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On the ergodicity of networks of ·/GI/1/N queues

Published online by Cambridge University Press:  01 July 2016

Panagiotis Konstantopoulos  and
Jean Walrand
Panagiotis Konstantopoulos*
Affiliation:
University of California, Berkeley
Jean Walrand*
Affiliation:
University of California, Berkeley
*
∗Present address: INRIA, Unité de Recherche Sophia-Antipolis, 2004 Route des Lucioles, 06565 Valbonne Cedex, France.
∗∗Postal address: Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA 94720, USA.
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Abstract

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In this paper we consider a network of ·/GI/1/N queues with finite-length buffers. A suitable Markov process for the time-evolution of this system is defined. This process is subsequently shown to be ergodic under the conditions of Borovkov (1987).

Keywords

QUEUEING NETWORKSREGENERATIVE PROCESSES
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 22 , Issue 1 , March 1990 , pp. 263 - 267
Copyright
Copyright © Applied Probability Trust 1990 

References

Asmussen, S. (1987) Applied Probability and Queues. Wiley, New York.Google Scholar
Borovkov, A. A. (1987) Limit theorems for queueing networks I. Theory Prob. Appl. 31, 413–427.Google Scholar
Feller, W. (1971) An Introduction to Probability Theory, Vol. II. Wiley, New York.Google Scholar
Gnedenko, B. and Kovalenko, I. N. (1968) An Introduction to Queueing Theory. Israel Program for Scientific Translations, Jerusalem.Google Scholar
Konstantopoulos, P. and Walrand, J. (1988) Ergodicity of networks with blocking. Proc. 27th CDC. Google Scholar
Sigman, K. (1989) Notes on the stability of closed queueing networks. J. Appl. Prob. 26, 678–682.Google Scholar
Walrand, J. (1988) An Introduction to Queueing Networks. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
Whitt, W. (1980) Continuity of generalized semi-Markov processes. Math. Operat. Res. 5, 494–501.CrossRefGoogle Scholar