Program evaluation and Review Technique based on Moment Generating Function and its application in software engineering

In software projects, Program Evaluation and Review Technique (PERT) is frequently used to estimate the schedule of the uncertain projects. However, classic PERT does not allow the existence of loop in PERT graph, and assuming that all the activities time subject to the β probability distribution. All these restrict the use of PERT. Firstly, by mapping PERT network to the Petri nets based model, this paper establishes a Petri nets based model that not only maintain the original properties of PERT, but also allow the existence of the loop. Secondly, by introducing Moment Generating Function (MGF), and associating with the analysis approach for Petri nets reachability graph, the reachability Graph of PERT model whose activities subject to arbitrary distribution can be obtained. Thirdly, based on reducing the vanishing states of reachability graph further, the transfer function is substituted with the MGF of the entire nets. Finally, according to the properties of the MGF, this paper gives an example to verify the applicability for this method in PERT of Software projects.