Dimension Reduction for Approximation of Advanced Retrial Queues : Tutorial and Review

Abstract

Retrial queues have been widely used to model the many practical situations arising from telephone systems, telecommunication networks and call centers. An approximation method for a simple Markovian retrial queue by reducing the two dimensional problem to one dimensional problem was presented by Fredericks and Reisner in 1979. The method seems to be a promising approach to approximate the retrial queues with complex structure, but the method has not been attracted a lot of attention for about thirty years. In this paper, we exposit the method in detail and show the usefulness of the method by presenting the recent results for approximating the retrial queues with complex structure such as multiserver retrial queues with phase type distribution of retrial time, impatient customers with general persistent function and/or multiclass customers, etc.