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Spatial birth-death processes with multiple changes and applications to batch service networks and clustering processes

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, Postbus 7161, 1007 MC Amsterdam, The Netherlands.
Postal address for both authors: Faculteit der Economische Wetenschappen en Econometrie, Vrije Universiteit, Postbus 7161, 1007 MC Amsterdam, The Netherlands.
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Abstract

Reversible spatial birth-death processes are studied with simultaneous jumps of multi-components. A relationship is established between (i) a product-form solution, (ii) a partial symmetry condition on the jump rates and (iii) a solution of a deterministic concentration equation. Applications studied are reversible networks of queues with batch services and blocking and clustering processes such as those found in polymerization chemistry. As illustrated by examples, known results are hereby unified and extended. An expectation interpretation of the transition rates is included.

Keywords

QUEUEING NETWORKPRODUCT FORMCONCENTRATION EQUATIONSYMMETRY PROPERTY
Type
Research Article
Information
Advances in Applied Probability , Volume 22 , Issue 2 , June 1990 , pp. 433 - 455
Copyright
Copyright © Applied Probability Trust 1990 

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