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1、.WirelessNetworkExperimentThree:QueuingTheoryABSTRACTThisexperimentisdesignedtolearnthefundamentalsofthequeuingtheory.MainlyabouttheM/M/SandM/M/n/nqueuingmodels.KEYWORDS:queuingtheory,M/M/s,M/M/n/n,ErlangB,ErlangC.INTRODUCTIONAqueueisawaitinglineandqueueingtheoryisthemathematicaltheoryofwaitinglines
2、.Moregenerally,queueingtheoryisconcernedwiththemathematicalmodelingandanalysisofsystemsthatprovideservicetorandomdemands.Incommunicationnetworks,queuesareencounteredeverywhere.Forexample,theincomingdatapacketsarerandomlyarrivedandbuffered,waitingfortheroutertodeliver.Suchsituationisconsideredasaqueu
3、e.Aqueueingmodelisanabstractdescriptionofsuchasystem.Typically,aqueueingmodelrepresents(1)thesystem'sphysicalconfiguration,byspecifyingthenumberandarrangementoftheservers,and(2)thestochasticnatureofthedemands,byspecifyingthevariabilityinthearrivalprocessandintheserviceprocess.Theessenceofqueueingthe
4、oryisthatittakesintoaccounttherandomnessofthearrivalprocessandtherandomnessoftheserviceprocess.ThemostcommonassumptionaboutthearrivalprocessisthatthecustomerarrivalsfollowaPoissonprocess,wherethetimesbetweenarrivalsareexponentiallydistributed.Theprobabilityoftheexponentialdistributionfunction...isft
5、=λe-λt.lErlangBmodelOneofthemostimportantqueueingmodelsistheErlangBmodel(i.e.,M/M/n/n).ItassumesthatthearrivalsfollowaPoissonprocessandhaveafinitenservers.InErlangBmodel,itassumesthatthearrivalcustomersareblockedandclearedwhenalltheserversarebusy.TheblockedprobabilityofaErlangBmodelisgivenbythefamou
6、sErlangBformula,wherenisthenumberofserversandA=λ/μistheofferedloadinErlangs,λisthearrivalrateand1/μistheaverageservicetime.Formula(1.1)ishardtocalculatedirectlyfromitsrightsidewhennandAarelarge.However,itiseasytocalculateitusingthefollowingiterativescheme:lErlangCmodelTheErlangdelaymodel(M/M/n)issim
7、ilartoErlangBmodel,exceptthatnowitassumesthatthearrivalcustomersarewaitinginaqueueforaservertobecomeavailablewithoutconsideringthelengthofthequeue.Theprobabilityofblocking(alltheserversarebusy)isgiven
