Structured construction and simulation of nondeterministic stochastic activity networks

In this work we deal with nondeterministic stochastic activity networks (NDSANs). Their stochastic character results from activity durations, which are given by nonnegative continuous random variables. The nondeterministic behavior of an NDSAN is a consequence of its variable topology, based on two additional features. First, by associating choice probabilities with the immediate successors of an activity, some branches of execution are not always taken. Second, by allowing iterated executions of a group of activities according to predetermined probabilities, the number of times an activity is to be executed is not determined a priori. These properties lead to a wide variety of activity networks, capable of modelling many real situations in process engineering and project management. We describe a simple, recursively structured construction of NDSANs, which both provides a coherent syntactic mechanism to incorporate the two abovementioned nondeterminism features and allows the analytic formulation of completion time. This construction also directly gives rise to a recursive simulation algorithm for NDSANs, whose repeated execution produces an estimate of the probability distribution of the completion time of the network. We also report on real-world case studies, using the Komolgorov–Smirnov statistic for validation.