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Connecting internally balanced quasi-reversible Markov processes

Part of: Operations research and management science Special processes Markov processes

Published online by Cambridge University Press:  01 July 2016

W. Henderson ,
C. E. M. Pearce ,
P. K. Pollett  and
P. G. Taylor
W. Henderson*
Affiliation:
University of Adelaide
C. E. M. Pearce*
Affiliation:
University of Adelaide
P. K. Pollett*
Affiliation:
University of Queensland
P. G. Taylor*
Affiliation:
University of Adelaide
*
∗Postal address: Department of Applied Mathematics, The University of Adelaide, GPO Box 498, Adelaide, SA 5001, Australia.
∗Postal address: Department of Applied Mathematics, The University of Adelaide, GPO Box 498, Adelaide, SA 5001, Australia.
∗∗Postal address: Department of Mathematics, The University of Queensland, QLD 4072, Australia.
∗Postal address: Department of Applied Mathematics, The University of Adelaide, GPO Box 498, Adelaide, SA 5001, Australia.
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Abstract

We provide a general framework for interconnecting a collection of quasi-reversible nodes in such a way that the resulting process exhibits a product-form invariant measure. The individual nodes can be quite general, although some degree of internal balance will be assumed. Any of the nodes may possess a feedback mechanism. Indeed, we pay particular attention to a class of feedback queues, characterized by the fact that their state description allows one to maintain a record of the order in which events occur. We also examine in some detail the problem of determining for which values of the arrival rates a node does exhibit quasi-reversibility.

Keywords

NETWORKSCACHE MANAGEMENTLIBRARY MODELS

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.) 90B22: Queues and service
Type
Research Article
Information
Advances in Applied Probability , Volume 24 , Issue 4 , December 1992 , pp. 934 - 959
Copyright
Copyright © Applied Probability Trust 1992 

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Footnotes

Research supported by the Australian Research Council.

References

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