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