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On First-Come First-Served Versus Random Service Discipline in Multiclass Closed Queueing Networks

Published online by Cambridge University Press:  27 July 2009

Ronald Buitenhek ,
Geert-Jan van Houtum  and
Jan-Kees van Ommeren
Ronald Buitenhek
Affiliation:
Faculty of Mechanical Engineering, University of Twente, 7500 AE Enschede, The Netherlands
Geert-Jan van Houtum
Affiliation:
Faculty of Mechanical Engineering, University of Twente, 7500 AE Enschede, The Netherlands
Jan-Kees van Ommeren
Affiliation:
Faculty of Applied Mathematics, University of Twente, 7500 AE Enschede, The Netherlands
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Abstract

We consider multiclass closed queueing networks. For these networks, a lot of work has been devoted to characterizing and weakening the conditions under which a product-form solution is obtained for the steady-state distribution. From this work, it is known that, under certain conditions, all networks in which each of the stations has either the first-come first-served or the random service discipline lead to the same (product-form expressions for the) steady-state probabilities of the (aggregated) states that for each station and each job class denote the number of jobs in service and the number of jobs in the queue. As a consequence, all these situations also lead to the same throughputs for the different job classes. One of the conditions under which these equivalence results hold states that at each station all job classes must have the same exponential service time distribution. In this paper, it is shown that these equivalence results can be extended to the case with different exponential service times for jobs of different classes, if the network consists of only one single-server or multiserver station. This extension can be made despite of the fact that the network is not a product-form network anymore in that case. The proof is based on the reversibility of the Markov process that is obtained under the random service discipline. By means of a counterexample, it is shown that the extension cannot be made for closed network with two or more stations.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 11 , Issue 3 , July 1997 , pp. 313 - 326
Copyright
Copyright © Cambridge University Press 1997

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