Project Completion Time in Dynamic PERT Networks with Generating Projects

Abstract

In this paper, an analytical method is developed to compute the project completion time distribution in a dynamic PERT network, where the activity durations are exponentially distributed random variables. The projects are generated according to a renewal process and share the same facilities. Thus, these projects cannot be analyzed independently. The authors' approach is to transform this dynamic PERT network into a stochastic network and, then, to obtain the project completion time distribution by constructing a proper continuous-time Markov chain. This dynamic PERT network is represented as a network of queues, where the service times represent the durations of the corresponding activities and the arrival stream to each node follows a renewal process. Finally, the proposed methodology is extended to the generalized Erlang activity durations.