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Calculation of sensitivities of throughputs and realization probabilities in closed queueing networks with finite buffer capacities

Published online by Cambridge University Press:  01 July 2016

Xi-Ren Cao
Xi-Ren Cao*
Affiliation:
Digital Equipment Corporation
*
∗Postal address: Digital Equipment Corporation, MRO1–1/L26, 200 Forest Street, Marlboro, MA 01752, USA.
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Abstract

Perturbation analysis is an efficient approach to estimating the sensitivities of the performance measures of a queueing network. A new notion, called the realization probability, provides an alternative way of calculating the sensitivity of the system throughput with respect to mean service times in closed Jackson networks with single class customers and single server nodes (Cao (1987a)). This paper extends the above results to systems with finite buffer sizes. It is proved that in an indecomposable network with finite buffer sizes a perturbation will, with probability 1, be realized or lost. For systems in which no server can directly block more than one server simultaneously, the elasticity of the expected throughput can be expressed in terms of the steady state probability and the realization probability in a simple manner. The elasticity of the throughput when each customer’s service time changes by the same amount can also be calculated. These results provide some theoretical background for perturbation analysis and clarify some important issues in this area.

Keywords

PERTURBATION ANALYSISFINITE BUFFER SIZE
Type
Research Article
Information
Advances in Applied Probability , Volume 21 , Issue 1 , March 1989 , pp. 181 - 206
Copyright
Copyright © Applied Probability Trust 1989 

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Footnotes

This work was supported in part by the U.S. Office of Naval Research Contracts N00014–79-C-0776 and N00014–84-K-0465, and by the National Science Foundation Grants ECS 82–13680 and CDR-85–001–08. This work was mainly done when the author was with the Division of Applied Sciences, Harvard University, Cambridge, MA 02138.

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