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A correspondence between product-form batch-movement queueing networks and single-movement networks

Part of: Operations research and management science Computer system organization Special processes

Published online by Cambridge University Press:  14 July 2016

J. L. Coleman ,
W. Henderson ,
C. E. M. Pearce  and
P. G. Taylor
J. L. Coleman*
Affiliation:
University of Adelaide
W. Henderson*
Affiliation:
University of Adelaide
C. E. M. Pearce*
Affiliation:
University of Adelaide
P. G. Taylor*
Affiliation:
University of Adelaide
*
∗ Postal address: Applied Mathematics Department, University of Adelaide, Adelaide 5005, South Australia.
∗ Postal address: Applied Mathematics Department, University of Adelaide, Adelaide 5005, South Australia.
∗ Postal address: Applied Mathematics Department, University of Adelaide, Adelaide 5005, South Australia.
∗ Postal address: Applied Mathematics Department, University of Adelaide, Adelaide 5005, South Australia.
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Abstract

A number of recent papers have exhibited classes of queueing networks, with batches of customers served and routed through the network, which have generalised product-form equilibrium distributions. In this paper we look at these from a new viewpoint. In particular we show that, under standard assumptions, for a network to possess an equilibrium distribution that factorises into a product form over the nodes of the network for all possible transition rates, it is necessary and sufficient that it be equivalent to a suitably-defined single-movement network. We consider also the form of the state space for such networks.

Keywords

BATCH-MOVEMENT QUEUEING NETWORKSPRODUCT-FORM EQUILIBRIUM DISTRIBUTIONSSTOCHASTIC PETRI NETS

MSC classification

Primary: 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.) 90B22: Queues and service 68M20: Performance evaluation; queueing; scheduling

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 1 , March 1997 , pp. 160 - 175
Copyright
Copyright © Applied Probability Trust 1997 

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