Chapter-06-Slides-additional

Chapter6Additionalexplanation6.1AterminatingsimulationExampleAstoreopensat9amwithnocustomerspresent,closesitsdoorat9pm,butcontinuesoperationforalittlewhilelongeruntilallcustomersare‘flushed’out.6.1Asteady-statesimulationThequantitiestobeestimatedaredefinedinthelongrun;i.e.,overatheoreticallyinfinitetimeframe.ExampleAnemergencyroomneverreallystopsorrestartsSometimespeopledoasteady-statesimulationofasystemthatactuallyterminatesinordertodesignforsomekindofworse-caseorpeak-loadsituation.6.2StrategyforDataCollectionandAnalysisTogettrue,statisticallyindependentandidenticallydistributed(IID)replicationsforterminatinganalysis,youneedtomakesurethatbothboxesarechecked.Thesechangeswillcausethesimulationtobereplicatedntimes,witheachreplicationstartingafresh(freshsystemstateandfreshstatisticalaccumulator)andusingseparatebasicrandomnumberstodrivethesimulation.Model6.1thebasecaseofModel5-3n=10InTable6-1,eachisan“observation”ofarandomvariableTheCategorybyReplicationreportTheCategoryOverviewreportArenainternallykeepstrackofalltheresultsinthereportsforallthereplications.Ifyouaremakingmorethanonereplication,theCategoryOverviewreportwillgiveyoutheaverageofeachresultoverthereplications,togetherwiththehalfwidthofa(nominal)95%confidenceintervalontheexpectedvalueoftheoutputresult.Savetobinary“.dat”filesIntheStatisticaldatamoduleTheOutputFileColumnContaindata6.3ConfidenceIntervalsforTerminatingSystemsToreducethehalfwidthoftheconfidenceinterval,Toincreasethesamplesizen.ToincreasethesamplesizenModel6.1------thebasecaseofModel5-3n=1021547.82±1604.82Model6.2------Model6.1n=110A95%confidenceintervalof2224.71±413.52Whatisaconfidenceinterval?EachreplicationproducesaTotalCostvalueforthatreplication,andduetorandominputs,thesevaluesvaryacrossreplications.Theaveragevalueofthe110valuesisprobablya“better”indicatorofwhattoexpectfroma“typical”runthanisanyoneoftheindividualvalues.Whatisaconfidenceinterval?Theexpectedaverage,ū,canbethoughtofastheTotalCostaveragedoveraninfinitenumberofreplications.Afinite-sampleestimatelikethe22,242.71fromour110replicationsWhatisaconfidenceinterval?Theconfidenceintervalcenteredaround22,241.71canbethoughtofasa“random”interval(thenextsetof110replicationswillgiveadifferentinterval)thathasapproximatelya95%(inthiscase)chanceofcontainingor“covering”ūinthesensethatifwemadealotofsetsof110replicationsandmadesuchanintervalfromeachset,about95%oftheseintervalswouldcoverū.Whatisaconfidenceinterval?Aconfidenceintervalgivesyoubotha“point”estimate(22,241.71)ofū,aswellasanideaofhowprecisethisestimateis.Whatisaconfidenceinterval?Aconfidenceintervalisnotanintervalinwhich,forexample,95%oftheTotalCostmeasuresfromreplicationswillfall.ApredictionintervalAconfidenceintervalwillshrinktoasinglepointasnincreases,butapredictionintervalwon’tsinceitneedstoallowforvariationsin(future)replications.AssumptionsforStatisticalAnalysisIIDNormalityHistogramforsymmetryModel6-3n=1000,fromModel6-2,n=110Savethe1000individualTotalCostvaluestoafilecalledTotalCost.dat,TheOutputFilecolumn,theStatisticaldatamoduleHistogramforsymmetryRantheArenaOutputAnalyzertoreadTotalCost.dat,ExportedittoaplainASCIItextfile(FileDataFileExportintheOutputAnalyzer)SaveditasaplainASCIItextfile,BroughtitintotheArenaInputAnalyzerIfthevalueyou’regettingoutofeachindividualreplicationisasumoraverageofsomething,asopposedtoanextremevalue,useofstandardnormal-theorystatistical-inferencemethodsisfairlysafe.SimulationExperience6.4ComparingTwoScenariosComparingdifferentversions,oralternatives,orscenarios,ofsomegeneralmodelFromasimpleparameterchangetofundamentaldifferentlogicToapplyappropriatestatisticalmethodsTodrawvalidconclusionsModel6-4Model6-3RunSetupReplicationParametersChangeton=110TheStatisticdatamoduleOutputFileColumnTotalCostrowTosavedatatothefileTotalCost.datTwoversionsThebasecaseThemoreresourcescenarioModel6-4,n=110fromModel5-3,n=5TrunkLinesNewTech1NewTech2NewTech3NewTechAllNewSalesBasecase2600000MoreResourcescenario2933333Onereplication?TotalCostPercentRejectedBaseCase21,281.2423,306.75More-ResourceScenario12.68360.2833OutputAnalyzerOperatesonoutputfilecreatedbyArenathroughtheStatisticdatamodule(the.datfiles)1.Gettinga.datfileTosavethevaluesofTotalCostforeachreplicationtoa.datfilefortheOutputAnalyzer,EnterTotalCost.datintheOutputFilecolumnfortheTotalCostrowintheStatisticdatamoduleAfterthesimulationhasbeenrun,thesefileswillcontainthe110valuesoftheseoutputperformancemeasuresoverthe110replications.2.ChangingfilenamesTochangetheirfilenamesintheArenamodelbeforeeachrunOrrenamethemoutintheoperatingsystemaftereachrunToavoidoverwritingthemonsubsequentrun3.RunOutputAnalyzerFileNewtoopenanewdatagroupSaveasModel06-04.dgrUsetheAddbuttontoselectthefilesofinterestAnalyzeCompareMeans3.RunOutputAnalyzerClearthecheckboxforScaleDisplayPuttingthegraphicdisplaysforthetwocomparisonsonthesamescaleIfThemeasurementunitswerethesameScalingthemtogether3.RunOutputAnalyzerThePaired-tapproachissomewhatmoregeneralTheresultsStatist