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<p>M.D. Beaudry (1978) proposed a simple method of computing the distribution of performability in a Markov reward process. Two extensions of Beaudry's approach are presented. The authors generalize the method to a semi-Markov reward process by removing the restriction requiring the association of zero reward to absorbing states only. The algorithm proceeds by replacing zero reward nonabsorbing states by a probabilistic switch; it is therefore related to the elimination of vanishing states from the reachability graph of a generalized stochastic Petri net and to the elimination of fast transient states in a decomposition approach to stiff Markov chains. The use of the approach is illustrated with three applications.</p>
performability analysis; vanishing states elimination; fast transient states elimination; semi-Markov reward processes; zero reward nonabsorbing states; probabilistic switch; reachability graph; stochastic Petri net; decomposition; stiff Markov chains; Markov processes; performance evaluation.

G. Ciardo, B. Sericola, K. Trivedi and R. Marie, "Performability Analysis Using Semi-Markov Reward Processes," in IEEE Transactions on Computers, vol. 39, no. , pp. 1251-1264, 1990.
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