The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 18, Number 6 (2008), 2156-2178.
A functional central limit theorem for the M/GI/∞ queue
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 of tempered distributions. We then establish the corresponding central limit theorem, that is, the approximation of the normalized error process by a -valued diffusion. We apply these results to provide fluid limits and diffusion approximations for some performance processes.
Ann. Appl. Probab., Volume 18, Number 6 (2008), 2156-2178.
First available in Project Euclid: 26 November 2008
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 60K25: Queueing theory [See also 68M20, 90B22] 60B12: Limit theorems for vector-valued random variables (infinite- dimensional case)
Decreusefond, Laurent; Moyal, Pascal. A functional central limit theorem for the M/GI/∞ queue. Ann. Appl. Probab. 18 (2008), no. 6, 2156--2178. doi:10.1214/08-AAP518. https://projecteuclid.org/euclid.aoap/1227708915