A functional central limit theorem for the M/GI/∞ queue - Archive ouverte HAL
Article Dans Une Revue The Annals of Applied Probability Année : 2008

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

Laurent Decreusefond

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/∞. 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.

Dates et versions

hal-03294585 , version 1 (21-07-2021)

Identifiants

Citer

Laurent Decreusefond, Pascal Moyal. A functional central limit theorem for the M/GI/∞ queue. The Annals of Applied Probability, 2008, 18 (6), ⟨10.1214/08-AAP518⟩. ⟨hal-03294585⟩
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