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