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Article Dans Une Revue The Annals of Applied Probability Année : 2008

A functional central limit theorem for the M/GI/infinity queue

Résumé

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/$\infty$. 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 is proved by compactness-uniqueness methods, and the deterministic fluid limit is the solution of an integrated equation in the space $\S^{\prime}$ of tempered distributions. We then establish the corresponding central limit theorem, i.e. the approximation of the normalized error process by a $\S^{\prime}$-valued diffusion.

Dates et versions

hal-00160001 , version 1 (04-07-2007)

Identifiants

Citer

Laurent Decreusefond, Pascal Moyal. A functional central limit theorem for the M/GI/infinity queue. The Annals of Applied Probability, 2008, 18 (6), pp.2156-2178. ⟨10.1214/08-AAP518⟩. ⟨hal-00160001⟩
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