A FUNCTIONAL CENTRAL LIMIT THEOREM FOR THE M/GI/∞ QUEUE
成果类型：
Article
署名作者：
Decreusefond, Laurent; Moyal, Pascal
署名单位：
Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); Universite de Technologie de Compiegne
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/08-AAP518
发表日期：
2008
页码：
2156-2178
关键词：
摘要：
In this paper, we present a functional fluid limit theorem and a functional central limit theorem for a queue with an infinity of servers M/GI/infinity. The system is represented by a point-measure valued process keeping track of the remaining processing times of the customers in service. The convergence in law of a sequence of such processes after rescaling is proved by compactness-uniqueness methods, and the deterministic fluid limit is the solution of an integrated equation in the space s' of tempered distributions. We then establish the corresponding central limit theorem. that is, the approximation of the normalized error process by a s'-valued diffusion. We apply these results to provide fluid limits and diffusion approximations for some performance processes.