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The superposition of independent discrete Markovian packet streams

Published online by Cambridge University Press:  14 July 2016

Marcel F. Neuts  and
Charles E. M. Pearce
Marcel F. Neuts*
Affiliation:
University of Arizona
Charles E. M. Pearce*
Affiliation:
University of Adelaide
*
∗Postal address: Department of Systems and Industrial Engineering, University of Arizona, Tucson, AZ 85721, USA.
∗∗Postal address: Department of Applied Mathematics, University of Adelaide, Adelaide, SA 5000, Australia.
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Abstract

In a finite, aperiodic, irreducible Markov chain, a visit to some states generates a one; to some others, a zero, while the remaining states are considered silent, in that neither symbol is generated. States during which either a one or a zero is generated are called active states, and sojourns in the set of active states correspond to messages. The output process is called a Markovian packet stream. Informally, a stream is called thin, if the steady-state fraction of time spent in the active states is small and messages are separated by silent periods of long durations. A limit theorem for the superposition of a large number of independent, stochastically identical and appropriately thin Markovian packet streams is obtained. The class of limit processes consists of a family of stationary, integer-valued, discrete-parameter processes of dependent Poisson random variables. Some properties of the limit processes are established.

Keywords

DISCRETE POINT PROCESSESLIMIT PROCESS OF SUPERPOSITION
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 1 , March 1991 , pp. 84 - 95
Copyright
Copyright © Applied Probability Trust 1991 

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Footnotes

This research was supported in part by Grants ECS-8803061 from the National Science Foundation and AFOSR-88–0076 from the Air Force Office of Scientific Research.

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