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Notes on the stability of closed queueing networks

Published online by Cambridge University Press:  14 July 2016

Karl Sigman
Karl Sigman*
Affiliation:
Columbia University
*
∗Postal address: Department of Industrial Engineering and Operations Research, Center For Telecommunications Research (CTR), Columbia University, Mudd Building, New York, NY 10027, USA.
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Abstract

A new proof of the stability of closed Jackson-type queueing networks (with general service-time distributions) is given and sufficient conditions are given for obtaining Cesaro, weak and total variation convergence of the continuous-time joint queue length and residual service-time process to a limiting distribution. The result weakens the sufficient conditions (for stability) of Borovkov (1986) by allowing more general service-time distributions.

Keywords

CLOSED NETWORKCONVERGENCE
Type
Short Communications
Information
Journal of Applied Probability , Volume 26 , Issue 3 , September 1989 , pp. 678 - 682
Copyright
Copyright © Applied Probability Trust 1989 

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References

[1] Asmussen, S. (1987) Applied Probability and Queues. Wiley, New York.Google Scholar
[2] Borovkov, A. A. (1986) Limit theorems for queueing networks. I. Theory Prob. Appl. 31, 413–427.CrossRefGoogle Scholar
[3] Borovkov, A. A. (1988) Limit theorems for queueing networks. II. Theory Prob. Appl. 32, 257–272.Google Scholar
[4] Feller, W. (1971) An Introduction to Probability Theory and its Applications, II, 2nd edn. Wiley, New York.Google Scholar
[5] Jackson, J. R. (1963) Jobshop-like queueing systems. Management Sci. 10, 131–142.CrossRefGoogle Scholar
[6] Wolff, R. (1989) Stochastic Modeling and the Theory of Queues. Prentice Hall, Englewood Cliffs, NJ.Google Scholar

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