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Insensitivity in processes with zero speeds

Published online by Cambridge University Press:  01 July 2016

P. Taylor
P. Taylor*
Affiliation:
University of Adelaide
*
∗Present address: Department of Mathematics, University of Western Australia, Nedlands, WA 6009, Australia.
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Abstract

Many authors have discussed the equivalence of partial balance and insensitivity in in stochastic processes. When speeds are introduced into a stochastic process there arises a difficulty in proving the necessity of partial balance for insensitivity. Previous authors have overcome this difficulty by assuming that a process has the property of instantaneous attention. This property enforces the requirement that no lifetime can be created in a state in which that lifetime has zero speed.

In this paper it is shown that for processes with a finite state space it is unnecessary to make this assumption provided the notion of partial balance is slightly changed. Thus we give a criterion, analogous to partial balance, which is necessary and sufficient for insensitivity even in processes which do not possess the property of instantaneous attention. When a process does have instantaneous attention this criterion is equivalent to partial balance.

Keywords

PARTIAL BALANCEPRODUCT FORMINSTANTANEOUS ATTENTION
Type
Research Article
Information
Advances in Applied Probability , Volume 21 , Issue 3 , September 1989 , pp. 612 - 628
Copyright
Copyright © Applied Probability Trust 1989 

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