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Realization probability in closed Jackson queueing networks and its application

Published online by Cambridge University Press:  01 July 2016

X. R. Cao
X. R. Cao*
Affiliation:
Harvard University
*
∗Present address: MRO1-1/L26, Digital Equipment Corporation, Marlboro, MA 01752, USA.
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Abstract

Perturbation analysis is a new technique which yields the sensitivities of system performance measures with respect to parameters based on one sample path of a system. This paper provides some theoretical analysis for this method. A new notion, the realization probability of a perturbation in a closed queueing network, is studied. The elasticity of the expected throughput in a closed Jackson network with respect to the mean service times can be expressed in terms of the steady-state probabilities and realization probabilities in a very simple way. The elasticity of the throughput with respect to the mean service times when the service distributions are perturbed to non-exponential distributions can also be obtained using these realization probabilities. It is proved that the sample elasticity of the throughput obtained by perturbation analysis converges to the elasticity of the expected throughput in steady-state both in mean and with probability 1 as the number of customers served goes to This justifies the existing algorithms based on perturbation analysis which efficiently provide the estimates of elasticities in practice.

Keywords

PERTURBATION ANALYSISCLOSED QUEUEING NETWORKSCONVERGENCE PROPERTIES
Type
Research Article
Information
Advances in Applied Probability , Volume 19 , Issue 3 , September 1987 , pp. 708 - 738
Copyright
Copyright © Applied Probability Trust 1987 

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Footnotes

This work was supported in part by the U.S. Office of Naval Contracts under N00014-79-C-0776 and N00014-84-K-0465, the National Science Foundation Grants ECS 82-13680 and CDR-85-001-08.

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