Chapter-02-Slides

Chapter2–FundamentalSimulationConceptsSlide1of46SimulationwithArena,3rded.Chapter2FundamentalSimulationConceptsLastrevisionJune7,2003Chapter2–FundamentalSimulationConceptsSlide2of46SimulationwithArena,3rded.WhatWe’llDo...•Underlyingideas,methods,andissuesinsimulation•Software-independent(settingupforArena)•CenteredaroundanexampleofasimpleprocessingsystemDecomposetheproblemTerminologySimulationbyhandSomebasicstatisticalissuesOverviewofasimulationstudyChapter2–FundamentalSimulationConceptsSlide3of46SimulationwithArena,3rded.TheSystem:ASimpleProcessingSystemArrivingBlankPartsDepartingFinishedPartsMachine(Server)Queue(FIFO)PartinService4567•Generalintent:EstimateexpectedproductionWaitingtimeinqueue,queuelength,proportionoftimemachineisbusy•TimeunitsCanusedifferentunitsindifferentplaces…mustdeclareBecarefultochecktheunitswhenspecifyinginputsDeclarebasetimeunitsforinternalcalculations,outputsBereasonable(interpretation,roundofferror)Chapter2–FundamentalSimulationConceptsSlide4of46SimulationwithArena,3rded.ModelSpecifics•Initially(time0)emptyandidle•Basetimeunits:minutes•Inputdata(assumegivenfornow…),inminutes:PartNumberArrivalTimeInterarrivalTimeServiceTime10.001.732.9021.731.351.7633.080.713.3943.790.624.5254.4114.284.46618.690.704.36719.3915.522.07834.913.153.36938.061.762.371039.821.005.381140.82..........•Stopwhen20minutesof(simulated)timehavepassedChapter2–FundamentalSimulationConceptsSlide5of46SimulationwithArena,3rded.GoalsoftheStudy:OutputPerformanceMeasures•Totalproductionofpartsovertherun(P)•Averagewaitingtimeofpartsinqueue:•Maximumwaitingtimeofpartsinqueue:N=no.ofpartscompletingqueuewaitWQi=waitingtimeinqueueofithpartKnow:WQ1=0(why?)N1(why?)NWQNii1iNiWQmax,...,1Chapter2–FundamentalSimulationConceptsSlide6of46SimulationwithArena,3rded.GoalsoftheStudy:OutputPerformanceMeasures(cont’d.)•Time-averagenumberofpartsinqueue:•Maximumnumberofpartsinqueue:•Averageandmaximumtotaltimeinsystemofparts(a.k.a.cycletime):Q(t)=numberofpartsinqueueattimet20)(200dttQ)(max200tQtiPiPiiTSPTSmax,...,11,TSi=timeinsystemofpartiChapter2–FundamentalSimulationConceptsSlide7of46SimulationwithArena,3rded.GoalsoftheStudy:OutputPerformanceMeasures(cont’d.)•Utilizationofthemachine(proportionoftimebusy)•Manyotherspossible(informationoverload?)tttBdttBtimeatidleismachinetheif0timeatbusyismachinetheif1)(,20)(200Chapter2–FundamentalSimulationConceptsSlide8of46SimulationwithArena,3rded.AnalysisOptions•EducatedguessingAverageinterarrivaltime=4.08minutesAverageservicetime=3.46minutesSo(onaverage)partsarebeingprocessedfasterthantheyarrive–Systemhasachanceofoperatinginastablewayinthelongrun,i.e.,mightnot“explode”–Ifallinterarrivalsandservicetimeswereexactlyattheirmean,therewouldneverbeaqueue–Butthedataclearlyexhibitvariability,soaqueuecouldformIfwe’dhadaverageinterarrivalaverageservicetime,andthispersisted,thenqueuewouldexplodeTruth—betweentheseextremesGuessinghasitslimits…Chapter2–FundamentalSimulationConceptsSlide9of46SimulationwithArena,3rded.AnalysisOptions(cont’d.)•QueueingtheoryRequiresadditionalassumptionsaboutthemodelPopular,simplemodel:M/M/1queue–Interarrivaltimes~exponential–Servicetimes~exponential,indep.ofinterarrivals–MusthaveE(service)E(interarrival)–Steady-state(long-run,forever)–Exactanalyticresults;e.g.,averagewaitingtimeinqueueisProblems:validity,estimatingmeans,timeframeOftenusefulasfirst-cutapproximationtime)E(servicetime)ivalE(interarr2SASAS,Chapter2–FundamentalSimulationConceptsSlide10of46SimulationwithArena,3rded.MechanisticSimulation•Individualoperations(arrivals,servicetimes)willoccurexactlyasinreality•Movements,changesoccurattheright“time,”intherightorder•Differentpiecesinteract•Install“observers”togetoutputperformancemeasures•Concrete,“brute-force”analysisapproach•NothingmysteriousorsubtleButalotofdetails,bookkeepingSimulationsoftwarekeepstrackofthingsforyouChapter2–FundamentalSimulationConceptsSlide11of46SimulationwithArena,3rded.PiecesofaSimulationModel•Entities“Players”thatmovearound,changestatus,affectandareaffectedbyotherentitiesDynamicobjects—getcreated,movearound,leave(maybe)Usuallyrepresent“real”things–Ourmodel:entitiesarethepartsCanhave“fake”entitiesformodeling“tricks”–Breakdowndemon,breakangelThoughArenahasbuilt-inwaystomodeltheseexamplesdirectlyUsuallyhavemultiplerealizationsfloatingaroundCanhavedifferenttypesofentitiesconcurrentlyUsually,identifyingthetypesofentitiesisthefirstthingtodoinbuildingamodelChapter2–FundamentalSimulationConceptsSlide12of46SimulationwithArena,3rded.PiecesofaSimulationModel(cont’d.)•AttributesCharacteristicofallentities:describe,differentiateAllentitieshavesameattribute“slots”butdifferentvaluesfordifferententities,forexample:–Timeofarrival–Duedate–Priority–ColorAttributevaluetiedtoaspecificentityLike“local”(toentities)variablesSomeautomaticinArena,someyoudefineChapter2–FundamentalSimulationConceptsSlide13of46SimulationwithArena,3rded.PiecesofaSimulationModel(cont’d.)•(Global)VariablesReflectsacharacteristicofthewholemodel,