简介:AfluidbuffermodelwithMarkovmodulatedinput-outputratesisconsidered.Whentrafficintensityisnearitscriticalvalue,thesystemisknownasinheavytraffic.Itisshownthatasuitablyscaledsequenceoftheequilibriumbuffercontentshasaweakordistributionallimitunderheavytrafficconditions.ThisweaklimitisafunctionalofadiffusionprocessdeterminedbytheMarkovchainmodulatingtheinputandoutputrates.Thefirstpassagetimeofthereflectedprocessisexamined.ItisshownthatthemeanfirstpassagetimecanbeobtainedviaasolutionofaDirichletproblem.ThenthetransitiondensityofthereflectedprocessisderivedbysolvingtheKolmogorovforwardequationwithaNeumannboundarycondition.Furthermore,whenthefastchangingpartofthegeneratoroftheMarkovchainisaconstantmatrix,therepresentationoftheprobabilitydistributionofthereflectedprocessisderived.Upperandlowerboundsoftheprobabilitydistributionarealsoobtainedbymeansofasymptoticexpansionsofstandardnormaldistribution.
简介:LetFbeafieldofcharacteristiczero.Wn=F[t(+1/2),t(+1/2),...,t(+1/n)]δ/δt1+...+F[t(+1/2),t(+1/2),...,t(+1/n)]δ/δtnistheWittalgebraoverF,Wn+=F[t1,t2...,tn]δ/δt+...+F[t1,t2...,tn]δ/δtnisLieshbalgebraofWn.ItiswellknownbothWnandWn+aresimpleinfinitedimensionalLiealgebra.InZhao'spaper,itwasconjecturedthatEnd(Wn^+)-{0}=Aut(Wn^+)anditwasprovedthatthevalidityofthisconjectureimpliesthevalidityofthewell-knownJacobianconjecture.Inthisshortnote,wechecktheconjectureaboveforn=1.WeshowEnd(W1^+)-{0}=Aut(W1^+).
简介:SIGN-REVERSALPROPERTYFORF-MATRICESANDN-MATRICESXUSong(GraduateSchool,ChinaAcademyofRailwaySciences,Beijing100081,China)Abstra...
简介:Thetraditionaluser-optimalassignmentmodelassumedthatthetrafficinformationisperfect,howerver,thelinktravelcostisAlwaysuncertainorfuzzyinrealsituations.ThepapergivesamodifiedFrank-Wolfemethodforfuzzyuser-optimalroutechoiceproblem.Theshortest-pathalgorithminF-Wissolvedbyanorderrelation(FSA)methodbetweenfuzzytravelcosts.Theresultsofasimpleexampleshowthatthemethodispractical.