Measurement and performance of the strong stability method

Abstract

Abstract. The aim of this paper is to show how to use in practice the strong stability method and also to prove its efficiency. That is why we chose the GI/M/1 model for which there exist analytical results.For this purpose, we first determine the approximation conditions of the characteristics of the GI/M/1 system. Under these conditions, we obtain the stability inequalities of the stationary distribution of the queue size.We finally elaborate upon an algorithm for the approximation of the GI/M/1 system by the M/M/1 system, which calculates the approximation error with an exact computation. In order to give some idea about its application in practice, we give a numerical example.The accuracy of the approach is evaluated by comparison with some known exact results.