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Strong stability in a Jackson queueing network

Authors: O. Lekadir and D. Aissani
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 77 (2007).
Journal: Theor. Probability and Math. Statist. 77 (2008), 107-119
MSC (2000): Primary 60K20, 60K25
Published electronically: January 16, 2009
MathSciNet review: 2432775
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Abstract: Non-product networks are extremely difficult to analyze, so they are often solved by approximate methods. However, it is indispensable to delimit the domain wherever these approximations are justified. Our goal in this paper is to prove the applicability of the strong stability method to the queueing networks in order to be able to approximate non-product form networks by product ones. Therefore, we established the strong stability of a Jackson network $ M/M/1\to M/M/1$ (ideal model) under perturbations of the service time distribution in the first station of a non-product network $ M/GI/1\to GI/M/1$ (real model).

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Additional Information

O. Lekadir
Affiliation: LAMOS Laboratory, University of Bejaia 06000, Algeria

D. Aissani
Affiliation: LAMOS Laboratory, University of Bejaia 06000, Algeria

Keywords: Queueing networks, strong stability, product form, Jackson networks, Markov chain, perturbation
Received by editor(s): February 10, 2006
Published electronically: January 16, 2009
Article copyright: © Copyright 2009 American Mathematical Society

American Mathematical Society