Waiting lines.ppt - Waiting Lines Supplement C u00a9 2007...

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© 2007 Pearson EducationWaiting LinesSupplement C
© 2007 Pearson EducationWaiting LinesWaiting line: One or more “customers” waiting for service.Customer population: An input that generates potential customers.Service facility: A person (or crew), a machine (or group of machines), or both, necessary to perform the service for the customer.Priority rule: A rule that selects the next customer to be served by the service facility.Service system: The number of lines and the arrangement of the facilities.
© 2007 Pearson EducationWaiting Line ModelsBasic ElementsService systemService systemCustomer Customer populationpopulationWaiting linePriority ruleService facilitiesServed Served customerscustomers
© 2007 Pearson Education© 2007 Pearson EducationWaiting Line ArrangementsSingle lineSingle lineService facilitiesService facilitiesMultiple linesMultiple linesService facilitiesService facilities
© 2007 Pearson EducationService Facility ArrangementsChannel:One or more facilities required to perform a given service.Phase: A single step in providing a service.Priority rule: The policy that determines which customer to serve next.
© 2007 Pearson EducationService Facility ArrangementsSingle channel, single phaseSingle channel, single phaseService facility
© 2007 Pearson EducationSingle channel, multiple phaseSingle channel, multiple phaseService Facility ArrangementsService facility 1Service facility 2
© 2007 Pearson EducationMultiple channel, single phaseMultiple channel, single phaseService Facility ArrangementsService facility 1Service facility 2
© 2007 Pearson EducationMultiple channel, multiple phaseMultiple channel, multiple phaseService Facility ArrangementsService facility 3Service facility 4Service facility 1Service facility 2
© 2007 Pearson EducationService facility 3Service facility 4Service facility 1Service facility 2Routing for : 1–2–4Routing for : 1–2–4Routing for : 2–4–3Routing for : 2–4–3Routing for : 3–2–1–4Routing for : 3–2–1–4Service Facility ArrangementsMixed ArrangementMixed Arrangement
© 2007 Pearson EducationPriority RuleThe priority rule determines which customer to serve next. Most service systems use the first-come, first-serve (FCFS) rule. Other priority rules include:Earliest promised due date (EDD) Customer with the shortest expected processing time (SPT)Preemptive discipline: A rule that allows a customer of higher priority to interrupt the service or another customer.
© 2007 Pearson EducationProbability DistributionsArrival TimesExample C.1Example C.1Arrival rate = Arrival rate = 2/hour/hourCustomer ArrivalsCustomer Arrivalsare usually random and can be are usually random and can be described by a Poisson distribution.

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