Networks of queues and the method of stages

In a recent article, Kelly [4] has been able to exhibit interesting equilibrium properties for a wide class of ‘quasi-reversible’ queue networks. The assumption of quasi-reversibility puts restrictions on queue discipline, but not on the distributions of the service requirements of customers: howeve...

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Bibliographic Details
Published in:Advances in applied probability 1976-09, Vol.8 (3), p.584-591
Main Author: Barbour, Andrew D.
Format: Article
Language:English
Subjects:
Markov chains
Markov processes
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Summary:In a recent article, Kelly [4] has been able to exhibit interesting equilibrium properties for a wide class of ‘quasi-reversible’ queue networks. The assumption of quasi-reversibility puts restrictions on queue discipline, but not on the distributions of the service requirements of customers: however, because of the method of proof he employed, Kelly was forced to impose the condition that the service requirements were finite mixtures of gamma distributions. The form of the results he obtained led him to conjecture that this condition was in fact unnecessary, as is shown to be the case in this paper. The method used to prove the conjecture is of potentially wide application, in problems where the ‘method of stages' leads to useful simplification.
ISSN:0001-8678
1475-6064
DOI:10.2307/1426145