NetworkDesignPerformanceNetworkDesignPerformanceQueuingTheory1?GraduateUniversity,ChineseacademyofQueueingSystemQueuingTheoryQueueingSystemQueuingTheory2?GraduateUniversity,ChineseacademyofOpenNetworksofClosedOpenNetworksofClosedNetworksofQueuingTheory3?GraduateUniversity,Chineseacademyof1.?Sofar,weanalyzed1.?Sofar,weanalyzedsingleoccupancy,delay,Movetowardinterconnectedqueuingperformancenetworkoptimizationandvariousnetwork?QueuingTheory4?GraduateUniversity,Chineseacademyof?Interconnectedqueueswithjobs?InterconnectedqueueswithjobsflowonequeuetoHere,wewillstudynetworksofqueueswithexponentialserversandPoissonexternal?QueuingTheory5?GraduateUniversity,ChineseacademyofQueuingTheory6QueuingTheory6?GraduateUniversity,ChineseacademyofAnOpenNetworkisonewherejobsarrivefromoutsidetooneormorequeuesandeventuallyleaveAnOpenNetworkisonewherejobsarrivefromoutsidetooneormorequeuesandeventuallyleavethenetworkfromsomeofthequeues.Ifanopennetworkhasmultiplejobclassesthenitmustbeopenforeachclassofjobs.QueuingTheory7?GraduateUniversity,ChineseacademyofAnClosedNetworkisonewherethereareaconstantnumberofjobsthatcontinuallycirculateinthenetworkwithnootherarrivalstothesystemordeparturesfromthesystem.AnClosedNetworkisonewherethereareaconstantnumberofjobsthatcontinuallycirculateinthenetworkwithnootherarrivalstothesystemordeparturesfromthesystem.IfaclosednetworkhasmultiplejobclassesthenitmustbeclosedforeachclassofjobsQueuingTheory8?GraduateUniversity,ChineseacademyofQueuingTheory9QueuingTheory9?GraduateUniversity,Chineseacademyof2.OpenNetworksof2.OpenNetworksofQueuingTheory?GraduateUniversity,Chineseacademyofl:totalmeanarrivall:totalmeanarrivalratetothemi:meanservicerateofithrsj:probabilitythatacustomerarrivingfromthesourcewillberoutedtoqueuejrjd:probabilitythatacustomerdepartingfromqueuejwillberoutedtothedestinationrjk:probabilitythatacustomerdepartingfromqueuejwillberoutedtoqueuekQueuingTheory?GraduateUniversity,ChineseacademyofStateDescriptionoftheStateDescriptionoftheQueuingTheory?GraduateUniversity,ChineseacademyofAverage istheaveragethroughputthroughqueue–Average istheaveragethroughputthroughqueue–meanrateofentering/leavingtheTraffic?Mfromrjiqj,i=,,...=+jQueuingTheory?GraduateUniversity,Chineseacademyof1?Findtheavgthroughputthrough1?FindtheavgthroughputthrougheachQueuingTheory?GraduateUniversity,ChineseacademyofGlobalBalanceEquations??)betheGlobalBalanceEquations??)betheprobabilityofbeinginWhatistherateofleavingArrivaltoanyFromQueuingTheory?GraduateUniversity,ChineseacademyofTheithUnitTheithUnitQueuingTheory?GraduateUniversity,ChineseacademyofGlobalBalanceEquations?WhatisGlobalBalanceEquations?WhatistherateofenteringQueuingTheory?GraduateUniversity,ChineseacademyofGlobalBalanceEquationsQueuingGlobalBalanceEquationsQueuingTheory?GraduateUniversity,ChineseacademyofLocalBalance?Usethese,plusLocalBalance?Usethese,plusglobalbalance,plustrafficequationstogetthesolutionQueuingTheory?GraduateUniversity,ChineseacademyofProductFormMp(n)=piMp(n))1ProductFormMp(n)=piMp(n))1-n=iiiir=miiNetworkbehavesasifallqueueswerestatisticallyindependentQueuingTheory?GraduateUniversity,Chineseacademyof2Inthenetworkofqueuesfromthepreviousexercise,assumePoissonarrivalsatanaveragerateof1,000packets/secandaverageservicetimes2Inthenetworkofqueuesfromthepreviousexercise,assumePoissonarrivalsatanaveragerateof1,000packets/secandaverageservicetimesateachqueueof0.2msec.WhatistheprobabilityofnopacketsbeingintheQueuingTheory?GraduateUniversity,ChineseacademyofNumberofcustomersanddelayNumberofcustomersanddelaytheQueuingTheory?GraduateUniversity,Chineseacademyof3Forthenetworkinthe3ForthenetworkinthetwopreviouswhattheaveragenumberofpacketsinthetheaveragedelaythroughtheQueuingTheory?GraduateUniversity,Chineseacademyof3.ClosedNetworksof3.ClosedNetworksofQueuingTheory?GraduateUniversity,Chineseacademyof?Closednetworksofqueuescan?Closednetworksofqueuescanbeusedtomodeldifferenttypesofsystems–inreality,systemisNumberofcustomersinthesystematanytimeisafixedvalueN?QueuingTheory?GraduateUniversity,Chineseacademyof?FinitepopulationmodelsEachof?FinitepopulationmodelsEachofKuserscanhaveatmost1callactiveatatime(max#ofcallsisK)SystemsunderheavyMulti-stagepacketswitchesw/finite#ofpacketsallowedin,andanewpacketalwaysreadytoenterwhenoneleavesWindow-basedflow–Maximum#ofpacketsintransitatany??QueuingTheory?GraduateUniversity,ChineseacademyofTrafficM,i=,TrafficM,i=,,...=jfromQueuingTheory?GraduateUniversity,ChineseacademyofGlobalBalanceQueuingTheoryGlobalBalanceQueuingTheory?GraduateUniversity,ChineseacademyofProductFormSolutionfor?ProductFormSolutionfor?G(M,N)isanormalizationQueuingTheory?GraduateUniversity,ChineseacademyofFindingQueuingTheoryFindingQueuingTheory?GraduateUniversity,ChineseacademyofExample?SeefigureinslideExample?Seefigureinslide“ClosedNetworksofComputersystemallows2activejobsatanygivenEachjobrequiresCPU&I/OWhenjobleavesCPU,thereare2Jobfinishedandinstantlyreplacedbyanother(probabilityp)JobrequiresI/O,thenmoreCPU(prob.1-QueuingTheory?GraduateUniversity,ChineseacademyofExample4.1–Getting??Example4.1–Getting??WritedownthetrafficWhatstatesareQueuingTheory?GraduateUniversity,ChineseacademyofExample4.1–StateExample4.1–StateQueuingTheory?GraduateUniversity,Chineseacademyof?Utilizationristheproportionoftime?UtilizationristheproportionoftimethattheisbusyistheActualarrivalratetoqueue?Inexample4.1,r1=QueuingTheory?GraduateUniversity,ChineseacademyofExample4.2–A??UsetheExample4.2–A??Usethesameset-upasinExampleLet4jobs/sec,1job/sec,p=CalculatethestateCalculatetheutilizationateachCalculatetheaveragenumberofcustomersineachqueuingsystemCalculatetheaveragedelaythrougheachqueuingQueuingTheory?GraduateUniversity,Chineseacademyof均值分析方法均值分析方法QueuingTheory?GraduateUniversity,Chineseacademyof均值分析方法令表示具有I個(gè)客戶的均值分析方法令表示具有I個(gè)客戶的網(wǎng)絡(luò)中，第j個(gè)隊(duì)列中的平均?表示客戶在隊(duì)列j中的平均花費(fèi)時(shí)間列j的平均客戶到達(dá)速率客戶在隊(duì)列j中的平均花費(fèi)時(shí)間為?QueuingTheory?GraduateUniversity,Chineseacademyof均值分析方法由Little公均值分析方法由Little公式QueuingTheory?GraduateUniversity,Chineseacademyof均值分析方法均值分析方法1.首先由Traffic2.對3.QueuingTheory?GraduateUniversity,Chineseacademyof?NewprogramsarriveataCPUaccordingtoaPoissonprocessofrateaasshowninFig.1?NewprogramsarriveataCPUaccordingtoaPoissonprocessofrateaasshowninFig.1.AprogramspendsanexponentiallydistributedexecutiontimeofinCPU.Attheendofthisservicetime,theprogramexecutioniscompletewithprobabilityporitrequiresretrievingadditionalinformationfromsecondarystoragewithprobability1-p.Supposethattheretrievalofinformationfromsecondarystoragerequiresanexponentiallydistributedamountoftimewith.FindthetimethateachprogramspendsintheQueuingTheory?GraduateUniversity,ChineseacademyofQueuingTheoryQueuingTheor