Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 54359, 16 pages
doi:10.1155/JAMSA/2006/54359

Stability of retrial queues with versatile retrial policy

Tewfik Kernane1 and Amar Aïssani2

1epartment of Probability and Statistics, Faculty of Mathematics, University of Sciences and Technology Houary Boumediene, Algiers, Algeria
2Faculty of Electronics and Computer Science, University of Sciences and Technology Houary Boumediene, USTHB, BP 32 El-Alia, Algiers 16111, Algeria

Received 19 December 2004; Revised 22 November 2005; Accepted 22 November 2005

Copyright © 2006 Tewfik Kernane and Amar Aïssani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider in this paper the stability of retrial queues with a versatile retrial policy. We obtain sufficient conditions for the stability by the strong coupling convergence to a stationary ergodic regime for various models of retrial queues including a model with two types of customers, a model with breakdowns of the server, a model with negative customers, and a model with batch arrivals. For all the models considered we assume that the service times are general stationary ergodic and interarrival and retrial times are i.i.d. sequences exponentially distributed. For the model with unreliable server we also assume that the repair times are stationary and ergodic and the occurrences of breakdowns follow a Poisson process.