Discrete-time Markov chains with two-time scales and a countable state space: limit results and queueing applications
文献类型：期刊论文
| 作者 | Yin, G.1; Zhang, Hanqin2
|
| 刊名 | STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES
 |
| 出版日期 | 2008 |
| 卷号 | 80期号:4页码:339-369 |
| 关键词 | Markov chain singular perturbation queueing network discrete time countable state space |
| ISSN号 | 1744-2508 |
| DOI | 10.1080/17442500701661711 |
| 英文摘要 | This work is concerned with discrete-time Markov chains having countable state spaces and two-time-scale structures. We examine two classes of Markov chains. In the first class, the state space of the Markov chain is nearly decomposable into a finite number of subspaces, each of which has countably many states, whereas in the second class, the state space is nearly decomposable into infinitely many subspaces each of which has finitely many states. Singular perturbation methods and two-time scales are used to alleviate the computational complexity. Under appropriate conditions, for the first class of models, we show that the formulation is 'equivalent' to a continuous-time Markov chain with a finite state space resulting in a substantial reduction of computational burden; for the second class of models, a similar 'equivalence' is established. These results are obtained using asymptotic expansions of probability vectors and transition matrices, and properties of aggregated processes. Moreover, we prove that suitably scaled sequences of occupation measures converge weakly to switching diffusion processes. An application to queueing networks is also presented. |
| 资助项目 | National Science Foundation[DMS-0603287] ; National Security Agency[MSPF-068-029] ; National Natural Sciences Foundation of China ; Chinese Academy of Sciences |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000207633000003 |
| 出版者 | TAYLOR & FRANCIS LTD |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/6605]  |
| 专题 | 应用数学研究所 |
| 通讯作者 | Yin, G. |
| 作者单位 | 1.Wayne State Univ, Dept Math, Detroit, MI 48202 USA 2.Acad Sinica, Inst Appl Math, Acad Math & Syst Sci, Beijing 100080, Peoples R China |
| 推荐引用方式 GB/T 7714 | Yin, G.,Zhang, Hanqin. Discrete-time Markov chains with two-time scales and a countable state space: limit results and queueing applications[J]. STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES,2008,80(4):339-369. |
| APA | Yin, G.,&Zhang, Hanqin.(2008).Discrete-time Markov chains with two-time scales and a countable state space: limit results and queueing applications.STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES,80(4),339-369. |
| MLA | Yin, G.,et al."Discrete-time Markov chains with two-time scales and a countable state space: limit results and queueing applications".STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES 80.4(2008):339-369. |
入库方式： OAI收割
来源：数学与系统科学研究院
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