管理科学13-排队论(等候理论)

Chapter13-QueuingAnalysis1Chapter13QueuingAnalysisIntroductiontoManagementScience8thEditionbyBernardW.TaylorIIIChapter13-QueuingAnalysis2ElementsofWaitingLineAnalysisTheSingle-ServerWaitingLineSystemUndefinedandConstantServiceTimesFiniteQueueLengthFiniteCallingProblemTheMultiple-ServerWaitingLineAdditionTypesofQueuingSystemsChapterTopicsChapter13-QueuingAnalysis3Significantamountoftimespentinwaitinglinesbypeople,products,etc.Providingquickserviceisanimportantaspectofqualitycustomerservice.Thebasisofwaitinglineanalysisisthetrade-offbetweenthecostofimprovingserviceandthecostsassociatedwithmakingcustomerswait.Queuinganalysisisaprobabilisticformofanalysis.Theresultsarereferredtoasoperatingcharacteristics.Resultsareusedbymanagersofqueuingoperationstomakedecisions.OverviewChapter13-QueuingAnalysis4Waitinglinesformbecausepeopleorthingsarriveataservicefasterthantheycanbeserved.Mostoperationshavesufficientservercapacitytohandlecustomersinthelongrun.Customershowever,donotarriveataconstantratenoraretheyservedinanequalamountoftime.Waitinglinesarecontinuallyincreasinganddecreasinginlength.andapproachanaveragerateofcustomerarrivalsandanaverageservicetime,inthelongrun.Decisionsconcerningthemanagementofwaitinglinesarebasedontheseaveragesforcustomerarrivalsandservicetimes.Theyareusedinformulastocomputeoperatingcharacteristicsofthesystemwhichinturnformthebasisofdecisionmaking.ElementsofWaitingLineAnalysisChapter13-QueuingAnalysis5Componentsofawaitinglinesystemincludearrivals(customers),servers,(cashregister/operator),customersinlineformawaitingline.Factorstoconsiderinanalysis:Thequeuediscipline.ThenatureofthecallingpopulationThearrivalrateTheservicerate.TheSingle-ServerWaitingLineSystem(1of2)Chapter13-QueuingAnalysis6Figure13.1TheFastShopMarketQueuingSystemTheSingle-ServerWaitingLineSystem(2of2)Chapter13-QueuingAnalysis7QueueDiscipline:Theorderinwhichwaitingcustomersareserved.CallingPopulation:Thesourceofcustomers(infiniteorfinite).ArrivalRate:Thefrequencyatwhichcustomersarriveatawaitinglineaccordingtoaprobabilitydistribution(frequentlydescribedbyaPoissondistribution).ServiceRate:Theaveragenumberofcustomersthatcanbeservedduringatimeperiod(oftendescribedbythenegativeexponentialdistribution).Single-ServerWaitingLineSystemComponentDefinitionsChapter13-QueuingAnalysis8Assumptionsofthebasicsingle-servermodel:AninfinitecallingpopulationAfirst-come,first-servedqueuedisciplinePoissonarrivalrateExponentialservicetimesSymbology:=thearrivalrate(averagenumberofarrivals/timeperiod)=theservicerate(averagenumberserved/timeperiod)Customersmustbeservedfasterthantheyarrive()oraninfinitelylargequeuewillbuildup.Single-ServerWaitingLineSystemSingle-ServerModel9Probabilitythatnocustomersareinthequeuingsystem:Probabilitythatncustomersareinthesystem:Averagenumberofcustomersinsystem:andwaitingline:1Po1nPonPn2LqLSingle-ServerWaitingLineSystemBasicSingle-ServerQueuingFormulas(1of2)10Averagetimecustomerspendswaitingandbeingserved:Averagetimecustomerspendswaitinginthequeue:Probabilitythatserverisbusy(utilizationfactor):Probabilitythatserverisidle:LW1WqU11UISingle-ServerWaitingLineSystemBasicSingle-ServerQueuingFormulas(2of2)11=24customersperhourarriveatcheckoutcounter=30customersperhourcanbecheckedoutsystemtheincustomersnoofyprobabilit.2024/30)-(11Posystemtheinavgtheoncustomers424)-24/(30Llinewaitingtheinavgtheoncustomers3.224)]-30(24)2/[30(2LqSingle-ServerWaitingLineSystemCharacteristicsforFastShopMarket(1of2)12Single-ServerWaitingLineSystemCharacteristicsforFastShopMarket(2of2)customerpersystemtheintimeavgmin)(10hour0.16724]-1/[30LW1linewaitingtheintimeavgmin)(8hour0.13324)]-24/[30(30Wqidlebewillserveryprobabilit.20busy,serveryprobabilit.8024/30UChapter13-QueuingAnalysis13Single-ServerWaitingLineSystemSteady-StateOperatingCharacteristicsBecauseofsteady-statenatureofoperatingcharacteristics:Utilizationfactor,U,mustbelessthanone:U1,or/1and.Theratioofthearrivalratetotheserviceratemustbelessthanoneor,theserviceratemustbegreaterthanthearrivalrate.Theservermustbeabletoservecustomersfasterthanthearrivalrateinthelongrun,orwaitinglinewillgrowtoinfinitesize.Chapter13-QueuingAnalysis14Managerwishestotestseveralalternativesforreducingcustomerwaitingtime:AdditionofanotheremployeetopackuppurchasesAdditionofanothercheckoutcounter.Alternative1:Additionofanemployee(raisesserviceratefrom=30to=40customersperhour).Cost$150perweek,avoidslossof$75perweekforeachminuteofreducedcustomerwaitingtime.Systemoperatingcharacteristicswithnewparameters:Po=.40probabilityofnocustomersinthesystemL=1.5customersontheaverageinthequeuingsystemSingle-ServerWaitingLineSystemEffectofOperatingCharacteristics(1of6)Chapter13-QueuingAnalysis15Systemoperatingcharacteristicswithnewparameters(continued):Lq=0.90customerontheaverageinthewaitinglineW=0.063houraveragetimeinthesystempercustomerWq=0.038houraveragetimeinthewaitingli