Combination of Approximation and Simulation Approaches for Distribution Functions in Stochastic Networks

This paper deals with the fundamental problem of estimating the distribution function (df) of the duration of the longest path in the stochastic activity network such as PERT network. First a technique is introduced to reduce variance in Conditional Monte Carlo Sampling (CMCS). Second, based on this technique a new procedure is developed for CMCS. Third, a combined approach of simulation and approximation procedures is introduced for the networks with activity discrete distribution function to enhance the accuracy of the approximation procedures. Application of the new approach proves that the error is drastically reduced in comparison with the best existing approximation approach.