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Closed-form solution for the distribution of the total time spent in a subset of states of a homogeneous Markov process during a finite observation period

Published online by Cambridge University Press:  14 July 2016

Bruno Sericola
Bruno Sericola*
Affiliation:
IRISA
*
∗Postal address: IRISA Campus de Beaulieu, 35042 Rennes Cedex, France.
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Abstract

Markov process are widely used to model computer systems. De Souza e Silva and Gail [3] calculated numerically the distribution of the cumulative operational time of repairable computer systems modelled by Markovian processes, that is, the distribution of the total time during which the system was in operation over a finite observation period. An extension of their approach is presented here. A closed-form solution is obtained for the distribution of the total time spent in a subset of states of a homogeneous Markov process during a finite observation period, which is theoretically and numerically interesting. We also give an application of this result to a fault-tolerant system.

Keywords

UNIFORMIZATION TECHNIQUECUMULATIVE OPERATIONAL TIMEREPAIRABLE COMPUTER SYSTEMS
Type
Short Communications
Information
Journal of Applied Probability , Volume 27 , Issue 3 , September 1990 , pp. 713 - 719
Copyright
Copyright © Applied Probability Trust 1990 

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References

[1] Ciardo, G., Marie, R., Sericola, B. and Trivedi, K. (1990) Performability analysis using semi-Markov process. IEEE Trans. Computers Google Scholar
[2] Ross, S. M. (1983) Stochastic Processes. Wiley, New York.Google Scholar
[3] 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