Convergence Of Generalized Truncation Method In Retrial Queues

Abstract

Changwon, Korea у wshin @ changwon. ac. lain many cases, the queue length processes in retrial queues are described by the spatially inhomogeneous Markov chain caused by transitions due to repeated attempts. This lack of homogeneity is one of the causes of analytical complexity of retrial queues and leads to an approximation method. Many authors approximate the original inhomogeneous system by the so-called generalized truncated system in which the retrial rates are restricted to be constant over a given level and the level is enlarged until the satisfactory solution is obtained. However, the rigorous mathematical proofs for the convergence of generalized truncation method are a few and are treated case by case. In this paper, we provide a proof of convergence of the approximation by using the tightness and the stochastic comparison between retrial queues. Some examples are presented to show the usefulness of our approach.