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Some renewal-theoretic investigations in the theory of sojourn times in finite semi-Markov processes

Published online by Cambridge University Press:  14 July 2016

Attila Csenki
Attila Csenki*
Affiliation:
Aston University
*
∗ Postal address: Department of Computer Science and Applied Mathematics, Aston University, Aston Triangle, Birmingham B4 7ET, UK.
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Abstract

In this note, an irreducible semi-Markov process is considered whose finite state space is partitioned into two non-empty sets A and B. Let MB(t) stand for the number of visits of Y to B during the time interval [0, t], t > 0. A renewal argument is used to derive closed-form expressions for the Laplace transform (with respect to t) of a certain family of functions in terms of which the moments of MB(t) are easily expressible. The theory is applied to a small reliability model in conjunction with a Tauberian argument to evaluate the behaviour of the first two moments of MB(t) as t →∞.

Keywords

RENEWAL THEORYLAPLACE TRANSFORMRELIABILITYTAUBERIAN THEOREM
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 4 , December 1991 , pp. 822 - 832
Copyright
Copyright © Applied Probability Trust 1991 

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References

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