Minimum Number Of Arcs In Conditional Monte Carlo Sampling Of Stochastic Networks

Publisher Website
Google Scholar
Abstract
Consider a stochastic activity network, such as PERT network. This paper deals with the problem of estimating the distribution function (df) of the duration of the longest path in the stochastic network. In particular, the paper concentrates on the methods of conditional Monte Carlo sampling which have been used to approximate the df of the longest path in stochastic networks. First, we show that none of the existing conditional Monte Carlo sampling procedures conditions on the minimum number of arcs. Secondly, a method in which the conditions of a minimum number of arcs is developed. The new procedure conditions on the arcs with the highest path indices, where a “path index” of an arc is the number of paths passing through the arc, A procedure to calculate the path indices of the arcs without identifying the paths is developed. Illustrative examples and comparison with the existing conditional procedures are provided.