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Basic Simulation Modeling II

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CONTENTS

• The Nature of Simulation• Sstems! Models! and Simulation

• "iscrete#E$ent Simulation

• %lternati$e %&&roaches to Modeling and CodingSimulations

• Ste&s in a Sound Simulation Stud

• Other T&es of Simulation

• %d$antages! "isad$antages! and 'itfalls of Simulation

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T)E N%T*+E O, SIM*-%TION

• Simulation Imitate the o&erations of a facilit or &rocess!usuall $ia com&uter 

 /  0hats eing simulated is the system

 /  To stud sstem! often ma3e assum&tions4a&&ro5imations! oth

logical and mathematical! aout ho6 it 6or3s /  These assum&tions form a model  of the sstem

 /  If model structure is sim&le enough! could use mathematical

methods to get e5act information on 7uestions of interest 8

analytical solution

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The Nature of Simulation :contd.;

• But most com&le5 sstems re7uire models that are alsocom&le5 :to e $alid;

 /  Must e studied $ia simulation 8 e$aluate model numericall and

collect data to estimate model characteristics

• E5am&le Manufacturing com&an considering e5tendingits &lant

 /  Build it and see if it 6or3s out<

 /  Simulate current! e5&anded o&erations 8 could also in$estigate

man other issues along the 6a! 7uic3l and chea&l

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The Nature of Simulation :contd.;

• Some :not all; a&&lication areas /  "esigning and anal>ing manufacturing sstems /  E$aluating militar 6ea&ons sstems or their logistics re7uirements

 /  "etermining hard6are re7uirements or &rotocols forcommunications net6or3s

 /  "etermining hard6are and soft6are re7uirements for a com&utersstem

 /  "esigning and o&erating trans&ortation sstems such as air&orts!free6as! &orts! and su6as

 /  E$aluating designs for ser$ice organi>ations such as call centers!fast#food restaurants! hos&itals! and &ost offices

 /  +eengineering of usiness &rocesses

 /  "etermining ordering &olicies for an in$entor sstem

 /  %nal>ing financial or economic sstems

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The Nature of Simulation :contd.;

• *se! &o&ularit of simulation /  Se$eral conferences de$oted to simulation! notal the 0inter

Simulation Conference :666.6intersim.org;

• Sur$es of use of O+4MS techni7ues :e5am&les @;

 /  -ongitudinal stud :1A(#1A; Simulation consistentl ran3edas one of the three most im&ortant techni7ues

 /  12A9 &a&ers in Interfaces :1AA; Simulation 6as second onl to

the road categor of Dmath &rogramming

http://www.wintersim.org/http://www.wintersim.org/

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The Nature of Simulation :contd.;

• Im&ediments to acce&tance! use of simulation /  Models of large sstems are usuall $er com&le5

But no6 ha$e etter modeling soft6are @ more general! fle5ile! ut still

:relati$el; eas to use

 /  Can consume a lot of com&uter time But no6 ha$e faster! igger! chea&er hard6are to allo6 for much etter

studies than Fust a fe6 ears ago @ this trend 6ill continue

)o6e$er! simulation 6ill also continue to &ush the en$elo&e on com&uting

 &o6er in that 6e as3 more and more of our simulation models

 /  Im&ression that simulation is DFust &rogramming Theres a lot more to a simulation stud than Fust Dcoding a model in some

soft6are and running it to get Dthe ans6er

 Need careful design and analsis of simulation models / simulation

methodolog

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SGSTEMS! MO"E-S! %N" SIM*-%TION

• System % collection of entities :&eo&le! &arts! messages!machines! ser$ers! @; that act and interact together to6ard

some end :Schmidt and Talor! 1AH;

 /  In &ractice! de&ends on oFecti$es of stud

 /  Might limit the oundaries :&hsical and logical; of the sstem /  udgment call le$el of detail :e.g.! 6hat is an entit

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Sstems! Models! and Simulation :contd.;

• T&es of sstems /  Discrete

State $ariales change instantaneousl at se&arated &oints in time

Ban3 model State changes occur onl 6hen a customer arri$es or de&arts

 /  Continuous State $ariales change continuousl as a function of time

%ir&lane flight State $ariales li3e &osition! $elocit change continuousl

• Man sstems are &artl discrete! &artl continuous

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• 0as to stud a sstem

Sstems! Models! and Simulation :contd.;

 /  Simulation is Dmethod oflast resort

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Sstems! Models! and Simulation :contd.;

• Classification of simulation models /  Static $s. dynamic

 /  Deterministic $s. stochastic

 /  Continuous $s. discrete

• Most o&erational models are dnamic! stochastic! and

discrete / 6ill e called discrete-event simulation models

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"ISC+ETE#EJENT SIM*-%TION

•  Discrete-event simulation Modeling of a sstem as ite$ol$es o$er time a re&resentation 6here the state$ariales change instantaneousl at se&arated &oints in time /  More &recisel! state can change at onl a countable numer of

 &oints in time

 /  These &oints in time are 6hen events occur 

•  Event  Instantaneous occurrence that ma change the stateof the sstem

 /  Sometimes get creati$e aout 6hat an De$ent is @ e.g.! end ofsimulation! ma3e a decision aout a sstems o&eration

• Can in &rinci&le e done hand! ut usuall done oncom&uter 

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"iscrete#E$ent Simulation :contd.;

• E5am&le Single#ser$er 7ueue /  Estimate e5&ected a$erage dela in 7ueue :line! notser$ice;

 /  State $ariales Status of ser$er :idle! us; / needed to decide 6hat to do

6ith an arri$al Current length of the 7ueue / to 3no6 6here to store an

arri$al that must 6ait in line Time of arri$al of each customer no6 in 7ueue / needed to

com&ute time in 7ueue 6hen ser$ice starts

 /  E$ents %rri$al of a ne6 customer  Ser$ice com&letion :and de&arture; of a customer  Mae / end#simulation e$ent :a Dfa3e e$ent; / 6hether

this is an e$ent de&ends on ho6 simulation terminates :amodeling decision;

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Time#%d$ance Mechanisms

• Simulation clock  Jariale that 3ee&s the current $alue of:simulated; time in the model

 /  Must decide on! e consistent aout! time units

 /  *suall no relation et6een simulated time and :real; time needed

to run a model on a com&uter 

• T6o a&&roaches for time ad$ance

 /  Next-event time advance :usuall used; @ descried in detail

 elo6

 /  Fixed-increment time advance :seldom used; @

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Time#%d$ance Mechanisms :contd.;

• More on ne5t#e$ent time ad$ance /  Initiali>e simulation cloc3 to H

 /  "etermine times of occurrence of future e$ents / event list 

 /  Cloc3 ad$ances to ne5t :most imminent; e$ent! 6hich is e5ecuted E$ent e5ecution ma in$ol$e u&dating e$ent list

 /  Continue until sto&&ing rule is satisfied :must e e5&licitl stated;

 /  Cloc3 DFum&s from one e$ent time to the ne5t! and doesnt De5ist

for times et6een successi$e e$ents @ &eriods of inacti$it are

ignored

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Com&onents and Organi>ation of a "iscrete#

E$ent Simulation Model

• Each simulation model must e customi>ed to target sstem• But there are se$eral common com&onents! general

organi>ation /  System state / $ariales to descrie state

 /  Simulation clock  / current $alue of simulated time /  Event list  / times of future e$ents :as needed;

 /  Statistical counters / to accumulate 7uantities for out&ut

 /  Initialization routine / initiali>e model at time H

 /  Timin routine / determine ne5t e$ent time! t&e ad$ance cloc3 

 /  Event routines / carr out logic for each e$ent t&e

 /  !ibrary routines / utilit routines to generate random $ariates! etc.

 /  "e#ort enerator  / to summari>e! re&ort results at end

 /  $ain #roram / ties routines together! e5ecutes them in right order 

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Com&onents and Organi>ation of a "iscrete#

E$ent Simulation Model :contd.;

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Com&onents and Organi>ation of a "iscrete#

E$ent Simulation Model :contd.;

• More on entities /  OFects that com&ose a simulation model

 /  *suall include customers! &arts! messages! etc. @ ma include

resources li3e ser$ers

 /  Characteri>ed data $alues called attributes /  ,or each entit resident in the model theres a record :ro6; in a

list ! 6ith the attriutes eing the columns

• %&&roaches to modeling

 /  Event-schedulin  / as descried ao$e! coded in general#&ur&ose

language

 /  %rocess / focuses on entities and their De5&erience! usuall

re7uires s&ecial#&ur&ose simulation soft6are

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"etermining the E$ents and Jariales

• ,or com&le5 models! it might not e o$ious 6hat thee$ents are

•  Event-ra#h method :Schruen 1A(! and suse7uent

 &a&ers; gi$es formal gra&h#theoretic method of anal>ing

e$ent structure

• Can anal>e 6hat needs to e initiali>ed! &ossiilit of

comining e$ents to sim&lif model

• Soft6are &ac3age :SILM%; to uild! e5ecute a simulationmodel $ia e$ent#gra&h re&resentation

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STE'S IN % SO*N" SIM*-%TION ST*"G

,igure 1.?

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OT)E+ TG'ES O, SIM*-%TION

• Continuous simulation /  T&icall! sol$e sets of differential e7uations numericall o$er

time

 /  Ma in$ol$e stochastic elements

 /  Some s&eciali>ed soft6are a$ailale some discrete#e$entsimulation soft6are 6ill do continuous simulation as 6ell

• Combined discrete-continuous simulation

 /  Continuous $ariales descried differential e7uations

 /  "iscrete e$ents can occur that affect the continuousl#changing

$ariales

 /  Some discrete#e$ent simulation soft6are 6ill do comined

discrete#continuous simulation as 6ell

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Other T&es of Simulation :contd.;

•  $onte Carlo simulation /  No time element :usuall; /  0ide $ariet of mathematical &rolems

 /  E5am&le E$aluate a Ddifficult integral -et &   *:a! b;! and let '   :b / a;  : & ; Then

%lgorithm Lenerate &   *:a! b;! let '   :b / a;  : & ; re&eat a$erage the ' s@ this a$erage 6ill e an uniased estimator of  I 

% % %L S S% % %L S %

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%"J%NT%LES! "IS%"J%NT%LES! %N"

'IT,%--S O, SIM*-%TION

• %d$antages /  Simulation allo6s great fle5iilit in modeling com&le5 sstems! sosimulation models can e highl $alid

 /  Eas to com&are alternati$es /  Control e5&erimental conditions /  Can stud sstem 6ith a $er long time frame

• "isad$antages /  Stochastic simulations &roduce onl estimates / 6ith noise /  Simulation models can e e5&ensi$e to de$elo& /  Simulations usuall &roduce large $olumes of out&ut / need to

summari>e! statisticall anal>e a&&ro&riatel

• 'itfalls /  ,ailure to identif oFecti$es clearl u& front /  Ina&&ro&riate le$el of detail :oth 6as; /  Inade7uate design and analsis of simulation e5&eriments /  Inade7uate education! training