Markov and Markov-Regenerative pert Networks

This paper investigates pert networks with independent and exponentially distributed activity durations. We model such networks as finite-state, absorbing, continuous-time Markov chains with upper triangular generator matrices. The state space is related to the network structure. We present simple and computationally stable algorithms to evaluate the usual performance criteria: the distribution and moments of project completion time, the probability that a given path is critical, and other related performance measures. In addition, we algorithmically analyze conditional performance measures—for example, project completion time, given a critical path—and present computational results. We then study extensions both to resource-constrained pert networks and to a special class of nonexponential pert networks.