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

Author(s): Mustapha Benaouicha; Djamil Aissani
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, vipusk 71 (2004).
Journal: Theor. Probability and Math. Statist. No. 71 (2005), 25-36.
MSC (2000): Primary 60K25, 68M20, 90B22
Posted: December 28, 2005
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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.

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D. Aissani and N. V. Kartashov, Ergodicity and stability of Markov chains with respect to operator topology in the space of transition kernels, Dokl. Akad. Nauk Ukr. SSR, ser. A 11 (1983), 3-5. MR 0728475 (85c:60110)

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D. Aissani and N. V. Kartashov, Strong stability of the imbedded Markov chain in an $ M/G/1$ system, Theor. Probab. Math. Statist. 29 (1984), 1-5. MR 0727097 (85d:60167)

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J. Banks, J. S. Carson, and B. L. Nelson, Discrete-Event System Simulation, Prentice Hall, New Jersey, 1996.

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L. Kleinrock, Queueing Systems, vols. 1 and 2, John Wiley and Sons, 1976.

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Additional Information:

Mustapha Benaouicha
Affiliation: Laboratory of Modelization and Optimization of Systems, Faculty of Sciences and Engineer Sciences, University of Béjaia, 06000, Algeria

Djamil Aissani
Affiliation: Laboratory of Modelization and Optimization of Systems, Faculty of Sciences and Engineer Sciences, University of Béjaia, 06000, Algeria
Email: lamos_bejaia@hotmail.com

DOI: 10.1090/S0094-9000-05-00645-9
PII: S 0094-9000(05)00645-9
Keywords: Queueing systems, strong stability, uniform ergodicity, perturbations, stability inequalities
Received by editor(s): 30/JUL/2003
Posted: December 28, 2005
Copyright of article: Copyright 2005, American Mathematical Society

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