A Monte Carlo Technique with Quasirandom Points for the Stochastic Shortest Path Problem

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Abstract
This paper develops a simulation procedure for estimating the distribution function and other parameters of the shortest path length in stochastic activity networks. The method builds on a recently developed conditional Monte Carlo method which involves both the uniformly directed cutsets and the unique arcs while exploiting the presence of series. We extend the estimation beyond the distribution function to other parameters related to the shortest path through a stochastic network. The method uses quasirandom points in lieu of independent random points in an attempt to further improve the efficiency of estimators. The technique is illustrated using a Monte Carlo sampling experiment for a network with 15 arcs. Using an extensive experimental design, the results reveal that the use of quasirandom points greatly enhances the performance of the method.