Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 536982, 13 pages
http://dx.doi.org/10.1155/2012/536982
Research Article

Stochastic Approximations and Monotonicity of a Single Server Feedback Retrial Queue

Mohamed Boualem,1 Natalia Djellab,2 and Djamil Aïssani1

1Laboratory of Modeling and Optimization of Systems, University of Béjaïa, Béjaïa 06000, Algeria
2Department of Mathematics, University of Annaba, Annaba 23000, Algeria

Received 30 October 2011; Accepted 16 January 2012

Academic Editor: M. D. S. Aliyu

Copyright © 2012 Mohamed Boualem et al. 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

This paper focuses on stochastic comparison of the Markov chains to derive some qualitative approximations for an 𝑀 / 𝐺 / 1 retrial queue with a Bernoulli feedback. The main objective is to use stochastic ordering techniques to establish various monotonicity results with respect to arrival rates, service time distributions, and retrial parameters.