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Product forms for queueing networks with state-dependent multiple job transitions

Published online by Cambridge University Press:  01 July 2016

Richard J. Boucherie  and
Nico M. Van DIJK
Richard J. Boucherie*
Affiliation:
Free University, Amsterdam
Nico M. Van DIJK*
Affiliation:
Free University, Amsterdam
*
∗Postal address for both authors: Faculteit der Economische Wetenschappen en Econometrie, Vrije Universiteit, de Boelelaan 1105, 1081 HV Amsterdam, The Netherlands.
∗Postal address for both authors: Faculteit der Economische Wetenschappen en Econometrie, Vrije Universiteit, de Boelelaan 1105, 1081 HV Amsterdam, The Netherlands.
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Abstract

A general framework of continuous-time queueing networks is studied with simultaneous state dependent service completions such as due to concurrent servicing or discrete-time slotting and with state dependent batch routings such as most typically modelling blocking. By using a key notion of group-local-balance, necessary and sufficient conditions are given for the stationary distribution to be of product form. These conditions and a constructive computation of the product form are based upon merely local solutions of the group-local-balance equations which can usually be solved explicitly for concrete networks. Moreover, a decomposition theorem is presented to separate service and routing conditions. General batch service and batch routing examples yielding a product form are hereby concluded. As illustrated by various examples, known results on both discrete- and continuous-time queueing networks are unified and extended.

Keywords

DISCRETE-TIME QUEUEING NETWORKBATCH SERVICEBATCH ROUTINGBLOCKINGGROUP-LOCAL-BALANCE
Type
Research Article
Information
Advances in Applied Probability , Volume 23 , Issue 1 , March 1991 , pp. 152 - 187
Copyright
Copyright © Applied Probability Trust 1991 

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