Supplementary Variable Technique Applied to Stochastic Activity Networks

This paper deals with stochastic activity networks with independent and continuously distributed activity durations. We show that such stochastic networks can be modeled as continuous-time Markov processes with a single absorbing state using a supplementary variable technique. The following quantities are obtained: (i) the probability distribution of the project completion time (longest path), (ii) the probability distribution of the shortest path length.