Diffusion approximations for some multiclass queueing networks with FIFO service disciplines

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	Diffusion approximations for some multiclass queueing networks with FIFO service disciplines
	Chen, H ; Zhang, HQ
	2000-11-01
发表期刊	MATHEMATICS OF OPERATIONS RESEARCH
ISSN	0364-765X
卷号	25 期号:4 页码:679-707
摘要	The diffusion approximation is proved for a class of multiclass queueing networks under FIFO service disciplines. Ln addition to the usual assumptions for a heavy traffic limit theorem, a key condition that characterizes this class is that a J x J matrix G, known as the workload contents matrix, has a spectral radius less than unity, where J represents the number of sen ice stations. The (j, l)th component of matrix G can be interpreted as the long-run average amount of future work for station j that is embodied in a unit of immediate work at station l. This class includes, as a special case, the feedforward multiclass queueing network and the Rybko-Stolyar network under FIFO service discipline. A new approach is taken in establishing the diffusion limit theorem. The traditional approach is based on an oblique reflection mapping, but such a mapping is not well defined for the network under consideration. Our approach takes two steps: first establishing the C-tightness of the scaled queueing processes, and then completing the proof for the convergence of the scaled queueing processes by invoking the weak uniqueness for the limiting processes, which are semimartingale reflecting Brownian motions.
关键词	multiclass queueing network diffusion approximations fluid approximations heavy traffic semimartingale reflecting Brownian motion
语种	英语
WOS研究方向	Operations Research & Management Science ; Mathematics
WOS类目	Operations Research & Management Science ; Mathematics, Applied
WOS记录号	WOS:000166210800010
出版者	INST OPERATIONS RESEARCH MANAGEMENT SCIENCES
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/15653
专题	应用数学研究所
通讯作者	Chen, H
作者单位	1.Univ British Columbia, Fac Commerce & Business Adm, Vancouver, BC V5Z 1M9, Canada 2.Acad Sinica, Inst Appl Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Chen, H,Zhang, HQ. Diffusion approximations for some multiclass queueing networks with FIFO service disciplines[J]. MATHEMATICS OF OPERATIONS RESEARCH,2000,25(4):679-707.
APA	Chen, H,&Zhang, HQ.(2000).Diffusion approximations for some multiclass queueing networks with FIFO service disciplines.MATHEMATICS OF OPERATIONS RESEARCH,25(4),679-707.
MLA	Chen, H,et al."Diffusion approximations for some multiclass queueing networks with FIFO service disciplines".MATHEMATICS OF OPERATIONS RESEARCH 25.4(2000):679-707.