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Measurement and performance of the strong stability method

Author(s): Louiza Bouallouche; Djamil Aïssani
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, vipusk 72 (2005).
Journal: Theor. Probability and Math. Statist. No. 72 (2006), 1-9.
MSC (2000): Primary 60K25, 68M20, 90B22
Posted: August 10, 2006
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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.

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Additional Information:

Louiza Bouallouche
Affiliation: L.A.M.O.S, Laboratory of Modelisation and Optimization of Systems, University of Béjaïa, 06000, Algeria
Email: lamos_bejaia@hotmail.com

Djamil Aïssani
Affiliation: L.A.M.O.S, Laboratory of Modelisation and Optimization of Systems, University of Béjaïa, 06000, Algeria

DOI: 10.1090/S0094-9000-06-00659-4
PII: S 0094-9000(06)00659-4
Keywords: Queueing system, Markov chain, stability, strong stability, performance evaluation, approximation
Received by editor(s): 30/JUL/2003
Posted: August 10, 2006
Copyright of article: Copyright 2006, American Mathematical Society

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