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A positive recurrence criterion associated with multidimensional queueing processes

Published online by Cambridge University Press:  14 July 2016

Zvi Rosberg
Zvi Rosberg*
Affiliation:
University of Illinois
*
∗Postal address: Department of Business Administration, University of Illinois at Urbana-Champaign, 350 Commerce Building (West), Urbana, IL 61801, U.S.A.
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Abstract

A criterion is given for positive recurrence of a multidimensional, aperiodic, irreducible Markov chain with a denumerable state space. This criterion extends to the multidimensional case Foster's one-dimensional criterion. The multidimensional criterion consists of several conditions, one for each coordinate of the process. The usefulness of this criterion is shown through a queueing network example.

Keywords

ERGODICITYMARKOV CHAINQUEUEING NETWORK
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 3 , September 1980 , pp. 790 - 801
Copyright
Copyright © Applied Probability Trust 1980 

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Footnotes

This research was done while the author was visiting at C.O.R.E., Université de Louvain.

References

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