the system,the level of admissible transmission power allocated to all mobile stations is reduced.

In the dimensioning process for the UMTS network, an appropriate dimen-

sioning of the connections in the access part (UTRAN) (that is, the radio interfacebetween the user and NodeB, and the Iub connections between NodeB and the radionetwork controller (RNC), has a particular significance. Successive sections of thechapter describe the analytical models for the WCDMA and Iub interfaces in theuplink and downlink directions, carrying a mixture R99 and HSPA traffic streams.

8.3 Model of the Full-Availability Group

with Multirate BPP TrafficThe full-availability group carrying a mixture of different multirate traffic streamsis the analytical model of radio and Iub interfaces. In this section, we introduce ananalytical model that is fundamental for the considerations presented in subsequentsections of the chapter.

8.3.1 Basic Assumptions

Considerthemodelofafull-availabilitygroupwiththecapacityofVbasicbandwidthunits (BBUs) presented in Figure 8.2 [11]. The group is offered two types of trafficstreams:mIErlang streams from the set I = {1, . . ., i, . . .,mI}, andmJ Engset

BBU

1

2

3...

V

...

class i:i, i, ti

...

mIclassErlang traffic

mJclassEngset traffic

...

classj:j,Nj,j,tj

...

Figure 8.2 Full-availability group with the Erlang and Engset traffic stream. [Withkind permission from Springer Science+Business Media: G/labowski, M., Modellingof state-dependent multi-rate systems carrying BPP traffic.Annals of Telecommu-nications, 63(78): 393407, August 2008.]

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streams from the set J = {1, . . ., j, . . ., mJ}. It has been assumed that the letteri denotes any class of Erlang traffic, the letter j any class of Engset traffic, and

the letter c any traffic class. The number of BBUs demanded by calls of class c isdenoted by the symboltc.

The call intensity for Erlang traffic (Poisson distribution) of class i is i. Theparameterj(nj) determines the call intensity for the Engset traffic stream of classj (binomial distribution). The intensityj(nj) depends on the number ofnj ofcurrently serviced calls of class jand decreases with the increasing number of servicedtraffic sources:

j(nj)=(Nj nj)j (8.1)

whereNjis the number of traffic sources of class j, while jis the call intensity ofcalls generated by a single free source of class j.

The total intensity of the Erlang traffic of classioffered to the group is:

Ai =i/i (8.2)

whereas the intensity of Engset traffic

jof class j, offered by one free source, isequal to:

j = j/j (8.3)

In Formulae 8.2 and 8.3, the parameter is the average service intensity with theexponential distribution.

8.3.2 Multidimensional ErlangEngset Modelat the Microstate Level

Let us now consider the multidimensional Markov process in the full-availabilitygroup with the capacity ofVBBUs, presented in Figure 8.3. The group is offeredtwo types of call streams: Poisson and Engset call streams. Each microstate of theprocess {x1, . . .,xi, . . .,xmI,y1, . . .,yj, . . .,ymJ }is defined by the number ofserviced calls of each class of offered traffic, wherexidenotes the number of serviced

callsofthePoissonstreamofclassi(Erlang traffic),yjdenotes the number of servicedcalls of the Engset stream of class j(Engset traffic). To simplify the description, themicrostate probability will be denoted by the symbol [p(. . .,xi,yj, . . . )]V.

The multidimensional service process in the ErlangEngset model is a reversibleprocess [11]. In accordance with Kolmogorov criterion, considering any cycle forthe microstates is shown in Figure 8.3, we always obtain equality in the intensity ofpassing (streams) in both directions. The property of reversibility implies the localequilibrium equations between any of two neighboring states of the process. Such

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{xi,yj+ 1}

{xi,yj}

{xi+ 1,yj+ 1}

{xi+ 1,yj}

(Njyj)j (Njyj)j(yj+ 1)j (yj+ 1)j

i

(xi+ 1)

i

i

(xi+ 1)i

Figure 8.3 Fragment of a diagram of the Markov process in the full-availabilitygroup. [With kind permission from Springer Science+Business Media: G/labowski,M., Modelling of state-dependent multi-rate systems carrying BPP traffic. Annalsof Telecommunications, 63(78): 393407, August 2008.]

an equation for an Erlang stream of class iand the Engset stream of class jcan bewritten in the following way(Figure 8.3):

xiip(. . .,xi,yj, . . .) =ip(. . ., xi1,yj, . . .) (8.4)

yjjp(. . .,xi,yj, . . .) =[Nj (yj 1)]jp(. . .,xi,yj 1, . . .) (8.5)

Since the call streams offered to the group are independent, we can add up, for themicrostate {. . ., xi,yj, . . . }, all mIequations of the type (Equation 8.4) for theErlang streams andmJ equations of the type (Equation 8.5) for the Engset streams.

Additionally, taking into consideration traffic intensity(Figures 8.2 and 8.3),weget:

p(. . .,xi,yj, . . .)

mIi=1

xiti+

mJj=1

yjtj

=

mIi=1

Aitip(. . .,xi 1, yj, . . .) +mJ

j=1

[Nj (yj 1)]jtjp(. . .,xi,yj 1 . . .)

(8.6)

8.3.3 Full-Availability Group with BPP Trafficat the Macrostate Level

It is convenient to consider the multidimensional process occurring in the consideredsystem at the level of the so-calledmacrostates. Each macrostate contains informationabout the number of busy BBUs in the considered group, regardless of the numberof serviced calls of particular classes.

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The macrostate probability [Pn]Vis then the occupancy probabilitynBBU ofthe group and can be expressed as the aggregation of the probabilities of appropriate

microstates:[Pn]V =

(n)

p(. . ., xi,yj, . . .) (8.7)

where (n) is a set of all such subsets{. . .,xi,yj, . . . }that fulfill the equation:

n=

mI

i=1xiti+

mJ

j=1yjtj (8.8)

The definition of the macrostate Equation 8.8 makes it possible to convertFormula 8.6 into the following form:

n p(. . .,xi,yj, . . .) =mI

i=1

Aitip(. . .,xi1,yj, . . .)

+

mJ

j=1

[Nj (yj 1)]jtjp(. . .,xi,yj 1, . . .)

Summing on both sides all microstates that belong to the set (n), we get:

n(n)

p(. . .,xi,yj, . . .) =mI

i=1

Aiti(n)

p(. . ., xi1,yj, . . .)

+

mJj=1

[Nj (yj 1)]jtj(n)

p(. . .,xi,yj 1, . . .)

(8.9)

Following the definition of macrostate probability, expressed by Formula 8.7,we are in a position to convert Formula 8.9 as follows:

n[Pn]V =mI

i=1

Aiti[Pnti]+mJ

j=1

[Nj (yj 1)]jtj(n)

p(. . .,xi,yj 1, . . .)

=

mIi=1

Aiti[Pnti]+mJ

j=1

jtj(n)

[Nj (yj 1)]

p(. . ., xi,yj 1, . . .)

(n) p(. . ., xi,yj 1 . . .)(n)

p(. . .,xi,yj 1, . . .) (8.10)

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In Formula 8.10 the sum:

(n)

[yj 1] p(. . .,xi,yj 1, . . .)

(n) p(. . .,xi,yj 1, . . .) = yj(ntj) (8.11)

determines the value of the average number of calls of class j in the occupancystatentj. When taking into consideration Equation 8.11, Formula 8.10 can berewritten in the following way:

n[Pn]V =

mIi=1

Aiti[Pnti]+

mJj=1

jtj[Nj yj(ntj)][Pntj]V (8.12)

where [Pntc]V = 0, ifn < tc, and the value [ P0]Vresults from the normativecondition

Vn=0[Pn]V =1.

Let us introduce the following notation for the offered traffic intensity in appro-priate occupancy states of the group:

Ai(n) = Ai, Aj(n)=j[Nj(yj(n))] (8.13)

Formula 8.12 can be now finally rewritten in the following form:

n[Pn]V =mI

i=1

Ai(nti)ti[Pnti]+mJ

j=1

Aj(ntj)tj[Pntj]V

=

mc=1

Ac(ntc)tc[Pntc]V

(8.14)

The average number of calls of class cin the group in staten+tccan be written asfollows:

yc(n+tc)= Ac(n)[Pn]V/[Pn+tc]V forn+tc V

0 forn+tc> V

(8.15)

Let us remark that if the system services the Erlang streams only, then Equa-tion 8.12 can be simplified to Kaufman-Roberts recursion [9,10]:

n[Pn]V =mI

i=1

Aiti[Pnti] (8.16)

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8.3.4 MIM-BPP Method

Let us now consider a full-availability group with Erlang and Engset multirate trafficEquation 8.12. Notice that in order to determine the parameteryc(n), it is necessaryto determine first the occupancy distribution [ P]V. Simultaneously, in order todetermine the occupancy distribution [P]V, it is necessary to determine the valueyc(n). This means Equations 8.14 and 8.15 form a set of confounding equationsthat can be solved with the help of iterative methods [11]. Let [ P(l)]Vdenote theoccupancy distribution determined in step l, and let y(l)c (n) denote the averagenumber of serviced calls of class c, determined in stepl. Then:

y(l+1)c (n) =

A(l)c (ntc)

P(l)ntc

V/

P(l)n

V for 0nV

0 in remaining instances(8.17)

where A(l)c =c[Nc y(l)c (n)].

In order to determine the initial distribution [P(0)ntc]V, it was assumed that:

A(0)c (n)= Ac = Ncc (8.18)

On the basis of the reasoning presented here, in [11] the MIM-BPP methodfor determining the occupancy distribution and the loss probability in the full-availability group with BPP traffic was proposed. The method can be presented inthe following way:

8.3.4.1 Method MIM-BPP

1. Setting the starting point of the iteration atl =0

2. Determination of initial values y(l)j (n),y(l)k (n):

1jmJ 0nV y(l)j (n) =0, 1kmK0nV y

(l)k (n) =0

3. Increase in each iteration step:l =l+14. Determination of the value of Engset traffic of class jon the basis of For-

mula 8.135. Determination of the state probabilities [ P(l)n ]V(Formula 8.14)

6. Determination of the average number of serviced calls y

(l)

j (n) i y

(l)

k (n) on thebasis of Formula 8.177. Repetition of steps 36 until a pre-defined occuracyof the iterative process

is achieved:

0nV

y(l1)j (n)y(l)j (n)

y(l)j (n)

0nV

y(l1)k (n)y(l)k (n)

y(l)k (n)

(8.19)

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8. Defining the blocking probabilityEcfor calls of class cand the loss probabilityBifor Erlang calls of classi, Bjfor Engset calls of class j

Ec =

Vn=Vtc+1

[Pn]V Bi = Ei (8.20)

Bj =

Vn=Vtj+1

[Pn]V[Nj yj(n)]j

Vn=0[Pn]V[Nj yj(n)]j

(8.21)

8.4 Model of the Full-Availability Groupwith Traffic Compression

This section presents a model of the full-availability group, carrying a mixture ofdifferent R99 and HSPA traffic classes, which is also known as the model of thefull-availability group with traffic compression. This model is applied in the chapterfor modeling the radio and Iub interfaces, carrying both R99 and HSPA traffic

streams.Let us assume now that a full-availability group services a mixture of different

multirate Erlang traffic streams with the compression property. This means the trafficmixture contains such calls for which a change in demands (requirements) is followeduniformly by overload of the system.

In this group, it is assumed that the system services simultaneously a mixture ofdifferent multirate Erlang traffic classes, while these classes are divided into two sets:classes with calls that can change requirements while being serviced, and classes that

do not change their demands in the service time.This section discusses two models of the systems with traffic compression.The presented models differ in the compression method. In the first model(Section 8.4.1), we assume that all traffic classes undergoing compression are com-pressed to the same degree (evenly). Whereas in the second model (Section 8.4.2), itis assumed that traffic classes with the compression property can be compressed to adifferent degree (unevenly).In all the models considered, the following notation is used:

Mkdenotes a set of classes capable of compression, whileMk = |Mk|is thenumber of compressed traffic classes.

Mnkis a set of classes without compression, and Mnk = |Mnk|denotes thenumber of classes without compression.

Further in the section, for simplicity of the description, we limited the considerations to PCT1traffic classes.

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8.4.1 Basic Model of the Full-Availability Groupwith Compression

Itwasassumedinthemodelthatallclassesundergoingcompressionwerecompressedto the same degree (evenly). The measure of a possible change in requirements isthe maximum compression coefficient, that determines the ratio of the maximumdemands to minimum demands for a given traffic class. The coefficientKmaxcan bedetermined on the basis of the dependence [16]:

jMk Kmax=tj,max

tj,min

, (8.22)

wheretj,maxandtj,mindenote, respectively, the maximum and minimum number ofbasic bandwidth units (BBUs) demanded by a call of class j. We assume the systemwill be treated as a full-availability group with multirate Erlang traffic.

Let us consider a system with maximum compression (i.e., under the assump-tion that the amount of resources required by calls of classes with the compres-sion property is minimum. In the case of a system carrying a mixture of traffic

streams that undergo and do not undergo compression, the occupancy distribution(Equation 8.16) will be more conveniently expressed after dividing the two types oftraffic:

n[Pn]V =Mnki=1

Aiti[Pnti]V +Mk

j=1

Ajtj,min[Pntj,min ]V (8.23)

where tj,minis the minimum number of BBUs demanded in a given occupation state

of the system by a call of class jthat belongs to the set Mk.The blocking and loss coefficient in the full-availability group will be determinedon the basis of Equation 8.16:

Ei = Bi =

Vn=Vti+1

[Pn]V for i Mnk

Vn=Vti,min+1

[Pn]V for i Mk

(8.24)

This assumption simplifies the description of the system to Kaufman-Roberts recursionEquation 8.16. In the case of the service of Erlang as well as Erlang and Engset streams, itis necessary to apply the MIP-BPP method described in Section 8.3.4.

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For Erlang and Engset traffic streams, after the application of the MIM-BPPmethod (Section 8.3.4), the blocking (loss) probability is determined on the basis

of Equation 8.20.In Equations 8.23 and 8.24, the model is characterized by the parameterti,min,

which is the minimum numberofBBUsdemandedbya callofclass iintheconditionsof maximum compression. Such an approach is indispensable in determining theblocking probabilities in the system with compression, since the blocking stateswill occur in the conditions of maximum compression. The maximum compressiondetermines such occupancy states of the system in which a further decrease in thedemands of classicalls is not possible.

In order to determine a possibility of the system compression, it is necessaryto evaluate the number and kind of calls serviced in a given occupancy state ofthe system. For this purpose, we can use Formula 8.15, which makes it possible todetermine the average number of calls of class iserviced in the occupancy state nBBUs. This dependence, under the assumption of the maximum compression, canbe written in the following way:

yi(n) =

AiPntiV[Pn]V for i

Mnk

Ai

Pnti,min

V

[Pn]Vfor i Mk

(8.25)

On the basis of Formula 8.25, knowing the demands of individual calls, we can thusdetermine the total average carried traffic in staten, under the assumption of themaximum compression:

Ymax(n) = Ynk(n)+Ykmax(n)=

Mnki=1

yi(n)ti+Mk

j=1

yj(n)tj,min (8.26)

whereYkmax(n) is the average number of busy BBUs in staten, occupied by calls thatundergo compression, whereasYnk(n) is the average number of busy BBUs in staten, occupied by calls without compression.

Let us assume that the value of the parameterYnk(n) refers to non-compressedtraffic and is independent of the compression of remaining calls. The real values ofcarried traffic, corresponding to staten(determined in the conditions of maximumcompression), will depend on the number of free BBUs in the system. We assumethe real system operates in such a way as to guarantee the maximum use of theresources (i.e., a call of a compressed class always tends to occupy free resources anddecreases its maximum demands to the least extent possible.) Thus, the real traffic

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value Y(n)carriedinthesysteminagivenstate,correspondingtostate n(determinedin maximum compression), can be expressed in the following way:

Y(n) = Ynk(n)+Yk(n)=Mnki=1

yi(n)ti+Mk

j=1

yj(n)tj(n) (8.27)

The parametertj(n) in Formula 8.27 determines the real value of a demand of classjin staten:

jMk tj,min < tj(n)tj,max (8.28)

The measure of the compression degree in state nis the compression coefficientk(n), which can be expressed in the following way:

tj(n)=tj,mink(n) (8.29)

When taking into consideration Equation 8.29, the average number of busyBBUs occupied by calls with compression can be written thus:

Yk(n)=Mk

j=1

yj(n)tj(n) = k(n)Mk

j=1

yj(n)tj,min (8.30)

We assume that in the considered model the system operates in such a waythat it guarantees the maximum use of available resources. This means that callsthat undergo compression will always tend to occupy free resources, decreasingtheir demands to the least possible. Another parameter of the considered system,

besides the blocking (loss) probability, is the average number of busy BBUs in thesystem, occupied by calls with compression (Formula 8.30). The knowledge of thecompression coefficient k(n) is indispensable to determine this parameter. Thiscoefficient can also be defined as the ratio of resources potentially available for theservice of calls with compression to the resources occupied by these calls in the stateof maximum compression. Thus, we can write(Figure 8.4):

k(n) =V Ynk(n)

Ykmax(n) =

V Ynk(n)

nYnk(n) (8.31)

The numerator in the Formula 8.31 expresses the total amount of system resourcesthatcanbeoccupiedbycallsoftheclasswithcompression.Whereasthedenominatorcan be interpreted as the amount of resources that can be occupied by calls of the

Further on in the description, to simplify the description, we will use the term in state n insteadof a given statenin maximum compression.

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tj,min(n)tj(n)

New calls

Capacityo

fthesystem(

V)

Capacityo

fthesystem(

V)

Before compression

Resources

occupied

by remaining calls

Resources

occupied

by remaining calls

Resources

occupied

by calls with

compressionResources

occupied

by calls with

compression

After compression

Figure 8.4 Exemplary system with compression, in which classicalls are maxi-mally compressed.

class with compression, under the assumption that the system (FAG) is in the state

nof busy BBUs. A constraint to the value of the coefficient 8.31 is the maximumcompression coefficient, determined on the basis of the dependence 8.22. Thisconstraint can be taken into account by formally defining the compression coefficientin the following way:

k(n) =

Kmax for k(n) Kmax

k(n) for 1 k(n) < Kmax(8.32)

The compression coefficient determined by Formula 8.32 is not dependent on thetraffic class. This results from the assumption adopted in the model of the samecompression degree for all traffic classes that undergo the mechanism of compression.

Knowing the value of the compression coefficient in every staten, we can deter-mine the average resources occupied by calls of class jwith compression:

Ykj =

Vn=0

yj(n)[k(n)tj,min][Pn]V (8.33)

On the basis of the average resources occupied by calls of class j, we can determinethe average resources occupied by calls of all traffic classes with compression:

Yk =

Mkj=0

Ykj (8.34)

Note that the valueYk in Formula 8.34 is the average traffic carried in the systemby calls that undergo compression.

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8.4.2 Model of the Full-Availability Groupwith Uneven Compression

In the model of the FAG with uneven compression, we assume that the systemwill be treated as a full-availability group with multirate traffic. The occupancydistribution in such a system can be expressed by the recursive KaufmanRobertsformula(Equation8.16),undertheassumptionthattheamountofresourcesrequiredby calls of the classes with the compression property is minimum. The blockingcoefficient in such a system will be determined by the dependence in Equation 8.24.

The basic assumption in this model is that classes undergoing compression can be

compressed to a different degree. The measure of a possible change in requirementsis the maximum compression coefficient Kj,max, which can determine the ratio ofmaximum demands to minimum demands for a given traffic class [18]:

jMk Kj,max=tj,max

tj,min(8.35)

wheretj,maxandtj,mindenote, respectively, the maximum and minimum number ofbasic bandwidth units (BBUs), demanded by a call of class j(cf. Equation 8.22).

Theintroductionofdifferentvaluesofthemaximumcompressioncoefficientalsoresultsinchangesinthedefinitionoftheaveragecompressioncoefficient,determinedby Formula (8.32):

j,k(n) =

Kj,max for k(n) Kj,max

k(n) for 1k(n) < Kj,max(8.36)

where the coefficientk(n) is determined on the basis of Equation 8.31.Knowing the value of the compression coefficient in every staten, we can deter-

mine the average resources occupied by calls of all traffic classes with compression,with the application of Equations 8.33 and 8.34:

Yk =

Mkj=0

Vn=0

yj(n)[j,k(n)tj,min][Pn]V (8.37)

whereyj(n) is determined on the basis of Equation 8.25.

8.5 Modeling and Dimensioning of the Radio Interface

In this section, we will present traffic issues that refer to the UMTS mobile system,which can be analyzed with the application of the models with multirate traffic,presented in Section 8.3.

A single cell of the mobile system can be treated as a full-availability group withhard or soft capacity, depending on a possible influence of the environment upon

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the load of the radio interface. The GSM system is a system with a hard capacityof cells. In this system, the maximum number of subscribers serviced by one cell is

determined unequivocally and depends exclusively on the number of used frequencychannels. The UMTS system is a system with soft capacity. Soft capacity indicatesa possibility of changing the capacity of a cell, depending on external influence, inwhich the element of essential importance is the degree of load in neighboring cells.

8.5.1 Resource Allocation in Mobile Systemswith Soft Capacity

The wideband code division multiple access (WCDMA) radio interface applied inthe UMTS system has a large theoretical flow capacity (throughput) of the separatedinterface. At the same time, the available throughput is limited by the admissiblelevel of the interference volume in the frequency channel. In every cellular systemwith spread signal spectrum, the capacity of the radio interface is constrained as theresult of a few types of interference [19]: co-channel interference within a cellfrom concurrent users of a frequency channel within the area of a given cell; externalco-channel interference within a cellfrom the concurrent users of the frequency

channel, working within the area of adjacent cells; adjacent channels interferencefrom the adjacent frequency channels of the same operator or other cellular telecom-munication operators; and all possible noise and interference from other systems andsources, both broadband and narrowband.

Summing up, in the WCDMA radio interface, a growth in load is accompaniedby a simultaneous growth in interference, generated by other users serviced by thesame cell or other cells. To secure an appropriate level of service, it is necessary tolimit the number of allocated resources by active traffic sources. It is estimated thatthe maximum usage of the radio interface resources without lowering the qualityof service will be equal to about 50% to 80% [19]. For the same reason, the softcapacity of the WCDMA radio interface is defined as the noise limited capacity(noise limited).

Multirate traffic in the UMTS system is composed of a few classes, and each ofthem demands a certain bit rate to service its own call. In the probabilistic analysisof radio systems that are offered multirate traffic streams, it is necessary to take intoconsideration the class of call and the bit rate demanded by a call of this class. TheUMTS systemin respect to the flow capacities of services carried outcan be then

considered a discrete multiservice switching network. In the following analysis of theradio interface, we will use the universally accepted notion of BBU, which will bedefined in Section 8.5.2.

Accurate signal reception in the receiver of the UMTS system is possible onlywhen the ratio of energy per bit Ebto noise spectral densityN0is appropriate. A toolow value ofEb/N0will cause the receiver to be unable to decode the received signal,while a too high value of the energy per bit in relation to noise spectral density willbe perceived by other users of the same radio channel as interference.

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The ratioEb/N0for a given traffic source of class ican be written as the followingdependence [17]:

Eb

N0

i

=W

iRi

Pi

Itotal Pi(8.38)

In Formula 8.38, the following notation is adopted: Pi, average signal powerreceived from the traffic source of classi; Itotal, total power of the received signal inthe base station, with thermal noise taken into consideration;W,flowcapacityofthespread signal (the so-called chip rate) (in the UMTS system it is conventionally 3.84Mchip/s i.e., the speed at the input signal is spread (data signal or speech signal); Ri,throughput of the data signal from the traffic source of classi; i, activity coefficientof the traffic source of class i, which denotes the percentage of occupancy time ofthe transmission channel in which the source is active (i.e., transmits a signal withthe flow capacityRi).

Formula 8.38 can be converted in such a way as to get the average power of thereceived signal from the traffic source of class i:

Pi =Itotal

1+ WEbN0

i

Rii

= LiItotal (8.39)

whereLiis the load factor, imposed by a class icall:

Li =1

1+ W EbN0

i

Rii

(8.40)

Sample loads of the WCDMA radio interface by calls of different classes are shown

in Table 8.2 [20].The method for dimensioning the WCDMA interface proposed in [7] can be

extended for the HSPA traffic. It should be noticed, however, that in the HSUPAtechnology, changes ensue at the required Eb/N0level in relation to R99, which islinked to the applied solutions. In HSUPA, the following factors will be conduciveto Eb/N0:

Outer loop power control target block terror (BLER). Transmit time interval (TTI)

: Transmit time of each block of data inHSUPA. Transport block size (TBS): The number of bits transmitted in each

transport block. The number of HARQ transmissions.

In the modeling proccess, we assumed that the load factor for the HSPA trafficbased on [21]can be determined by a simulation procedure. Sample values of loadfactors for an exemplary HSUPA traffic stream (service) are shown in Table 8.3 [21].

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Table 8.2 Sample WCDMA Radio Interface Loads by Calls of DifferentClasses

Service

Parameters Speech (Voice) Video Data Data

W (Mchip/s) 3,84

Ri (kbps) 12,2 64 144 384

i 0,67 1 1 1

Eb/N0(dB) 4 2 1,5 1

L i 0,005 0,026 0,050 0,112

Source: With kind permission from Springer Science+Business Media:Stasiak, M., Wi sniewski, A., Zwierzykowski, P., Blocking probabil-ity calculation in the uplink direction for cellular systems withWCDMA radio interface, In 3rd Polish-German Teletraffic Sympo-sium, pp. 6574, Dresden, 2004. 2004 IEEE.

8.5.1.1 Uplink

Let us remark that the load coefficient is non-dimensional and defines the fractionof a possible interface load. The coefficient also shows the nonlinear dependencebetween the percentage load of the interface and the throughput of the traffic sourceof a given class. On the basis of the known load coefficients of single traffic sources,

Table 8.3 Sample HSPA Radio Interface Loads by Calls of DifferentClasses

Service

Parameters Service 1 Service 2 Service 3

W (Mchip/s) 3,84

Ri (kbps) 54,72 800,12 82,1

i 1 1 1

Eb/N0(dB) 4,84 4,55 3,74

L i 0,041624641 0,372667591 0,0481371632

Source: From Engineering Services Group, Aspects of HSUPA Network Plan-ning, Qualcomm Incorporated, Technical Report, No. 80-W1159-1,Revision B, San Diego, 2007.

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it is possible to determine the total loadU Lfor the uplink:

UL =M

i=1

NiLi (8.41)

where Ni is the number of serviced traffic sources of class i in the uplink underconsideration.

Dependence 8.41 determines the ideal maximum interface load in a system ofone isolated cell. In real circumstances, however, the traffic generated in other cells,which also influences the capacity of the radio interface of a given cell, has to be

taken into consideration. Hence, Formula 8.41 is complemented with a coefficientthat takes into account interference from other cells. To achieve that, a parameter, defined as the ratio of the interference from other cells to the interference of themeasured cell, is introduced. This coefficient, in the case of the uplink, is determinedin the receiver of the base station [19]. The total load for the uplink can thus takeon the following form [17]:

UL=(1+ )

Mi=1

NiLi (8.42)

Itisgenerallyassumedthatthemaximumusageoftheresourcesoftheradiointerface,without lowering the quality of service, amounts to 50% to 80% of its theoreticalcapacity [17].

It should be emphasized that the influence of inter-cellular interference can alsobe taken into consideration by applying the so-called fixed-point methodology [1,7].

8.5.1.2 Downlink

The total load for the downlink can be written in the following way [17]:

DL =

Mi=1

NiLi(1 i+ i) (8.43)

whereiis the orthogonality factor for the class itraffic. It indicates the degree of

interference reduction between the users of the same cell through the applicationof channel codes based on the OVSF (orthogonal variable spreading factor). Thismeans they can have different dispersion coefficients and their mutual correlation is(theoretically) equal to zero [22]. Usually, coefficient valuesiand iare similar [17],so the influence of the interference upon the decrease in loadability of the downlinkcan be omitted.

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8.5.2 Allocation Units in the WCDMA Radio Interface

In systems with soft capacity, the available capacity of a system can vary and can bedifferent from the theoretical maximum capacitywhere the capacity of the idealisolatedcell,notexposedtoexternalinfluences,canberegardedasthemeasureunitto a certain minimum capacity, when the influence of the load of the neighboringcells is at its maximum. In the system under consideration, the use of bit rates asthe measure for allocation is not very convenient. It is much more convenient tomeasure the state of allocated resources more appropriately in other units, reflectingthephysicalnatureofagivensystem.Formulae8.42and8.43clearlyindicatethatthemeasure of resource allocation in the WCDMA radio interface can be the percentageof noise load of the interface. Therefore, in the radio interface: allocation is not basedon adding bit rates but on adding noise loads.

A single interface load imposed by a traffic source can be applied as the allocationunit. The way of changing resource allocation, expressed in kbps, into the resourceallocation, expressed in the percentage of the load of the radio interface, is shown inFigure 8.5 [18].

In the UMTS system, servicing many traffic classes with different flow capacitiesand treated as a multirate system, it is assumed that the value of a BBU should

be lower or equal to the greatest common divisor of the resources demanded byindividual call streams [23,24]. For the WCDMA radio interface, we can write:

LBBU =GCD(L1,L2, . . .,LM) (8.44)

Then, the interface capacity can be expressed by the number of the defined BBUsin Equation 8.44:

V = U L/DL/LBBU (8.45)

x[kbps]

Available throughput Interface load in %

y[%]Rj Lj

%100

Figure 8.5 Resource allocation in the WCDMA radio interface. (From Stasiak,M. and Zwierzykowski, P., Modelling full availability groups with adaptive-rate.Internal report 9/2008, Poznan University of Technology, September 2008.)

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whereU L/DLis the radio interface capacity for the uplink or the downlink. In asimilar way we can express the number of BBUs required by a call of a given class:

ti = Li/LBBU (8.46)

In the considerations presented in this section, we have assumed, for simplicity,thattheinfluenceofinterferenceontheflowcapacityoftheWCDMAradiointerfacecan be determined by the parametersandi[19].

8.5.3 Analytical Model of the WCDMA InterfaceIn this section, we will analyze four GoS parameters, important for the dimension-ing and optimization process of the WCDMA interface, carrying R99 and HSPAtraffic: blocking probability, loss probability, average throughput, and availablethroughput.

TheWCDMAinterfaceinaUMTSnetworkcanbetreatedasthefull-availabilitygroup (FAG) with multirate traffic. In the model, we assume that the radio interfacecarries both R9 and HSPA traffic streams. We also assume that there are traffic

classes belonging to the HSPA traffic that calls that can change occupied resourcesin the service time. Therefore, it is assumed that the system services simultaneously amixture of different multirate traffic classes, while these classes are divided into twosets: Mkclasses with calls that can change requirements while being serviced, andMnkclasses that do not change their demands in the service time. Let us assume thatthetotalcapacityofthegroupisequalto Vbasic bandwidth units (BBUs). The groupis offeredM independent classes of Poisson traffic streams, having the intensities:1,2, . . .,M.Theclass icall requires tiBBUs to set up a connection. The holding

time for calls of particular classes has an exponential distribution with the parameters:1,2, . . ., M. Thus, the mean traffic offered to the system by the classitrafficstream is equal to:

Ai =i

i(8.47)

The resources demanded in the group for servicing particular classes can be treatedas a call demanding an integer number of BBUs. The value of BBU (i.e., tBBU)

is calculated as the greatest common divisor (GCD) of all resources demanded bytraffic classes offered to the system (Equation 8.44):

LBBU =GCD(L1, . . .,LM) (8.48)

M= Mk+Mnk, where Mk = |Mk|and Mnk = |Mnk| In the analytical model, for simplicity, we assume that the system carries only Erlang traffic

streams. In the case of Erlang and Engset traffic streams, we can use the MIM-BPP algorithm.

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where Li is the load factor for a user of the class i call (Table 8.2), defined inEquation 8.40.

The multidimensional Markov process in the FAG can be approximated bythe one-dimensional Markov chain, which can be described by Kaufman-Robertsrecursion (Equation 8.15):

n[Pn]V =Mnki=1

Aiti[Pnti]V +Mk

j=1


where [Pn]Vis the probability state ofnBBUs being busy, andtiandtj,minare thenumbers of BBUs required by classes not undergoing and undergoing compression,respectively (Equation 8.46):

ti =

Li

LBBU

tj,min =

Lj,min

LBBU

(8.50)

The interface capacityVis defined as follows [25]:

V=

DL

1+ i for downlink directionUL

1+for uplink direction

(8.51)

where DL and U Lare the physical capacities of the WCDMA interface in thedownlink and in the uplink direction, respectively [7].

8.5.3.1 Blocking (and Loss) Probability

The blocking probabilityBifor the classiof Erlang traffic streams can be expressedin the following form (Equation 8.24):

Ei = Bi =

Vn=Vti+1

[Pn]V for i Mnk

V

n=Vti,min +1

[Pn]V for i Mk

(8.52)

The loss and blocking probabilities for Erlang traffic streams are determined byidentical formulas 8.20.

8.5.3.2 Average Throughput

The radio interface carries both Release 99 and HSPA traffic streams. The classesbelonging to R99 do not undergo compression. Therefore, the determination of

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the average throughput is important only for those traffic classes of the HSPA traf-fic that can undergo compression. Moreover, the application of a given analytical

model depends on the mechanisms applied in the solutions used by the equipmentmanufacturers and providers of UMTS networks. Therefore, in this chapter we willdiscuss potential applications of models with compression to determine the averagethroughput separately for the uplink and for the downlink.

8.5.3.3 Downlink Direction

Let us consider a scenario in which the average bandwidth is allocated to all sub-scribers equally. Let us further assume that the subscribers have different classes ofterminals at their disposal. This means the average throughput offered to a givensubscriber depends mainly on the network load, while, with a small network load, theclass of users terminals is also a constraint. Assume that the subscribers with newermobile user terminals can achieve higher maximum throughput. Such a scenariocan be considered for use to describe the system, which can be modeled with evencompression, presented in Section 8.4.1.

The first step to determine the average throughput is to determine the com-pression coefficient k(n). The coefficient, on the basis of the dependence in

Equations 8.31 and 8.32, takes on the following form:

k(n) =

Kmax for V Ynk(n)

nYnk(n) Kmax

V Ynk(n)

nYnk(n) for 1

V Ynk(n)

nYnk(n) < Kmax

(8.53)

where theYnk

(n) parameter is expressed by Equation 8.27 andYk

(n) can be deter-mined based on Equation 8.30.In the next step, we can obtain the average resources occupied by calls of class j

(average throughput) on the basis of the following Equation 8.33:

Ykj =

Vn=0

yj(n)[k(n)tj,min][Pn]V (8.54)

8.5.3.4 Uplink Direction

Let us consider now a scenario in which the average bandwidth is allocated unevenlyand a decrease in the throughput offered to a given subscriber depends on the currentnetwork load and on the kind of subscriptions assigned to them. Assume that thethroughput will be decreased first to the group of users that generate the least profitfor the operator. Therefore, the order in which the throughput will be decreased isdirectly dependable on the amount of the subscription fee. Additionally, the upper

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limit will also be the class of terminal operated by the user. This scenario is matchedby the model of the system with uneven compression, described in Section 8.4.2.

The determination of the average throughput will be initiated, as earlier, bydetermining the compression coefficient k,j(n). Thus, based on Equations 8.31and 8.36, we obtain:

k,j(n)=

Kj,max for V Ynk(n)

nYnk(n) Kj,max

V Ynk(n)

nYnk(n) for 1

V Ynk(n)

nYnk(n)

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HSDPA calls is equal to:

Tx =V

n=0

V

Mnki=1

yi(n)ti

[Pn]V (8.59)

8.5.3.6 Summary

The models presented in this section can be used for the analysis and dimensioningof the WCDMA interface that services a mixture of different R99 iHSPA traffic

classes, both in the uplink and the downlink directions. The proposed models enableus to determine four different GoS parameters, to which different priorities can beassigned, depending on the preferred optimization and development policy of theUMTS network operator. Therefore, the interface dimensioning process calculationsof the quality parameters are to be repeated iteratively, each time with an increase inthe interface capacityand checking if the GoS parameters, significant for the operator,arecorrect.Thedimensioningprocessisterminatedwhentheserequirementsaremet.

Trying to maximize the simplicity of the described analytical models, we assume

that the WCDMA radio interface services traffic generated by an infinite number ofusers (Erlang traffic). When the radio interface services a number of users of a givenclass that is lower or only slightly higher than the interface capacity, the proposedmodels should also include Engset traffic. The method for determining the charac-teristics of the system with Erlang and Engset traffic is presented in Section 8.3.4.

The proposed analytical methods are based on the well-known and verifiedKaufman-Roberts distribution. The calculations made with the formulas presentedin the method are not complicated or complex; this is, undoubtedly, an advantagefrom the network designers point of view.

8.6 Dimensioning of the Iub Interfacewith HSPA Traffic

8.6.1 Exemplary Architecture of the Iub Interface

Having in mind the duration time of network expansion and the huge costs involved,as well as possible savings in expenditures, the operators of cellular networks are in-

clined to implement technological solutions that optimize investments but still retainthe complex quality of service. One such solution, frequently used in real networks, isthe separation of links on the Iub interface. The operator is in a position to configuretwovirtualpaths(VPs)ofATM(asynchronustransfermode)systemontheIubinter-face and assign them respectively to real-time traffic and best-effort traffic. Assumingthat the best effort VC (virtual channel) will not allocate the maximum demandedbandwidth in the same time, the total bandwidth can be co-shared among the VCs,which results in its better utilization. This method should thus be recommended

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RNC

Real time VP

Best effort VP

2 Mbps

2 Mbps PS interactivebackground

(HSDPA user data)

CS: Conversational

CS: Streaming

PS: Streaming

PS: Conversational

PS: Interactive/Background

2 Mbps

2 Mbps

2 Mbps

2 Mbps

2 Mbps

lub interface

IMA

IMA

Node B

Figure 8.6 One of the most common ways of carrying out a connection betweenthe UMTS base station and radio network controller with the application of IMAtechnology. (With kind permission from Springer Science+Business Media: Stasiak,

M., Zwierzykowski, P., Wiewiora, J., and Parniewicz, D., European PerformanceEngineering Workshop, volume 5652 of LNCS, Analytical Model of Traffic Com-pression in the UMTS network, pp. 7993. Springer, London, July 2009.)

even for distinguishing parameters needed for the designing/dimensioning of net-works with different QoS requirements for different clients. Obviously, in the caseof bandwidth overload, part of the ATM cells will be lost. An example of physicalrealization of a solution of this type on the Iub interface, with the application of IMA

(inverse multiplexing for ATM) [26], is shown in Figure 8.6 [16]. The applicationof IMA makes it possible to create two logical ATM paths on the basis of separatephysical links. Table 8.4 shows an example of UMTS packet switched (PS) and cir-cuit switched (CS) services, carried out by logical ATM paths dedicated to servicingbest-effort traffic and real-time traffic, respectively, and corresponding to Figure 8.6.

Additionally, it should be mentioned that this solution paves the way for furtheroptimization of capacity since with the application of traffic concentration devicesbetween NodeB and RNC, the paths of the real-time type will be carried by the

concentration device in the capacity ratio 1:1, while the paths of the best-efforttype can be carried, for example, in the ratio 2:1 (a two-fold higher capacity at theinput of the concentration device than at the output). Using the properties of offeredtraffic (e.g., different busy hours), we can get further savings, at least by means ofdeveloping or expanding RNC that has a limited number of input ports. A very goodtechnology that ensures successful realization of the task, simultaneously facilitating

Figure 8.6 assumes that the links constituting IMA have throughput of 2 Mbps

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Table 8.4 An Example of Service Class Mapping into ATM Classes

ATM Class of Service UMTS Class of Service Exemplary ServiceBest-effort VP Interactive background Web browsing

(HSDPA user data)

Real-time VP CS: Conversational Voice

Real-time VP CS: Streaming Modem connection

Real-time VP PS: Interactive/background FTP, realtime gaming

Real-time VP PS: Conversational Speech (VoIP)

Real-time VP PS: Streaming Mobile TV

the construction of the Iub interface, is LMDS (local multipoint distribution ser-vice) [27].

Regrettably, this rapid pace in the development of relevant technologies is notappropriately matched by mathematical models that could enable us to plan anddimension networks in accordance with required service predictions.

8.6.2 Analytical Model of the Iub Interface

The Iub interface in a UMTS network can be treated as the full-availability group(FAG) with multirate traffic. In the model, we assume, similar to the WCDMAinterface, that the Iub interface carries both R9 and HSPA traffic streams. We alsoassumetherearetrafficclassesbelongingtotheHSPAtrafficwithcallsthatcanchangeoccupied resources in the service time. Therefore, it is assumed that the systemservices

simultaneously a mixture of different multirate traffic classes, while these classes aredivided into two sets: Mkclasses whose calls can change requirements while beingserviced, and Mnkclasses that do not change their demands in the service time. Letus assume that the total capacity of the group is equal toVbasic bandwidth units(BBUs). The group is offered M independent classes of Poisson traffic streams,

having the intensities: 1,2, . . .,M. The classicall requirestiBBUs to set upa connection. The holding time for calls of particular classes has an exponentialdistribution with the parameters: 1,2, . . .,M. Thus, the mean traffic offered

to the system by the classitraffic stream is equal to:

Ai =i

i(8.60)

M= Mk+Mnk, whereMk = |Mk|and Mnk = |Mnk| In the analytical model, for simplicity, we assume the system carries only Erlang traffic streams.

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The resources demanded in the group for servicing particular classes can be treatedas a call demanding an integer number of BBUs. The value of BBU (i.e., RB BU, is

calculated as the greatest common divisor (GCD) of all resources demanded by thetraffic classes offered to the system (Equation 8.44):

RBBU =GCD( R1, . . ., RM) (8.61)

whereRiis the amount of the resources demanded by the class icall inkbps.The multidimensional Markov process in the FAG can be approximated by

the one-dimensional Markov chain, which can be described by Kaufman-Robertsrecursion (Equation 8.15):

n[Pn]V =Mnki=1

Aiti[Pnti]V +Mk

j=1


where [Pn]V is the probability state ofnBBUs being busy, and ti and tj,min arethe number of BBUs required by a class that is not undergoing, and a class that isundergoing, compression, respectively (Equation 8.46):

ti =

Ri

RBBU

tj,min =

Rj,min

RBBU

(8.63)

where Rj,min is the minimum amount of resources demanded by class j trafficundergoing compression, in kbps. In Equation 8.62, the interface capacity V isdefined as follows:

V = Vphy/RBBU (8.64)

whereVphyis the physical capacity of the group in kbps.In this section, we will also analyze four GoS parameters: blocking probability,

loss probability, average throughput, and available throughput.

8.6.2.1 Blocking (and Loss) Probability

On the basis of Formula 8.62, the blocking probability Bi for the class iErlangtraffic stream can be expressed in the following form [Equation 8.24]:

Ei = Bi =

Vn=Vti+1

[Pn]V for i Mnk

Vn=Vti,min +1

[Pn]V for i Mk

(8.65)

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8.6.2.2 Average Throughput

Determination of the average throughput is only important for those traffic classesof the HSDPA traffic that can undergo compression. The application of a givenanalytical model depends on particular mechanisms used in the solutions providedby manufacturers of equipment for the UMTS network. Let us consider a scenario inwhich the average bandwidth is assigned to all users unevenly. Let us further assumethat the subscribers in this network have terminals of different classes, while thosesubscribers that have newer terminals are capable of achieving higher maximumthroughput. This scenario can be further considered with the application of themodel with uneven compression, presented in Section 8.4.2.

In the first stage of the determination of average throughput we determine thecompression coefficient k(n). The coefficient, following the dependencies Equa-tions 8.31 and 8.36, takes on the following form:

k,j(n) =

Kj,max for V Ynk(n)

nYnk(n) Kj,max

V Ynk(n)

nYnk(n) for 1

V Ynk(n)

nYnk(n) < Kj,max

(8.66)

where theYnk(n) parameter is expressed in the following way (Equation 8.27):

Ynk(n)=Mnki=1

yi(n)ti (8.67)

andYk(n) can be determined based on Equation 8.30:

Yk(n)=k(n)Mk

j=1

yj(n)tj,min (8.68)

In Equations 8.67 and 8.68, the average number of calls of class i, serviced in theoccupancy statenBBUs [yj(n)], can be determined as follows (Equation 8.25):

yi(n)=

Ai

Pnti

V

[Pn]Vfor i Mnk

Ai

Pnti,min

V

[Pn]Vfor i Mk

(8.69)

HSPA traffic is limited only to the downlink direction, because in the uplink direction HSPAtraffic is services-based on R99 resources [12].

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In the next step, we can obtain the average resources occupied by calls of class j(average throughput) on the basis of the following formula (Equation 8.33):

Ykj =

Vn=0

yj(n)[k,j(n)tj,min][Pn]V (8.70)

8.6.2.3 Average Throughput Available for HSDPA Users

The average capacity of the Iub interface available to the HSDPA traffic can be

determined in a similar way as the available throughput of the WCDMA interfacepresented in Section 8.5.3.5.

8.7 Conclusion

This chapter presents analytical methods that allow us to determine such a capacityof individual elements of the UMTS system that will guaranteewith the assumedload of the systema pre-defined level of GoS. The most characteristic constraints inthe dimensioning of the UMTS system are the radio interface and the Iub interface.The chapter describes the application of the analytical models to these interfaces. Inthe models, it was assumed that the system carried a mixture of different R99 andHSPA traffic classes.

References

[1] M. Glabowski, M. Stasiak, A. Wisniewski, and P. Zwierzykowski.Performance Modellingand Analysis of Heterogeneous Networks,chapterUplinkBlockingProbabilityCalculationforCellular Systems with WCDMA Radio Interface and Finite Source Population, pp. 301318. Information Science and Technology. River Publishers, 2009.

[2] Y. Ishikawa, S. Onoe, K. Fukawa, and H. Suzuki. Blocking Probability Calculation UsingTraffic Equivalent Distributions in sir-based Power Controlled w-cdma Cellular Systems.IEICE Transactions on Communications, E88-B(1):312324, 2005.

[3] V. B. Iversen and E. Epifania. Teletraffic Engineering of Multi-band W-CDMA Systems.InNetwork Control and Engineering for QoS, Security and Mobility II, pp. 90103, Norwell,MA, 2003. Kluwer Academic Publishers.

[4] I. Koo and K. Kim. Erlang Capacity of Multi-service Multi-access Systems with a LimitedNumber of Channel Elements According to Separate and Common Operations.IEICETransactions on Communications, E89-B(11):30653074, 2006.

[5] D. Staehle and A. Mader. An Analytic Approximation of the Uplink Capacity in a UMTSNetwork with Heterogeneous Traffic. 18th International Teletraffic Congress, pp. 8191,Berlin, 2003.

[6] M. Stasiak, J. Wiewira, and P. Zwierzykowski. Analytical Modelling of the Iub Inter-face in the UMTS Network. Proceedings of the 6th Symposium on Communication Systems,Networks, and Digital Signal Processing, Graz, Austria, July 2008.

8/14/2019 9781439806500-12

34/34


[7] M. Stasiak, A. Wisniewski, P. Zwierzykowski, and M. Glabowski. Blocking Probabil-ity Calculation for Cellular Systems with WCDMA Radio Interface Servicing PCT1 and

PCT2 Multirate Traffic.IEICE Transactions on Communications, E92-B(4):11561165,April 2009.

[8] H. Akimuru and K. Kawashima. Teletraffic: Theory and Application. Berlin-Heidelberg-NewYork, 1999.

[9] J. S. Kaufman. Blocking in a Shared Resource Environment.IEEE Transactions on Com-munications, 29(10):14741481, 1981.

[10] J. W. Roberts. A Service System with Heterogeneous User Requirements Applicationto Multi-service Telecommunications Systems. In G. Pujolle, editor,Proceedings of Perfor-mance of Data Communications Systems and Their Applications, pp. 423431, Amsterdam,1981.

[11] M. Glabowski. Modelling of State-Dependent Multirate Systems Carrying BPP Traffic.Annals of Telecommunications, 63(7-8):393407, August 2008.

[12] H. Holma and A. Toskala.HSDPA/HSUPA for UMTS: High Speed Radio Access for MobileCommunications. John Wiley and Sons, 2006.

[13] F.P. Kelly. Loss Networks.The Annals of Applied Probability, 1(3):319378, 1991.[14] I. D. Moscholios, M. D. Logothetis, andG. K. Kokkinakis.Connection-dependentThresh-

old Model: A Generalization of the Erlang Multiple Rate Loss Model.Performance Evalua-tion48:177200, May 2002.

[15] S. Racz, B. P. Gero, and G. Fodor. Flow Level Performance Analysis of a Multi-service

System Supporting Elastic and Adaptive Services.Performance Evaluation, 49(1-4):451469, 2002.

[16] M. Stasiak, P. Zwierzykowski, J. Wiewiora, and D. Parniewicz.European Performance En-gineering Workshop, vol. 5652 of LNCS, chapter Analytical Model of Traffic Compressionin the UMTS Network, pp. 7993. Springer, London, July 2009.

[17] J. Laiho, A. Wacker, and T. Novosad. Radio Network Planning and Optimization for UMTS.John Wiley and Sons, Ltd., 2006.

[18] M. Stasiak and P. Zwierzykowski. Modelling FullAvailability Groups withAdaptive-Rate.Internal report 9/2008, Poznan University of Technology, September 2008.

[19] H. Holma and A. Toskala.WCDMA for UMTS. Radio Access for Third Generation MobileCommunications. John Wiley and Sons, 2000.[20] M. Stasiak, A. Wisniewski, and P. Zwierzykowski. Blocking Probability Calculation in

the Uplink Direction for Cellular Systems with WCDMA Radio Interface, In 3rd Polish-German Teletraffic Symposium, pp.6574, Dresden, 2004.

[21] Engineering Services Group,Aspects of HSUPA Network Planning, Qualcomm Incorporated,Technical Report, No. 80-W1159-1, Revision B, San Diego, 2007.

[22] S. Faruque.Cellular Mobile Systems Engineering. Artech House, London, 1997.[23] J. W. Roberts, ed.Performance Evaluation and Design of Multiservice Networks, Final Report

COST 224. Commission of the European Communities, Brussels, 1992.

[24] J. W. Roberts, V. Mocci, and I. Virtamo, ed.Broadband Network Teletraffic, Final Reportof Action COST 242, Springer, Berlin, 1996.

[25] M. Stasiak, P. Zwierzykowski, J. Wiewiora, and D. Parniewicz. European PerformanceEngineering Workshop, vol. 5261 of LNCS, chapter An Approximate Model of the

WCDMA Interface Servicing a Mixture of Multirate Traffic Streams with Priorities,pp. 168180. Springer, Palma de Mallorca, September 2008.

[26] J B i P M h d S C C T h l i f 3G N k IP UMTS

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