STOCHASTIC INEQUALITIES FOR M G/1 RETRIAL QUEUES/

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