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1、WirelessNetworkExperimentThree:QueuingTheoryABSTRACTThisexperimentisdesignedtolearnthefundamentalsofthequeuingtheory.MainlyabouttheM/M/SandM/M/n/nqueuingmodels.KEYWORDS:queuingtheory,M/M/s,M/M/n/n,ErlangB,ErlangC.INTRODUCTIONAqueueisawaitinglineandqueueingtheoryis
2、themathematicaltheoryofwaitinglines.Moregenerally,queueingtheoryisconcernedwiththemathematicalmodelingandanalysisofsystemsthatprovideservicetorandomdemands.Incommunicationnetworks,queuesareencounteredeverywhere.Forexample,theincomingdatapacketsarerandomlyarrivedan
3、dbuffered,waitingfortheroutertodeliver.Suchsituationisconsideredasaqueue.Aqueueingmodelisanabstractdescriptionofsuchasystem.Typically,aqueueingmodelrepresents(1)thesystem'sphysicalconfiguration,byspecifyingthenumberandarrangementoftheservers,and(2)thestochasticnat
4、ureofthedemands,byspecifyingthevariabilityinthearrivalprocessandintheserviceprocess.Theessenceofqueueingtheoryisthatittakesintoaccounttherandomnessofthearrivalprocessandtherandomnessoftheserviceprocess.Themostcommonassumptionaboutthearrivalprocessisthatthecustomer
5、arrivalsfollowaPoissonprocess,wherethetimesbetweenarrivalsareexponentiallydistributed.Theprobabilityoftheexponentialdistributionfunctionisft=λe-λt.lErlangBmodelOneofthemostimportantqueueingmodelsistheErlangBmodel(i.e.,M/M/n/n).ItassumesthatthearrivalsfollowaPoisso
6、nprocessandhaveafinitenservers.InErlangBmodel,itassumesthatthearrivalcustomersareblockedandclearedwhenalltheserversarebusy.TheblockedprobabilityofaErlangBmodelisgivenbythefamousErlangBformula,wherenisthenumberofserversandA=λ/μistheofferedloadinErlangs,λisthearriva
7、lrateand1/μistheaverageservicetime.Formula(1.1)ishardtocalculatedirectlyfromitsrightsidewhennandAarelarge.However,itiseasytocalculateitusingthefollowingiterativescheme:lErlangCmodelTheErlangdelaymodel(M/M/n)issimilartoErlangBmodel,exceptthatnowitassumesthatthearri
8、valcustomersarewaitinginaqueueforaservertobecomeavailablewithoutconsideringthelengthofthequeue.Theprobabilityofblocking(alltheserversarebusy)isgivenbyth
