Strong stability in a $G/M/1$ queueing system

Abstract

In this paper, we study the strong stability of the stationary distribution of the imbedded Markov chain in the $G/M/1$ queueing system, after perturbation of the service law (see Aissani, 1990, and Kartashov, 1981). We show that under some hypotheses, the characteristics of the $G/G/1$ queueing system can be approximated by the corresponding characteristics of the $G/M/1$ system. After clarifying the approximation conditions, we obtain the stability inequalities by exactly computing the constants.