Performability analysis using semi-Markov reward processes

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