Séminaire Mathématique de Béjaia
Volume 12, Numéro 1, Pages 37-50
2013-12-31

A Closure Approximation For Some Multi-servers Queue Using The Strong Stability Method



Authors : Cherfaoui Mouloud . Aïssani Djamil . Adjabi Smail .

Abstract

In this paper, we analyzed the stability of the M/M/oo system using the strong stability method, when this system is subject to a little perturbation at the level of the : s arrivals rate (GI/M/oo), s structure (GI/M/s) and s service rate (M/GI/oo). For this purpose, we first determine the approximation conditions of the characteristics of the perturbed queuing system by those of the ideal system. Subsequently, under these conditions, we obtain the stability inequalities of the stationary distribution of the queue size. Finally, to evaluate the performance of the strong stability method, we develop an algorithm that allows us to calculate the different theoretical results obtained and this in order to compare its output results with those of the simulation and to conclude on the quality of the method in question.

Keywords

Multi-servers queue; Infinite-servers queue; Embedded Markov chain ; Perturbation; Strong stability ; Stability inequalities.

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