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1、实用标准WirelessNetworkExperimentThree:QueuingTheoryABSTRACTThisexperimentisdesignedtolearnthefundamentalsofthequeuingtheory.MainlyabouttheM/M/SandM/M/n/nqueuingmodels.KEYWORDS:queuingtheory,M/M/s,M/M/n/n,ErlangB,ErlangC.INTRODUCTION文案大全实用标准Aqueueisawaitinglineandqueuein
2、gtheoryisthemathematicaltheoryofwaitinglines.Moregenerally,queueingtheoryisconcernedwiththemathematicalmodelingandanalysisofsystemsthatprovideservicetorandomdemands.Incommunicationnetworks,queuesareencounteredeverywhere.Forexample,theincomingdatapacketsarerandomlyarr
3、ivedandbuffered,waitingfortheroutertodeliver.Suchsituationisconsideredasaqueue.Aqueueingmodelisanabstractdescriptionofsuchasystem.Typically,aqueueingmodelrepresents(1)thesystem'sphysicalconfiguration,byspecifyingthenumberandarrangementoftheservers,and(2)thestochastic
4、natureofthedemands,byspecifyingthevariabilityinthearrivalprocessandintheserviceprocess.Theessenceofqueueingtheoryisthatittakesintoaccounttherandomnessofthearrivalprocessandtherandomnessoftheserviceprocess.Themostcommonassumptionaboutthearrivalprocessisthatthecustomer
5、arrivalsfollowaPoissonprocess,wherethetimesbetweenarrivalsareexponentiallydistributed.Theprobabilityoftheexponentialdistributionfunctionisft=λe-λt.lErlangBmodelOneofthemostimportantqueueingmodelsistheErlangBmodel(i.e.,M/M/n/n).ItassumesthatthearrivalsfollowaPoissonpr
6、ocessandhaveafinitenservers.InErlangBmodel,itassumesthatthearrivalcustomersareblockedandclearedwhenalltheserversarebusy.TheblockedprobabilityofaErlangBmodelisgivenbythefamousErlangBformula,wherenisthenumberofserversandA=λ/μistheofferedloadinErlangs,λisthearrivalratea
7、nd1/μistheaverageservicetime.Formula(1.1)ishardtocalculatedirectlyfromitsrightsidewhennandAarelarge.However,itiseasytocalculateitusingthefollowingiterativescheme:lErlangCmodelTheErlangdelaymodel(M/M/n)issimilartoErlangBmodel,exceptthat文案大全实用标准nowitassumesthatthearriv
8、alcustomersarewaitinginaqueueforaservertobecomeavailablewithoutconsideringthelengthofthequeue.Theprobabilityofblocking(alltheserver
