A fluid model for a relay node in an ad hoc network..the case of heavy-tailed input .pdf

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1、MathMethOperRes(2009)70:357384DOI10.1007/s00186-008-0272-3ORIGINALARTICLEAfluidmodelforarelaynodeinanadhocnetwork:thecaseofheavy-tailedinputR.Bekker·M.MandjesReceived:4September2007/Revised:25August2008/Publishedonline:7November2008©TheAuthor(s)2008.Thisarticleispublishedwithopenaccessat

2、Springerlink.comAbstractRelaynodesinanadhocnetworkcanbemodelledasfluidqueues,inwhichtheavailableservicecapacityissharedbytheinputandoutput.Inthispapersucharelaynodeisconsidered;jobsarriveaccordingtoaPoissonprocessandbringalongarandomamountofwork.Thetotaltransmissioncapacityisfairlyshared

3、,meaningthat,whennjobsarepresent,eachjobtransmitstrafficintothequeueatrate1/(n+1)whilethequeueisdrainedatthesamerateof1/(n+1).Wherepreviousstudiesmainlyconcentratedonthecaseofexponentiallydistributedjobsizes,thepresentpaperaddressesregularlyvaryingjobs.Thefocusliesonthetailasymptoticsoft

4、hesojourntimeS.Usingsample-patharguments,itisproventhatP{S>x}behavesroughlyastheresidualjobsize,i.e.,ifthejobsizesareregularlyvaryingofindex−ν,thetailofSisregularlyvaryingofindex1−ν.Inaddition,weaddressthetailPartoftheresearchwasconductedwhileR.BekkerwasaffiliatedtoCWI.HansvandenBerg(Tel

5、ecomICT)isacknowledgedforbringingthismodelunderourattention.R.Bekker(B)DepartmentofMathematics,VrijeUniversiteit,DeBoelelaan1081a,1081HVAmsterdam,TheNetherlandse-mail:rbekker@few.vu.nlM.MandjesKorteweg-deVriesInstituteforMathematics,PlantageMuidergracht24,1018TVAmsterdam,TheNetherlandsM

6、.MandjesCWI,Amsterdam,TheNetherlandsM.MandjesEURANDOM,Eindhoven,TheNetherlandse-mail:M.R.H.mandjes@uva.nl123358R.Bekker,M.Mandjesasymptoticsofotherperformancemetrics,suchastheworkloadinthequeue,theflowtransfertimeandthequeueingdelay.KeywordsQueueing·Asymptotics·Regularvariation·Adhocnetw

7、orks1IntroductionAdhocnetworksareself-configuringnetworksofmobilerouters,connectedbywire-lesslinks.Theyenableinfrastructure-freecommunication:nofixedequipmentisneeded,butinsteadeachclientactsasahub.Wheninformationneedstobetrans-mittedacrossthenetwork,itissentfromthesendertotherec