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On Poisson traffic processes in discrete-state Markovian systems by applications to queueing theory

Published online by Cambridge University Press:  01 July 2016

Benjamin Melamed
Benjamin Melamed*
Affiliation:
Northwestern University
*
∗Postal address: Department of Industrial Engineering and Management Science, Northwestern University, Evanston, Illinois 60201, U.S.A.
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Abstract

This paper considers a regular Markov process with continuous parameter, countable state space, and stationary transition probabilities, and defines a class of traffic processes over it. The possibility that multiple traffic processes constitute mutually independent Poisson processes is investigated.

A variety of independence conditions on a traffic process and the underlying Markov process are shown to lead to Poisson-related properties; these conditions include weak pointwise independence, and pointwise independence. Some examples of queueing-theoretic applications are given.

For the class of traffic processes considered here in a queueing-theoretic context, Muntz's MM property, Gelenbe and Muntz's notion of completeness, and Kelly's notion of quasi-reversibility are shown to be essentially equivalent to pointwise independence of traffic and state. The relevance of the theory to queueing network decomposition is pointed out.

Keywords

MARKOV PROCESSESTRAFFIC PROCESSESPOISSON PROCESSESQUEUEING THEORYQUEUEING NETWORKSTRAFFIC IN QUEUEING NETWORKSDECOMPOSITION OF QUEUEING NETWORKS
Type
Research Article
Information
Advances in Applied Probability , Volume 11 , Issue 1 , March 1979 , pp. 218 - 239
Copyright
Copyright © Applied Probability Trust 1979 

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Footnotes

This research was supported jointly by the National Science Foundation Grant NSF-ENG-75-20223, Air Force Office of Scientific Research Grant AFOSR-76-2903, and by the Office of Naval Research Contract N00014-75-C-0492 (NR 042-296).

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