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The insensitivity of stationary probabilities in networks of queues

Published online by Cambridge University Press:  01 July 2016

R. Schassberger
R. Schassberger*
Affiliation:
University of Calgary
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Abstract

The stationary probabilities for certain networks of queues as defined by Kelly [4] were recently shown by Barbour [1] to depend on the service-time distributions involved only through their means. This type of insensitivity has been studied by König and Jansen [5] for a general class of stochastic processes. Kelly's networks yield special cases of such processes. We point this out in the present paper, thus shedding new light on the insensitivity phenomenon observed in these networks and its connection with the phenomenon of local balance. As a consequence of our recent study [8] we also obtain a new insensitivity result for these networks.

Keywords

GENERALIZED SEMI-MARKOV PROCESSESINSENSITIVITYLOCAL BALANCENETWORKS OF QUEUES
Type
Research Article
Information
Advances in Applied Probability , Volume 10 , Issue 4 , December 1978 , pp. 906 - 912
Copyright
Copyright © Applied Probability Trust 1978 

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References

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