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1、TechnicalReportIC/2004/53http://lcawww.epfl.ch/Publications/LeBoudec/LeBoudecV04.pdfUnderstandtheSimulationofMobilityModelswithPalmCalculusJean-YvesLeBoudecJune28,2004AbstractThesimulationofmobilitymodelssuchastherandomwaypointoftencausesubtleprob-lems,forexamplethedecayofaveragespeedasthesi
2、mulationprogresses,adifferencebe-tweenthelongtermdistributionofnodesandtheinitialone,andsometimestheinstabilityofthemodel.Allofthishastodowithtimeaveragesversuseventaverages.Thisisawellun-derstood,butlittleknowntopic,calledPalmcalculus.Inthispaperwerstgiveaveryshort,easytograspbackgroundonP
3、almcalculus.Thenweapplyittotherandomwaypointmodelandvariants(withpausetime,randomwalk).Weshowhowtosimplyobtainthestationarydistributionofnodesandspeeds,onaconnected(possiblynonconvex)area.Wealsoshowhowtoperformaperfect(i.e.transientfree)simulationwithoutcomputingcomplicatedinte-grals.Last,we
4、analyzedecayandexplainitaseitherconvergencetosteadystateorlackofconvergence.Keywords:MobilityModel,RandomWaypoint,RandomWalk,PalmCalculus,PerfectSimula-tion.1IntroductionThispaperisatutorialabouttherandomwaypointmodelandPalmcalculus.Thesimulationoftherandomwaypointmodelposesasurprisingnumber
5、ofchallenges,suchas:“Unfortunately,thevastmajorityofmobilitymodels[...]sufferfromdecay;averagespeeddecreasesuntilconvergingtosomelong-termaverage.Suchdecayprovidesanunsoundbasisforsimulationstudiesthatcollectresultsaveragedovertime,complicatingtheexperi-mentalprocess”[13].“Therandomwaypoin
6、tmodelisconsideredharmful”[12].The“harmfulness”ofrandomwaypointcanbeattributedtotheuniformselectionofspeedovertheinterval[vmin;vmax],withvmin=0.Takingvmin>0solvestheproblem.1Simulationofsomerandomwaypointmodelscanbestartedinsteady-state[7,10]Thedistributionofnodesisnotuniform[4]Thesequesti
7、onshavebeenaddressedinanad-hocfashionintheliterature.Thederivationsinvolvelongandcomplexcomputations,leavingthereaderwithlittleunderstandingofthe“why”.OurstartingpointistheobservationthatallofthiscanbeveryeasilyunderstoodwithalittlebitofPalmcalculu
