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Insensitivity of processes with interruptions

Published online by Cambridge University Press:  14 July 2016

W. Henderson  and
P. Taylor
W. Henderson*
Affiliation:
University of Adelaide
P. Taylor*
Affiliation:
University of Western Australia
*
∗ Postal address: Applied Mathematics Department, The University of Adelaide, P.O. Box 498, Adelaide, SA 5001, Australia.
∗∗ Postal address: Mathematics Department, The University of Western Australia, Nedlands, WA 6009, Australia.
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Abstract

The theory of insensitivity within generalised semi-Markov processes is extended to cover classes of models in which the generally distributed lifetimes can be terminated prematurely by the deaths of negative exponentially distributed lifetimes. As a consequence of this approach it is shown that there exist classes of processes which are insensitive with respect to characteristics of the general distributions other than the mean. Two examples are given. The first is an analysis of networks of queues in which the generally distributed service times can be interrupted with resulting changes in routing probabilities. The second is a model for the effect of disturbances on the evolution of a vegetation community.

Keywords

GENERALISED SEMI-MARKOV PROCESSESPARTIAL BALANCEPRODUCT FORM
Type
Research Papers
Information
Journal of Applied Probability , Volume 26 , Issue 2 , June 1989 , pp. 242 - 258
Copyright
Copyright © Applied Probability Trust 1989 

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