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

  • Richard J. Boucherie (a1) and Nico M. Van DIJK (a1)

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.

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Corresponding author

Postal address for both authors: Faculteit der Economische Wetenschappen en Econometrie, Vrije Universiteit, de Boelelaan 1105, 1081 HV Amsterdam, The Netherlands.

References

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Keywords

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

  • Richard J. Boucherie (a1) and Nico M. Van DIJK (a1)

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