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 the authors 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.
