b n + a n+1 gamma c n+1)

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1、SubexponentialLossRatesinaGI/GI/1QueuewithApplicationsPredragR.JelenkovicDepartmentofElectricalEngineeringColumbiaUniversityNewYork,NY10027AbstractConsiderasingleserverqueuewithi.i.d.arrivalandserviceprocesses,fA;A;n1gandnBfC;C;n1g,respectively,andnitebuerB.ThequeuecontentprocessfQ;n0gisre-n

2、nBB++cursivelydenedasQ=min((Q+A?C);B),q=max(0;q).WhenE(A?C)<0,n+1n+1nn+1andAhasasubexponentialdistribution,weshowthatthestationaryexpectedlossrateforthisqueueB+E(Q+A?C?B)hasthefollowingexplicitasymptoticcharacterizationn+1n+1nB++E(Q+A?C?B)E(A?B)asB!1;n+1n+1nindependentlyoftheserverprocessC.nFora

3、 uidqueuewithcapacityc,M/G/1arrivalprocessa,characterizedbyintermediatelytonBregularlyvaryingOnperiods,thatarrivewithPoissonrate,theaveragelossratesatiseslossBon+E(?B)asB!1;losswhere=r+?c,=Ea

4、tionsisveriedwithextensivenumericalandsimulationexperiments.Theseexplicitformulashavepotentialapplicationindesigningcommunicationnetworksthatwillcarrytracwithlong-tailedcharacteristics,e.g.,Internetdataservices.Keywords:Long-tailedtracmodels;Subexponentialdistributions;Long-rangedependency;Net-

5、workmultiplexer;Finitebuerqueue;Fluid owqueue;M/G/1process.QueueingSystems,SpecialIssueonLong-TailedDistributions,1999,toappear.1IntroductionAnincreasingbodyofliteratureonstatisticaldataanalysishasdemonstratedthepresenceoflong-tailed/subexponentialcharacteristicsincommunicationnetworktracstreams

6、.Earlydiscoveriesonthelong-tailednatureofEthernettracwasreportedin[32].Long-tailedcharacteristicsofthescenelengthdistributionofMPEGvideostreamswereexploredin[25,29].TheimplicationsoftransportingInternetdataapplicationsoverthetraditionalPublicSwitchedTelephoneNetworkwereinvestigatedin[22].Theseemp

7、iricalndingshaveencouragedtheoreticaldevelopmentsinthemodelingandanalysisoflong-tailed(heavy-tailed)phenomena.Inthisareatherehavebeentwobasicapproaches:self-similarprocessesand uidrenewalmodelswithlong-tailedren