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Sojourn times in finite Markov processes

Published online by Cambridge University Press:  14 July 2016

Gerardo Rubino  and
Bruno Sericola
Gerardo Rubino
Affiliation:
IRISA
Bruno Sericola*
Affiliation:
IRISA
*
∗ Postal address for both authors: IRISA, Campus de Beaulieu, 35042 Rennes Cedex, France.
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Abstract

Sojourn times of Markov processes in subsets of the finite state space are considered. We give a closed form of the distribution of the nth sojourn time in a given subset of states. The asymptotic behaviour of this distribution when time goes to infinity is analyzed, in the discrete time and the continuous-time cases. We consider the usually pseudo-aggregated Markov process canonically constructed from the previous one by collapsing the states of each subset of a given partition. The relation between limits of moments of the sojourn time distributions in the original Markov process and the moments of the corresponding holding times of the pseudo-aggregated one is also studied.

Keywords

AGGREGATIONTRANSIENT ANALYSISPERFORMANCE EVALUATIONRELIABILITY MODELING
Type
Research Papers
Information
Journal of Applied Probability , Volume 26 , Issue 4 , December 1989 , pp. 744 - 756
Copyright
Copyright © Applied Probability Trust 1989 

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References

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