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Level phase independence for GI/M/1-type Markov chains

Published online by Cambridge University Press:  14 July 2016

Guy Latouche*
Affiliation:
Université Libre de Bruxelles
P. G. Taylor*
Affiliation:
University of Adelaide
*
Postal address: Université Libre de Bruxelles, Département d'Informatique, CP 212, Bd du Triomphe, 1050 Brussels, Belgium. Email address: latouche@ulb.ac.be
∗∗ Postal address: Department of Applied Mathematics, University of Adelaide, South Australia 5005, Australia.

Abstract

GI/M/1-type Markov chains make up a class of two-dimensional Markov chains. One dimension is usually called the level, and the other is often called the phase. Transitions from states in level k are restricted to states in levels less than or equal to k+1. For given transition probabilities in the interior of the state space, we show that it is always possible to define the boundary transition probabilities in such a way that the level and phase are independent under the stationary distribution. We motivate our analysis by first considering the quasi-birth-and-death process special case in which transitions from any state are restricted to states in the same, or adjacent, levels.

Type
Research Papers
Copyright
Copyright © by the Applied Probability Trust 2000 

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