HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information

On stochastic recursive equations and infinite server queues

1 MAESTRO - Models for the performance analysis and the control of networks
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : The purpose of this paper is to investigate some performance measures of the discrete time G/G/$\infty$ queue under a general arrival process. We assume more precisely that at each time unit a batch with a random size may arrive, where the sequence of batch sizes need not be i.i.d. All we request is that it would be stationary ergodic and that the service duration has a phase type distribution. Our goal is to obtain explicit expressions for the first two moments of number of customers in steady state. We obtain this by computing the first two moments of some generic stochastic recursive equations that our system satisfies. We then show that these class of recursive equations allow to solve not only the G/PH/$\infty$ queue but also a network of such queues. We finally investigate the process of residual activity time in a G/G/$\infty$ queue under general stationary ergodic assumptions, obtain the unique stationary solution and establish coupling convergence to it from any initial state.
Keywords :
Document type :
Reports
Domain :

Cited literature [1 references]

https://hal.inria.fr/inria-00070782
Contributor : Rapport de Recherche Inria Connect in order to contact the contributor
Submitted on : Friday, May 19, 2006 - 9:36:48 PM
Last modification on : Thursday, January 20, 2022 - 4:19:24 PM
Long-term archiving on: : Sunday, April 4, 2010 - 8:10:14 PM

Identifiers

• HAL Id : inria-00070782, version 1

Citation

Eitan Altman. On stochastic recursive equations and infinite server queues. RR-5211, INRIA. 2004, pp.13. ⟨inria-00070782⟩

Record views