HEAVY TRAFFIC LIMIT THEOREMS IN FLUID BUFFER MODELS-中国期刊网

摘要 AfluidbuffermodelwithMarkovmodulatedinput-outputratesisconsidered.Whentrafficintensityisnearitscriticalvalue,thesystemisknownasinheavytraffic.Itisshownthatasuitablyscaledsequenceoftheequilibriumbuffercontentshasaweakordistributionallimitunderheavytrafficconditions.ThisweaklimitisafunctionalofadiffusionprocessdeterminedbytheMarkovchainmodulatingtheinputandoutputrates.Thefirstpassagetimeofthereflectedprocessisexamined.ItisshownthatthemeanfirstpassagetimecanbeobtainedviaasolutionofaDirichletproblem.ThenthetransitiondensityofthereflectedprocessisderivedbysolvingtheKolmogorovforwardequationwithaNeumannboundarycondition.Furthermore,whenthefastchangingpartofthegeneratoroftheMarkovchainisaconstantmatrix,therepresentationoftheprobabilitydistributionofthereflectedprocessisderived.Upperandlowerboundsoftheprobabilitydistributionarealsoobtainedbymeansofasymptoticexpansionsofstandardnormaldistribution.

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HEAVY TRAFFIC LIMIT THEOREMS IN FLUID BUFFER MODELS

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HEAVY TRAFFIC LIMIT THEOREMS IN FLUID BUFFER MODELS

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