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

Decreusefond, Laurent; Moyal, Pascal

Decreusefond, Laurent; Moyal, Pascal (2008), A functional central limit theorem for the M/GI/infinity queue, The Annals of Applied Probability, 18, 6, p. 2156-2178. http://dx.doi.org/10.1214/08-AAP518

Type

Article accepté pour publication ou publié

External document link

http://fr.arxiv.org/abs/math/0608258

Date

2008

Journal name

The Annals of Applied Probability

Volume

Number

Publisher

Institute of Mathematical statistics

Pages

2156-2178

Abstract (EN)

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.

Subjects / Keywords

queueing theory; pure delay system; central limit theorem; fluid limit; Measure-valued Markov process