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Some distribution and moment formulae for the Markov renewal process

Published online by Cambridge University Press:  24 October 2008

A. M. Kshirsagar  and
R. Wysocki
A. M. Kshirsagar
Affiliation:
Southern Methodist University, Dallas, Texas 75222
R. Wysocki
Affiliation:
Southern Methodist University, Dallas, Texas 75222
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Extract

1. Introduction. A Markov Renewal Process (MRP) with m(<∞) states is one which records at each time t, the number of times a system visits each of the m states up to time t, if the system moves from state to state according to a Markov chain with transition probability matrix P0 = [pij] and if the time required for each successive move is a random variable whose distribution function (d.f.) depends on the two states between which the move is made. Thus, if the system moves from state i to state j, the holding time in the state i has Fij(x) as its d.f. (i, j = 1,2, …, m).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 68 , Issue 1 , July 1970 , pp. 159 - 166
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

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