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1、*Breakthrough Management GroupQUEUING ANALYSIS* *, Breakthrough Management Group. Unpublished proprietary work available only under license. All rights reserved. Module ObjectivesqObtain an overview of differing types of Queuing SystemsqBe able to do simple calculations to examine different strategi
2、es for queue management2* *, Breakthrough Management Group. Unpublished proprietary work available only under license. All rights reserved. Queuing AnalysisqMathematical approach to the analysis of waiting linesqThe practical purpose of Queuing Analysis is to provide tools to examine queuing systems
3、, so that these systems may be made more efficient.qQueuing Analysis examines the progress of customers in a queue (people, loans, applications, phone calls, boats, etc.) pursuing a service or product in various stages of completionqQueues are an economic necessity since most attempts at designing s
4、ervice systems to satisfy demand instantly have been found to be too costly.3* *, Breakthrough Management Group. Unpublished proprietary work available only under license. All rights reserved. A Simple Queuing SystemProcess or Service“Customer” arrives“Customer” leaves4* *, Breakthrough Management G
5、roup. Unpublished proprietary work available only under license. All rights reserved. A Simple Queuing SystemPopulationArrivalsWaiting LineProcess or ServiceExitLine too long? Customer balks (never enters queue)Line, Time too long? Customer reneges (abandons queue)A Simple Queue5* *, Breakthrough Ma
6、nagement Group. Unpublished proprietary work available only under license. All rights reserved. A Simple Queuing SystemArrivalRate ()Service Rate ()Average Number in Queue (Lq)Average Wait in Queue (Wq)Average Time in System (W)Average Number in System (L)Number of Serving Channels (M)M - number of
7、Channels6* *, Breakthrough Management Group. Unpublished proprietary work available only under license. All rights reserved. Complex Queuing SystemsSingle channel, single phaseSingle channel, multiple phaseMultiple channel, single phaseMultiple channel, multiple phase7* *, Breakthrough Management Gr
8、oup. Unpublished proprietary work available only under license. All rights reserved. Still More Complex QueuesHigh levels ofComplexityrequireSimulation8* *, Breakthrough Management Group. Unpublished proprietary work available only under license. All rights reserved. Useful Distributions for Queuing
9、 Analysis00.050.10.150.20.250123456789 10 11 12 Customers per Time UnitPoisson Distribution Customer Arrivals per Unit timeTimeExponential Distribution Customer Service TimesP(x)f(t)9* *, Breakthrough Management Group. Unpublished proprietary work available only under license. All rights reserved. C
10、lassifying Queuing ModelsqThere are numerous queuing models from which to choose.qSuccessful analysis starts with selecting the best model.qModel choice is affected by the characteristics of the system being evaluated.qKey model characteristics include:mPopulation SourcemNumber of Servers (Channels)
11、mArrival and service patternsmQueue discipline (order of service)10* *, Breakthrough Management Group. Unpublished proprietary work available only under license. All rights reserved. Classifying Queuing ModelsqTwo simple queuing models are:mSingle Queue, Single ServermSingle Queue, Multiple Serversq
12、For the simple models: easy-to-use formulae exist for analysisqFor other than the simplest cases, the formulae applied for analysis are complex, and for real-world solutions, require the development of custom-designed simulations.11* *, Breakthrough Management Group. Unpublished proprietary work ava
13、ilable only under license. All rights reserved. One Queue and One ServerqEquations terms and calculations:mLet = mean service rate = mean arrival ratemLet = / = utilizationmThen:Length of Queue (Lq) = Prob ( 0 units in system) = 1 ( / ) = 1- Total Length Queue+Service (L) =Expected Waiting Time in Q
14、ueue (Wq)=Expected Total Waiting Time (W) =12* *, Breakthrough Management Group. Unpublished proprietary work available only under license. All rights reserved. Class ExerciseqAt the Literature Fulfillment department, requests for forms, brochures, and other items from the whole organization arrive
15、daily. All of these requests are handled by one person.qAs a result of changing business conditions, the rate of requests increase by 100%qA decision has been made to redefine the fulfillment mission to not include packaging and mailing, assigning these to a shipping department. This change is estim
16、ated to reduce order processing time by 50%. Management considers this change to offset the increase in demand.qIs this a good strategy? By cutting the service time in half to match the increase in the arrival rate, have things stayed the same?qHint: If and become 2 and 2 what happens to Queue Lengths and Queue Times relative to the original situation?13* *, Breakthrough Management Group.
