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Realization factors and sensitivity analysis of queueing networks with state-dependent service rates

Published online by Cambridge University Press:  01 July 2016

Xi-Ren Cao
Xi-Ren Cao*
Affiliation:
Digital Equipment Corporation
*
∗Postal address: Digital Equipment Corporation, MRO1-2/S10, 200 Forest Street, Marlboro, MA 01752, USA.
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Abstract

The paper studies the sensitivity of the throughput with respect to a mean service rate in a closed queueing network with exponentially distributed service requirements and state-dependent service rates. The study is based on perturbation analysis of queueing networks. A new concept, the realization factor of a perturbation, is introduced. The properties of realization factors are discussed, and a set of equations specifying the realization factors are derived. The elasticity of the steady state throughput with respect to a mean service rate equals the product of the steady state probability and the corresponding realization factor. This elasticity can be estimated by applying a perturbation analysis algorithm to a sample path of the system. The sample path elasticity of the throughput with respect to a mean service rate converges with probability 1 to the elasticity of the steady state throughput. The theory provides an analytical method of calculating the throughput sensitivity and justifies the application of perturbation analysis.

Keywords

STEADY STATE PERFORMANCESAMPLE-PATH ELASTICITIESPERTURBATION ANALYSIS
Type
Research Article
Information
Advances in Applied Probability , Volume 22 , Issue 1 , March 1990 , pp. 178 - 210
Copyright
Copyright © Applied Probability Trust 1990 

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Footnotes

This work was initiated when the author was with the Division of Applied Sciences, Harvard University, Cambridge, MA 02138, USA.

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