WaitingLineManagementOperationsManagementForCompetitiveAdvantageCHASEAQUILANOJACOBSnintheditionTechnicalNote6WaitingLineManagementOperatiTechnicalNote6

WaitingLineManagementWaitingLineCharacteristicsSuggestionsforManagingQueuesExamples(Models1,2,3,and4)TechnicalNote6

WaitingLineComponentsoftheQueuingSystemCustomerArrivalsServersWaitingLineServicingSystemExitQueueor

ComponentsoftheQueuingSystCustomerServicePopulationSourcesPopulationSourceFiniteInfiniteExample:Numberofmachinesneedingrepairwhenacompanyonlyhasthreemachines.Example:Thenumberofpeoplewhocouldwaitinalineforgasoline.CustomerServicePopulationSoServicePatternServicePatternConstantVariableExample:Itemscomingdownanautomatedassemblyline.Example:Peoplespendingtimeshopping.ServicePatternServiceConstantTheQueuingSystem

QueueDiscipline

Length

NumberofLines&LineStructuresServiceTimeDistributionQueuingSystemTheQueuingSystemQueueDisciExamplesofLineStructuresSingleChannelMultichannelSinglePhaseMultiphaseOne-personbarbershopCarwashHospitaladmissionsBanktellers’windowsExamplesofLineStructuresSinDegreeofPatienceNoWay!BALKNoWay!RENEGDegreeofPatienceNoWay!BALKNSuggestionsforManagingQueues1.Determineanacceptablewaitingtimeforyourcustomers.2.Trytodivertyourcustomer’sattentionwhenwaiting.3.Informyourcustomersofwhattoexpect.4.Keepemployeesnotservingthecustomersoutofsight.5.Segmentcustomers.SuggestionsforManagingQueueSuggestionsforManagingQueues(Continued)6.Trainyourserverstobefriendly.7.Encouragecustomerstocomeduringthe

slackperiods.8.Takealong-termperspectivetowardgetting

ridofthequeues.SuggestionsforManagingQueueWaitingLineModelsModelLayoutSourcePopulationServicePattern1SinglechannelInfiniteExponential2SinglechannelInfiniteConstant3MultichannelInfiniteExponential4SingleorMultiFiniteExponentialThesefourmodelssharethefollowingcharacteristics:·Singlephase·Poissonarrival·FCFS·UnlimitedqueuelengthWaitingLineModelsModelLayoutExample:Model1Drive-upwindowatafastfoodrestaurant.Customersarriveattherateof25perhour.Theemployeecanserveonecustomereverytwominutes.AssumePoissonarrivalandexponentialservicerates.A)Whatistheaverageutilizationoftheemployee?B)Whatistheaveragenumberofcustomersinline?C)Whatistheaveragenumberofcustomersinthesystem?D)Whatistheaveragewaitingtimeinline?E)Whatistheaveragewaitingtimeinthesystem?F)Whatistheprobabilitythatexactlytwocarswillbeinthesystem?Example:Model1Drive-upwindExample:Model1A)Whatistheaverageutilizationoftheemployee?Example:Model1A)WhatistExample:Model1B)Whatistheaveragenumberofcustomersinline?C)Whatistheaveragenumberofcustomersinthesystem?Example:Model1B)WhatistExample:Model1D)Whatistheaveragewaitingtimeinline?E)Whatistheaveragewaitingtimeinthesystem?Example:Model1D)WhatistExample:Model1F)Whatistheprobabilitythatexactlytwocarswillbeinthesystem(onebeingservedandtheotherwaitinginline)?Example:Model1F)WhatistExample:Model2Anautomatedpizzavendingmachineheatsanddispensesasliceofpizzain4minutes.Customersarriveatarateofoneevery6minuteswiththearrivalrateexhibitingaPoissondistribution.Determine:A)Theaveragenumberofcustomersinline.B)Theaveragetotalwaitingtimeinthesystem.Example:Model2AnautomatedExample:Model2A)Theaveragenumberofcustomersinline.B)Theaveragetotalwaitingtimeinthesystem.Example:Model2A)TheaveraExample:Model3RecalltheModel1example:Drive-upwindowatafastfoodrestaurant.Customersarriveattherateof25perhour.Theemployeecanserveonecustomereverytwominutes.AssumePoissonarrivalandexponentialservicerates.Ifanidenticalwindow(andanidenticallytrainedserver)wereadded,whatwouldtheeffectsbeontheaveragenumberofcarsinthesystemandthetotaltimecustomerswaitbeforebeingserved?Example:Model3RecalltheMoExample:Model3AveragenumberofcarsinthesystemTotaltimecustomerswaitbeforebeingservedExample:Model3AveragenumbeExample:Model4Thecopycenterofanelectronicsfirmhasfourcopymachinesthatareallservicedbyasingletechnician.Everytwohours,onaverage,themachinesrequireadjustment.Thetechnicianspendsanaverageof10minutespermachinewhenadjustmentisrequired.AssumingPoissonarrivalsandexponentialservice,howmanymachinesare“down”(onaverage)?Example:Model4ThecopycentExample:Model4N,thenumberofmachinesinthepopulation=4M,thenumberofrepairpeople=1T,thetimerequiredtoserviceamachine=10minutesU,theaveragetimebetweenservice=2hoursFromTableTN6.11