Estimating critical path and arc probabilities in stochastic activity networks

This paper describes a new procedure for estimating parameters of a stochastic activity network of N arcs. The parameters include the probability that path m is the longest path, the probability that path m is the shortest path, the probability that arc i is on the longest path and the probability that arc i is on the shortest path. The proposed procedure uses quasirandom points together with information on a cutset H of the network to produce an upper bound of O((log K)N-IHI+l/K) on the absolute error of approximation where K denotes the number of replications. This is a deterministic bound and is more favorable than the convergence rate of I/K1/2 that one obtains for the standard error for K independent replications using random sampling. It is also shown how series reduction can improve the convergence rate by reducing the exponent on log K . The technique is illustrated using a Monte Carlo sampling experiment for a network of 16 relevant arcs with a cutset of H=7 arcs. The illustration shows the superior performance of using quasirandom points with a cutset (plan A) and the even better performance of using quasirandom points with the cutset together with series reduction (plan B) with regard to mean-square error. However, it also shows that computation time considerations favor plan A when K is small and plan B when K is large