Countable-state-space Markov chains with two time scales and applications to queueing systems

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	Countable-state-space Markov chains with two time scales and applications to queueing systems
	Yin, G ; Zhang, HQ
	2002-09-01
发表期刊	ADVANCES IN APPLIED PROBABILITY
ISSN	0001-8678
卷号	34 期号:3 页码:662-688
摘要	Motivated by various applications in queueing systems, this work is devoted to continuous-time Markov chains with countable state spaces that involve both fast-time scale and slow-time scale with the aim of approximating the time-varying queueing systems by their quasistationary counterparts. Under smoothness conditions on the generators, asymptotic expansions of probability vectors and transition probability matrices are constructed. Uniform error bounds are obtained, and then sequences of occupation measures and their functionals are examined. Mean square error estimates of a sequence of occupation measures are obtained; a scaled sequence of functionals of occupation measures is shown to converge to a Gaussian process with zero mean. The representation of the variance of the limit process is also explicitly given. The results obtained are then applied to treat M(t)/M(t)/1 queues and Markov-modulated fluid buffer models.
关键词	Markov chain singular perturbation countable state space asymptotic expansion occupation measure functional central limit theorem M(t)/M(t)/1 queue fluid model
语种	英语
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000178811500011
出版者	APPLIED PROBABILITY TRUST
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/17691
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, Acad Math & Syst Sci, Inst Appl Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Yin, G,Zhang, HQ. Countable-state-space Markov chains with two time scales and applications to queueing systems[J]. ADVANCES IN APPLIED PROBABILITY,2002,34(3):662-688.
APA	Yin, G,&Zhang, HQ.(2002).Countable-state-space Markov chains with two time scales and applications to queueing systems.ADVANCES IN APPLIED PROBABILITY,34(3),662-688.
MLA	Yin, G,et al."Countable-state-space Markov chains with two time scales and applications to queueing systems".ADVANCES IN APPLIED PROBABILITY 34.3(2002):662-688.