HEAVY TRAFFIC LIMIT THEOREMS IN FLUID BUFFER MODELS  

作　　者：YINGang ZHANGHanqin 

机构地区：[1]DepartmentofMathematics,WayneStateUniversity,Detroit,MI48202,USA) [2]InstituteofAppliedMathematics,AcademyofMathematicsandSystemsSciences,ChineseAcademyofSciences,Beijing100080,China

出　　处：《Journal of Systems Science & Complexity》2004年第1期1-15,共15页系统科学与复杂性学报（英文版）

基　　金：The research of this author was supported in part by the National Science Fundation under grant DMS 0304928.The research of this author was supported in part by a Distinguished Young Investigator Grant from the National Natural Sciences Foundation of Chi

摘　　要：A fluid buffer model with Markov modulated input-output rates is considered.When traffic intensity is near its critical value, the system is known as in heavy traffic.It is shown that a suitably scaled sequence of the equilibrium buffer contents has a weakor distributional limit under heavy traffic conditions. This weak limit is a functional of adiffusion process determined by the Markov chain modulating the input and output rates.The first passage time of the reflected process is examined. It is shown that the mean firstpassage time can be obtained via a solution of a Dirichlet problem. Then the transitiondensity of the reflected process is derived by solving the Kolmogorov forward equation witha Neumann boundary condition. Furthermore, when the fast changing part of the generatorof the Markov chain is a constant matrix, the representation of the probability distributionof the reflected process is derived. Upper and lower bounds of the probability distributionare also obtained by means of asymptotic expansions of standard normal distribution.

关 键 词：fluid model markov chain singular perturbation diffusion process 

分 类 号：U491[交通运输工程—交通运输规划与管理]