| HEAVY TRAFFIC LIMIT THEOREMS IN FLUID BUFFER MODELS |
| |
| 作者姓名： | YINGang ZHANGHanqin |
| |
| 作者单位： | Department of |
| |
| 基金项目： | 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 e
|
| 关 键 词： | 大流量交通限制理论 流体缓冲模型 Markov链 Dirichlet问题 交通密度 概率分布 |
HEAVY TRAFFIC LIMIT THEOREMS IN FLUID BUFFER MODELS |
| |
| YINGang ZHANGHanqin.HEAVY TRAFFIC LIMIT THEOREMS IN FLUID BUFFER MODELS[J].Journal of Systems Science and Complexity,2004,17(1):1-15. |
| |
| Authors: | YIN Gang |
| |
| Abstract: | 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 weak or distributional limit under heavy traffic conditions. This weak limit is a functional of a diffusion 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 first passage time can be obtained via a solution of a Dirichlet problem. Then the transition density of the reflected process is derived by solving the Kolmogorov forward equation with a Neumann boundary condition. Furthermore, when the fast changing part of the generator of the Markov chain is a constant matrix, the representation of the probability distribution of the reflected process is derived. Upper and lower bounds of the probability distribution are also obtained by means of asymptotic expansions of standard normal distribution. |
| |
| Keywords: | Fluid model Markov chain singular perturbation diffusion process |
| 本文献已被 CNKI 维普 等数据库收录！ |
