Queueing Systems

, Volume 64, Issue 3, pp 227–252

Unreliable M/G/1 retrial queue: monotonicity and comparability


DOI: 10.1007/s11134-009-9158-1

Cite this article as:
Taleb, S. & Aissani, A. Queueing Syst (2010) 64: 227. doi:10.1007/s11134-009-9158-1


In this paper we investigate the monotonicity properties of an unreliable M/G/1 retrial queue using the general theory of stochastic ordering. We show the monotonicity of the transition operator of the embedded Markov chain relative to the strong stochastic ordering and increasing convex ordering. We obtain conditions of comparability of two transition operators and we obtain comparability conditions of the number of customers in the system. Inequalities are derived for the mean characteristics of the busy period, number of customers served during a busy period, number of orbit busy periods and waiting times. Inequalities are also obtained for some probabilities of the steady-state distribution of the server state. An illustrative numerical example is presented.


Stochastic ordering Monotonicity Comparability Ageing distributions Unreliable retrial queue Stationary distribution 

Mathematics Subject Classification (2000)

60E15 60K10 60K25 

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Probability and Statistics, Faculty of MathematicsUniversity of Sciences and Technology Houari Boumediene USTHBAlgiersAlgeria
  2. 2.Department of Computer Sciences, Faculty of Electronics and Computer SciencesUniversity of Sciences and Technology Houari Boumediene USTHBAlgiersAlgeria

Personalised recommendations