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On the relation between partial balance and insensitivity

Published online by Cambridge University Press:  14 July 2016

D. Fakinos
D. Fakinos*
Affiliation:
University of Thessaloniki
*
∗Postal address: Department of Mathematics, University of Thessaloniki, 54006 Thessaloniki, Greece.
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Abstract

Direct and simple proofs are given of the equivalence of partial balance over a set of states and the fact that the corresponding equilibrium distribution is insensitive to nominal sojourn time in that set and independent of its past and remaining duration. By a counter-example it is shown that solely insensitivity is not sufficient for partial balance.

Keywords

MARKOV PROCESSESSOJOURN TIMES
Type
Short Communications
Information
Journal of Applied Probability , Volume 27 , Issue 2 , June 1990 , pp. 445 - 451
Copyright
Copyright © Applied Probability Trust 1990 

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