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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

[1] De Souza E Silva, E. and Gail, H. R. (1986) Calculating cumulative operational time distributions of repairable computer systems. IEEE Trans. Computers 35, 322–332.CrossRefGoogle Scholar
[2] Meyer, J. F. (1980) On evaluating the performability of degradable computing systems. IEEE Trans. Computers 29, 720–731.CrossRefGoogle Scholar
[3] Kemeny, J. G. and Snell, J. L. (1976) Finite Markov Chains. Springer-Verlag, New York.Google Scholar
[4] Rubino, G. and Sericola, B. (1989) On weak lumpability in Markov chains. J. Appl. Prob. 26(3).CrossRefGoogle Scholar
[5] Ross, S. M. (1983) Stochastic Processes. Wiley, New York.Google Scholar
[6] Kulkarni, V. G., Nicola, V. F., Smith, R. M. and Trivedi, K. S. (1986) Numerical evaluation of performability and job completion time in repairable fault-tolerant systems. In Proc. IEEE 16th Fault-Tolerant Computing Symposium (Vienna, Austria) Google Scholar