Stochastic inequalities for M/G/1 retrial queues

Authors:
Z. Khalil;G. Falin
Affiliations:
Department of Mathematics and Statistics, Concordia University, 7141 Sherbrooke Str. W., Montreal, Quebec H4B 1R6, Canada;Moscow State University, Moscow, Russian Federation
Venue:
Operations Research Letters
Year:
1994

Citing 1
Cited 2

A survey of retrial queues

Queueing Systems: Theory and Applications - Special issue of queueing systems, theory and applications

Stochastic inequalities for M/G/1 retrial queues with vacations and constant retrial policy

Mathematical and Computer Modelling: An International Journal
Service station factors in monotonicity of retrial queues

Mathematical and Computer Modelling: An International Journal

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Abstract

Consider an M/G/1 retrial queue. The performance characteristics of such a system are available in explicit form; however they are cumbersome (these formulas include integrals of Laplace transform, solutions of functional equations, etc.) In this paper we use the general theory of stochastic orderings to investigate the monotonicity properties of the system relative to the strong stochastic ordering, convex ordering and Laplace ordering. These results imply in particular simple insensitive bounds for the stationary distribution of the number of customers in the system and the mean number of customers served during a busy period.