Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-10T17:27:01.862Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

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

References

Foster, F.G. (1953) On the stochastic matrices associated with certain queueing processes. Ann. Math. Statist. 24, 355–360.CrossRefGoogle Scholar
Kingman, J. F. C. (1961) The ergodic behaviour of random walks. Biometrika 48, 391–396.Google Scholar
Kushner, H. (1971) Introduction to Stochastic Control. Holt, Rinehart and Winston, New York.Google Scholar
Lippman, S. A. (1975) Applying a new device in the optimization of exponential queueing systems. Operat. Res. 23, 687–710.CrossRefGoogle Scholar
Marlin, P. G. (1973) On the ergodic theory of Markov chains. Operat. Res. 21, 617–622.CrossRefGoogle Scholar
Pakes, A. G. (1969) Some conditions of ergodicity and recurrence of Markov chains. Operat. Res. 17, 1058–1061.CrossRefGoogle Scholar
Rosberg, Z. (1978) Service Policies in a Queueing Network with Exponential Service Stations (in Hebrew). Ph.D. Thesis, The Hebrew University of Jerusalem.Google Scholar