Abstract
The following results are obtained in this paper: (1) The probability generating function of the simultaneous distribution of all the Nj(t)'s, where Nj(t) represents the number of times the jth state (j = 1, 2, ... , m) is visited in time t, in a Markov Renewal Process ; (2) the covariance between Nj(t) and Nk(t); (3) the probability generating function and moments of Nj(t)'s in a General Markov Renewal Process i.e., a Markov Renewal Process with a random origin; (4) Cumulative processes associated with a Markov Renewal Process along with its first passage time and (5) Equilibrium Markov Renewal Processes.
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