Analysis and simulation of Optical Networks Xin Liu.

Analysis and simulation of Optical Networks

Xin Liu

Outline• Analytic Approach

Probability: Expectation values, Variance

Network Global Expectation Model

Stochastic Process: Markov chain

Packet Delay in OCS networks

• Simulation

Discrete Event Simulation Model

OCS and OBS extension on NS

Analytic Approach

• Methods: formal derivation, considered approximation,semi-empirical observation.

• Intent:To formulate analytic or closed form;To complement, not supplant more accurate, but computationally intensive tools based on numerical simulation.

Simulation

• Methods:

To implement discrete event simulation model using generic languages;

To extend known simulation platform.

• Intent:

To be close to the real network.

Network Global Expectation Model

• Key idea: Use expectation values to describe required quantities of key network and network element resources.

• Significance: Provide approximate results for the preliminary evaluation and design of dynamic networks.

• Assumption: single-tier backbone networks, location-independent traffic demands.

Network Global Expectation Model

the total network cost

the number of network elements of type i

the unit cost of network element of type i.

T ii

C c

TC

iv

ic

T i ii

C v c Challenge: iv

Network Global Expectation Model

• Expectation value

• Example: L is the number of links and N is the number of nodes.

1

1 m

ii

q qm

T l nC L c N c

Primary Model Variables (Input)

• Network graph

adjacent matrix

• Network traffic

T : the total ingress/egress traffic

D : the number of demands

: demand matrix

( , )G L N

[ ]ijg

[ ]ijd

Primary Model Variables

• Specify the difference between one-way and two-way links

2 1

2 1

2 1

Links: 2

Total Traffic: 2

Total Demands: 2

L L L

T T T

D D D

Output

• Number of Demands

• Traffic Demand Bit-Rate

• Degree of Node

1,

N

ij ni j

D d N d

1 2

1 2

T T

D D

1L

N

Output

• Number of Hops

well known a demand model 1[ ] [ ]

D

ij ij iji j

g h h hD

Number of Hops

1 nodes

N

2

1

Nh

4

Divide the network into 4 sectors centered on the selected node

square root relation

Number of Hops

0-hop 1-hop 2-hops D=3-hops

1

The Moore bound results from the construction of a tree whose root is the parent of vertices and each subsequent vertex is itself the parent ofvertices.

max

max 1 1

Logarithmic relation

Number of Hops

1 maxmax max max

max1

( 1) 11 ( 1) 1

2

D Dh

h

n

max

maxmin

max

2ln 1 ( 1)

ln( 1)

n

D

2ln 1 ( 1)

ln( 1)

nh

Output• Demands on Link

• Restoration Capacity

11

Do

iji j

D h d hW h

L L

(1 )k oW W k

a bk

b

Inverse dependency upon the degree of the nodes

Output

• Traffic on Link

• Number of Ports

D TW h h

L L

ADD DROP THRUP P P P

Number of ports

Drop+Thru Add+Thru

Add Drop d d

ADD DROPP P d

( 1)THRUP d h

Packet Delay in OCS Networks

• The paper first presents the queue length distribution and the packet delay distribution in a single logical buffer of the edge router, and then extends that discussion to a network of edge routers.

• To ensure computational tractability, the framework approximates the evolution of each buffer independently.

Model Formulation

• A circuit is a unidirectional lightpath connecting a pair of source-destination edge routers capable of transmitting C b/s uninterruptedly for a period of T seconds.

• Circuits are allocated to the logical buffers using a policy R based on the queue lengths at all logical buffers.

Model Formulation

• Consider J data streams, each associated with a source-destination pair of edge routers, Qos class, a route and wavelength assignment sequence from the source to the destination, and other external classifications.

• So there are J logical buffers.

Model Formulation

• Normalized lightpath arrival rates

• Normalized lightpath transmission rates K

• Circuit switching decision epoch n

{ ,1 }jA j J

Model Formulation• The queue length in logical buffer j at epoch n

• The system state at epoch n

• A binary vector indicating which of the logical buffers are allocated circuits at state

( )jX n

1 2( ) ( ( ), ( ), , ( ))Jn X n X n X nX

1 2( ) ( ( ), ( ), , ( ))R R R RJx x x x δ

( )nX

Mathematical Model

• The process is a Markov chain.

• But each is not a Markov chain.

• Let be the probability that algorithm R allocates a circuit to buffer j with length i at epoch n.

( ( ), 0)n n X

( )jX n

( 1) [ ( ) ( ( )) ]Rj j j jX n X n A n K X

( , )j i n

[ ] , with probability ( , );( 1)

, with probability 1 ( , );

j jj

j j

i A K i nX n

i A i n

Simulation

• Discrete Event Simulation Model.

• OCS and OBS extension on NS.

Discrete Event Simulation Model

N

INIT（）Initialize System1. simulation timer2. system status3. event list4. performance statistics

TIMING（）Timing control1. Schedule events accordingto the event list, return thenext event to happen2. Modify timer

EVENT（）Handle differentevents from TIMING()1. Modify system status2. Modify performance statistics3. Get the time of the nextevent and add it into event list

Simulation Over

Y

1. Obtain performance statistics2. Print results

Event handling• Accept

Execute RWA for connection requests;Modify the number of arriving requests, the number of successfully established working path;Modify the information of network resource. Create the next event according to assumed distribution and append it into event list.

• Service OverRelease the resource of working channel which is not alive.

Basic Modules• Phy-Topo : Generate physical topology, such as TORUS, NSFNet.• Routing : Implement known routing algorithms, such as Dijkstra’s

Algorithm, Floyd-based SPF, K-Shortest-With-Loop-Path.• Graph Theory Algorithm : provide basic graph theory algorithms,

such as MaxFlow, MinCost-Flow.• Survival : provides protection and restoration schemes.• Resource : 　 Different policies, such as routing, wavelength

assignment, control management, survivability schemes, will lead to different efficiency in resource usage.

• Wave-Assign : Combined with routing Module, it completes the RWA function in WDM networks.

• V-Topo : This module controls the virtual topology in IP layer. • Traffic : It contains Poisson, Gaussian, Self-Similar traffic module. It

is used to generate the random sequence of connection requests.• Pseudo-Random Number : Generate random number in (0, 1)

uniformly.• DES : discrete event simulation module. • Performance Metrics Statistic : In each DES process, track

interested statistics variables. After simulation is over, prints out the values of performance metrics.

Basic Modules

Wave-AssignVirtual

TopologyGraph Theory

Traffic Arrive Routing

Pseudo-RandomNumber

Link-Failure-Occur

PhysicalTopology

TimingLink-Failure-

OverSurvival

PerformanceMetricsStatistic

Server Over Resource

OBS extension on NS• OBS-ns (UMBC)

Use centralized structure to assign resource;

Add new classes for new types;

Ignore the architecture of NS.

• OBS-extension

Keep to the distributed architecture of NS;

Add new component in existing composite classes for new features.

OBS-extension Task

• WDM link extension

No multi-channel link model in NS;

To add a multi-server queue in normal link model.

• Assembly Module in Ingress Nodes of OBS Networks

• Signaling, Qos and contention resolution

Normal Link Model

enqT_ revT_ttlT_linkT_queueT_ deqT_

drophead_ drpT_

Link

head_

head_ The entry of a link

queue_ The queue reference of a link

link_ The reference of a link with delay and bandwidth property

ttl_ The reference of TTL management

drophead_ The reference of the head of the drop queue

WDM link extension

WvAssign

queueT_

Wavelength classifier

WvAssign : Queue

WaveClassifier : Classifier

Wavelength ClassifierReceive packet

Process packet head

Get Wavelengthnumber

Support Wavelengthconversion

Execute WAalgorithm

Y

N

Wavelength available

Any port available

Modify packet headreturn wavelength

number

return wavelengthnumber

Y

return -1

return -1

N

N

Y

WDM link extension

enqT_ revT_ttlT_linkT_deqT_

drophead_ drpT_

Link

head_

WvAssign

queueT_

#Create WDM link $ns duplex-link $n3 $n4 1Mb 20ms WvAssign 4 FirstFit 1

OBS extension

• Redirector

Redirecting table and redirecting buffer. Similar to route table and cache in traditional router.

• Assembly Agent

Set assembly scheme, parameters and signaling .

OBS extension

UDP

CBR

IP router

Ingress

Assembly

core

NULL

egress

Disssembly

Packet flow

Burst flow

WDM

OBS

Assembly agent

Addressclassifier

Portclassifier

Assembly

Redirector

Packet flow

Burst flow

WDM link WDM link

OBS ingress node

Test

Reference• Steven K. Korotky, “Network Global Expectation

Model: A Statistical Formalism for Quickly Quantifying Network Needs and Costs”, Journal of Lightwave Technology Preprint, 2004.

• Zvi Rosberg, “Packet Delay in Optical Circuit-Switched Networks”, 2004.

• Zvi Rosberg, “Analysis of OBS Networks with Limited Wavelength Conversion”, 2004.

• Jean-Francois Labourdette, “Fast Approximate Dimensioning and Performance Analysis of Mesh Optical Networks”, Design of Reliable Communication Networks 2003, 428-438.

• Damon J. Wischik, “Mathematical Modeling of Optical Burst-Switched (OBS) Networks”, 2004.