Stochastic Simulation of Communication Networks and their ... · Stochastic Simulation of Communication Networks and their Protocols Prof. Dr. Carmelita Görg [email protected]

Stochastic Simulation of Communication Networks

and their Protocolsand their Protocols

Prof. Dr. Carmelita Görg

[email protected]

Prof. Dr. C. Görg www.comnets.uni-bremen.de VSIM 1 - 1

Table of Contents

1 General Introduction1 General Introduction2 Random Number Generation3 S i i l E l i3 Statistical Evaluation4 ComNets Class Library (CNCL)5 OPNET6 Network Simulator (ns)6 Network Simulator (ns)7 SDL + OpenWNS8 l d M h d8 Simulation Speed-Up Methods


OverviewOverv ew• What is simulation?

Wh simul ti ns??

• Why simulations?• Classification of simulations• Discrete Event Simulation (DES)

E t S h d li– Event Scheduling– Random Number Generation– Statistical Evaluation

• Simulation systems and applicationsSimulation systems and applications


References• P. Bratley, B.L. Fox, L.E. Schrage: A Guide to

Simulation. Springer 1983, 1987.• B.P. Zeigler, H. Praehofer, T.G. Kim: Theory of

Modeling and Simulation, Academic Press 1976, 2000.D Möll M d llbild Si l ti d • D. Möller: Modellbildung, Simulation und Identifikation dynamischer Systeme. Springer Lehrbuch 1992.

• R.Y. Rubinstein, B. Melamed: Modern Simulation and Modeling. Wiley Series in Probability and Statistics 19981998.

• P.A.W. Lewis, E.J. Orav: Simulation Methodology for Statisticians Operation Analysts and Engineers Vol Statisticians, Operation Analysts, and Engineers. Vol. 1. Wadsworth 1989.


References• G.S. Fishman: Principles of Discrete Event

Simulation. J. Wiley and Sons. New York, S mu at on. J. W y an Sons. N w Yor , 1978.

• A.M. Law, W.D. Kelton: Simulation Modeling & .M. L w, W.D. K n mu n M ng &Analysis. McGraw-Hill, 1991.

• Kreutzer W.: System Simulation -Kreutzer, W.: System Simulation Programming Styles and Languages, Addison Wesley Publishers - Reading (U.S.A.) 1986.Wesley Publishers Reading (U.S.A.) 1986.

• L. Devroye: Non-Uniform Random Variate Generation. Springer, New York, 1986.Generation. Springer, New York, 1986.


Web References• www.informs-sim.org • ...


Historical Development• Pre-computer era, e.g.:

Buffon (1777) coin experiments 4040 trialsBuffon (1777) coin experiments, 4040 trialsPearson (1857-1936) 24000 trialsKendall (approx 1938): random number Kendall (approx. 1938): random number generation using the London telephone directory directory

• Von Neumann (1944): Monte Carlo Method for the calculation of complex formulas in nuclear the calculation of complex formulas in nuclear physics1946 1956 “t ffi hi ”• 1946-1956: “traffic machines”simulation of telephone systems


Historical Development• Development of special simulation languages

– GPSS (IBM 1961 General Purpose Simulation – GPSS (IBM, 1961, General Purpose Simulation System)

– SIMULA (class concept Norwegian Computing SIMULA (class concept, Norwegian Computing Center, 1963, Simula 67)

– SIMSCRIPT (based on FORTRAN)SIMSCRIP (based on FOR RAN)• Development of special multiprocessor

simulatorssimulators– network structure (Chandy 1981)– function oriented structure – function oriented structure

(Lehnert 1979, Barel 1983)


Random Experiments and their Application Areas

h i i l iStochastic Simulationof

Complex Systems

ComputerRandom

Experiments

Improved Simulation Controlby

New Evaluation MethodsExperiments New Evaluation Methods

Modeling and Validationof

Statistical Concepts


Statistical Concepts

Communication Network Examplese.g.

S & W i P l• Stop & Wait Protocol• WLAN MAC ProtocolWLAN MAC Protocol• Ad hoc networks• TCP/IP Protocols• HSDPA ProtocolsHSDPA Protocols• ...


Evaluation Goals• Goal of the study of systems or their models

i th l ti f h t i ti f is the evaluation of some characteristics of the system

• Gain insight into system operation on a more conceptual level

• Compare two systems with respect to particular metricsp

• Tune system behavior for specific situations• Judge a priori the effects of • Judge a priori the effects of

reconfiguration/upgradingReduce c sts


• Reduce costs

Ways to study a systemy y ySystem

Experiment h h

Experiment h with the

actual systemwith a

system model

Mathematical Model

Physical Model ModelModel

SimulationAnalytical Solution


What is simulation?• simulation is imitation

h b d f t t i • has been used for many years to train, explain, evaluate and entertain

• the facility or process of interest is usually called a systemy y

• the assumptions, which usually take the form of mathematical or logical form of mathematical or logical relationships, constitute a modelsimul ti ns nd th ir m d ls r • simulations and their models are abstractions of reality


Why Simulations?y• Extensively used to verify

the correctness of designsg• Realistic models are often too complex to

evaluate analyticallyy y• The simulation approach gives more

flexibility and conveniencey• Accelerates and replaces effectively

the "wait and see" anxieties• Safely plays out the "what-if"

scenario from the artificial world


Real System PlannedSystemy System

ModelingModeling

Model

Measurement Simulation AnalyticCalculation

Result Result Result

Realizeplanned

ModifyPlanned

Validation


plannedsystem

Planned System

Performance Evaluation Cycle

Simulation Classification

dynamic staticy

discrete hybridcontinuous

t h ti d t i i tistochastic deterministic

event driven activity orientedtransaction driven


Classification of Simulations1. Static vs. Dynamic Simulation models

Static model: representation of a s st m t p ti l tim s st m system at a particular time, or a system in which time simply plays no role.Example: Monte Carlo model

Dynamic model: represents a system as it evolves over timeit evolves over time.Example: a WLAN network


Classification of Simulations2. Deterministic vs. Stochastic Simulation

ModelsDeterministic model: If a simulation model does not contain any probabilistic (i.e., y prandom) components, it is called deterministic.

Example: a system of differential equationsd ibi h i l ti i ht b h describing a chemical reaction might be such a model.

Stochastic model: Many systems however Stochastic model: Many systems, however, must be modeled as having at least some random input components and these give rise random input components, and these give rise to stochastic simulation models.

Example: Most queueing and inventory systems are


p q g y ymodeled stochastically.

Classification of Simulations3. Continuous vs. discrete time

Simulation modelsDefined analogous to the way discrete and Defined analogous to the way discrete and continuous systems are defined, i.e.,

a discrete system is one in which the state a r t y t m n n w t tat variables change instantaneously at separated points in time, andin a continuous system the state variables change continuously with respect to time.

It is important to mention that a discrete model is not always used to model a discrete


ysystem, and vice-versa.

Application Areas• Determining hardware requirements or

protocols for communication networksp

• Determining hardware and software requirements for

g qa computer system

• Designing and analyzing logistic systems (manufacturing and transport)(manufacturing and transport)

• Designing and operating transportation systems such as airports, freeways, ports and sub-waysE l ti d i f i i ti h • Evaluating designs for service organizations such as call centers, fast-food restaurants, hospitals, post offices, gas stations, …p g

• Re-engineering of business processes• Evaluating military systems or their logistic

requirements


requirements• ...

Drawbacks• No exact answers, only approximationsy pp• Get random output from stochastic

simulations careful output analysis simulations, careful output analysis necessary as standard statistical

th d i ht t kmethods might not work• Development of the model pm f m

takes a lot of time


Discrete-Event Simulation• State variables change instantaneously at

t i t i ti separate points in time

• State transitions are triggered by eventsState transitions are triggered by events

• Thus, simulation models considered here are di t t d i d t h tidiscrete-event, dynamic and stochastic

• Example: Example: CNCL (Communication Network Class Library)-a portable C++ library providing a base for all p y p gC++ applications


G/G/1 Model

1Arrival (λa) Server (λb)b

b λτ 1

=

FIFO- QueueFIFO- Queue


Discrete Event SimulationsExample: A simple queuing system


System Terminologyy gy• State:

A variable characterizing an attribute in the system, b f b f e.g., number of jobs waiting for processing or

level of stock in inventory systems• Event: An occurrence at a point in time which may • Event: An occurrence at a point in time which may

change the state of the system, e.g., arrival of a customer or start of work on a job

• Entity: An object that passes through the system, e.g., jobs in the queue or orders in a factory. Often an event (e g arrival) is associated with an Often an event (e.g., arrival) is associated with an entity (e.g., customer).

• Queue: QA queue is not only a physical queue of people, but any place where entities are waiting to be processed


System Terminologyy gy• Creating: Creating is causing an arrival of a new

entity to the system at some point in timeS h d li S h d li i th t f i i • Scheduling: Scheduling is the act of assigning a new future event to an existing entity

• Random Variable: • Random Variable: A random variable is a quantity that is uncertain– Interarrival time between two incoming jobs (e.g.

fl h f f g j ( g

message, flights, number of defective parts in a shipment)

• Random Variate: A random variate is an Random Variate: A random variate is an artificially generated random variable

• Distribution: A distribution is the mathematical Distribution A d str but on s the mathematical law which governs the probabilistic features of a random variable

E ti ti l l di t ib tiProf. Dr. C. Görg www.comnets.uni-bremen.de VSIM 1 - 26

– E.g. negative exponential or normal distribution

Steps of a SimulationpProblem Formulation

• Identify controllable and uncontrollable inputsy p• Identify constraints on the decision variables• Define measure of system performance

d bj ti f tiand an objective function• Develop a preliminary model structure to interrelate

the inputs and the measure of performancethe inputs and the measure of performance

S tControllable Input OutputSystemControllable Input Output

Uncontrollable Input


(from the outside world)

Steps of the Simulation• Descriptive Analysis

D t C ll ti d A l i f I t V i bl– Data Collection and Analysis of Input Variables– Computer Simulation Model Development

V lid i– Validation

and finallyand finally

• Performance Evaluation– Pre-scriptive Analysis:

Optimization or Goal Seeking– Post-prescriptive Analysis:

Sensitivity and What-If Analysis


Steps in a Simulation Studyp y

Problem formulation Set objectives and plans Conceptual modelProblem formulation Set objectives and plans Conceptual model

Collect dataValidation

Create simulation model

Production runs and analysis Experimental designDocumentation

and report


Structure of a Simulation System Prof. Dr. C. Görg www.comnets.uni-bremen.de VSIM 1 - 30

Structure of a Simulation System (adapted from Kreutzer 1986)

D t il f th t h t t Prof. Dr. C. Görg www.comnets.uni-bremen.de VSIM 1 - 31

Detail of the event approach structure (from Kreutzer 1986)

(Future) Event List

also called SQS (sequencing set) in Simula

t1 ≤ t2 ≤ tn

t1

E1

t2

E2

tn

En

time t


Event List• The event list controls

the simulationSimulation at Mensa

the simulation• It contains all the

future events (FEL) 1t arrival

t i l tithat are scheduled• It is ordered by

increasing time of

2t service completion at cashier 2

increasing time of event scheduler

• Events can be

service completionat meal 1

3t

Some state variablesE nt can categorized as primary and conditional events

4t finish eatingSome state variablesPeople in line 1People at meal line 1&2

conditional events• E.g.: CNEventHandler,

CNEventScheduler, 5t finish eating

People at cashier 1&2People eating at tables


NEventScheduler, etc. in CNCL

List of Events

Discrete Event Simulation: “Model Time“ and “Processing Time“

t : E t : E t : Emodel time =simulation time

t1, E1 t2, E2 t3, E3

t1 : E1 t2 : E2 t3 : E3

e.g., h, ms, μs

e.g., ms, μs

T T

processing time = CPU time

Ts TsTE1 Ts TE2 TE3

ti : event / (process) planning timeEi : event routine resp. processTs : administration time


Ts administration timeTEi : processing time event Ei

Example: Simulation IntroductionAssume the example of a gas station (or super market, doctor‘s office, …)• Why do we simulate?• What does the model of the gas station look like?What does the model of the gas station look like?

Make a diagram of the model identifying the system components.Name the parameters needed to characterize the system.Which results could be obtained by the simulation?

• How can you best model a queue on a computer and why?• How can you best model a queue on a computer and why?What would an implementation look like?What is the difference between a queue and a list?Which functions are needed for a queue (list)?

h d l f h d f h l • Is the model of the gas station a good mapping of the real system?What potential improvements are possible?

• Describe a traffic model for the gas station model? Which additional parameters are needed?Which additional parameters are needed?

• Why are event-oriented systems usually preferred to other systems (e.g. periodic)?What are the advantages?N h i h i l i f h i • Name the events in the simulation of the gas station.

• Describe the idealized usage of simulation for the introduction of a new (mobile) communication network


for the introduction of a new (mobile) communication network.

Exercise 1: Probability and Correlation 1. The cumulative distribution function (cdf)(Verteilungsfunktion) FX(x)of a random variable (RV) Xof a random variable (RV) Xresp. the probability density function (pdf) fX(x)is defined as:

∫ ∞−=≤=

w

XX dxxfwXPwF )(}{)(

xdF )(resp.

A random variable is defined: X = 10i dx

xdFxf XX

)()( =

where i stands for all possible realizations of arandom experiment tossing a fair die. Draw the cdf and the pdf of this experiment!Draw the cdf and the pdf of this experiment!


Exercise 1.2 (cont.)Distributions can be characterized by their moments. The most prominent moments are expectation (Erwartungswert) (mean, Mittelwert)

and variance (Varianz), that are a measure for the distribution of the samples (Stichprobenwerte) around the mean value. of th samp s (St chpro nw rt ) aroun th m an a u .

The expectation E{X} resp. μX and the variance бX of a random variable X are defined as:

∫∫

∞+

+∞

∞−== dxxxfXE X )(}{ μ

where бX is called standard deviation (Standardabweichung) (бX ≥ 0).In a simulation experiment only a finite sample of values is available from the possible result set.

∫∞+

∞−−=−= dxxfxXE

X)()(}){( 222 μμσ

p y f p f f pThis leads to the usage of estimators (Schätzer), that will approach the exact value for mean

value and variance as more values are added to the sample.The following estimators are used as expectation and variance:

1~}{N

XE ∑2

1

22

1

)(1

1~

1~}{

X

N

iiX

iX

xN

xN

XE

Xμσσ

μμ

∑

∑

=

−−

=≈

=≈=

Which problems are to be expected when using these estimators in a simulation program?Can the estimator of the variance be rearranged in such a way that it is better suited for

implementation? Which disadvantages can this rearranged estimator have?

1i=


Which disadvantages can this rearranged estimator have?

Exercise 1.3 (cont.)An important aspect in simulation experiments is the dependency of values

between each other, called correlation (Korrelation). A measure for the correlation of two random variables is the (global) (g )

correlation coefficient (Korrelationskoeffizient) : ρ. First the covariance (Kovarianz) C of two random variables X and Y is defined

as follows:

Using the definition of the global correlation coefficient shows the following:

}{}{}{)})({( YEXEXYEYXEC YX −=−−= μμ

and YX

Cσσ

ρ =YXC σσ≤||

and thus |ρ| ≤ 1.

What is the value of C and ρ in the uncorrelated case?


Documents

Stochastic Simulation of Communication Networks and their ... · Stochastic Simulation of Communication Networks and their Protocols Prof. Dr. Carmelita Görg [email protected]