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

	Countable-state-space Markov chains with two time scales and applications to queueing systems
	Yin, G ; Zhang, HQ
刊名	ADVANCES IN APPLIED PROBABILITY
	2002-09-01
卷号	34 期号:3 页码:662-688
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
ISSN号	0001-8678
英文摘要	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.
WOS研究方向	Mathematics
语种	英语
出版者	APPLIED PROBABILITY TRUST
WOS记录号	WOS:000178811500011
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/17690]
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, 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.