Discrete-time Markov chains with two-time scales and a countable state space: limit results and queueing applications

doi:10.1080/17442500701661711

	Discrete-time Markov chains with two-time scales and a countable state space: limit results and queueing applications
	Yin, G.1; Zhang, Hanqin 2
刊名	STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES
	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
出版者	TAYLOR & FRANCIS LTD
WOS记录号	WOS:000207633000003
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/6605]
专题	中国科学院数学与系统科学研究院
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.