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Tight bounds on the sensitivity of generalised semi-Markov processes with a single generally distributed lifetime

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

A. J. Coyle  and
P. G. Taylor
A. J. Coyle
Affiliation:
University of Adelaide
P. G. Taylor*
Affiliation:
University of Adelaide
*
∗Postal address: Applied Mathematics Department, The University of Adelaide, GPO Box 498, Adelaide, SA 5001, Australia.
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Abstract

There are some generalised semi-Markov processes (GSMP) which are insensitive, that is the value of some performance measures for the system depend only on the mean value of lifetimes and not on their actual distribution. In most cases this is not true and a performance measure can take on a number of values depending on the lifetime distributions. In this paper we present a method for finding tight bounds on the sensitivity of performance measures for the class of GSMPs with a single generally distributed lifetime. Using this method we can find upper and lower bounds for the value of a function of the stationary distribution as the distribution of the general lifetime ranges over a set of distributions with fixed mean. The method is applied to find bounds on the average queue length of the Engset queue and the time congestion in the GI/M/n/n queueing system.

Keywords

SENSITIVITY BOUNDSPERFORMANCE MEASURESQUEUEING SYSTEMS

MSC classification

Primary: 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.)
Secondary: 90B22: Queues and service
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 1 , March 1995 , pp. 63 - 73
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

This work was supported by Australian Research Council Grant A69132151.

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