The relevance of the criticial index in the simulation of stochastic networks

This article describes the relevance of the criticality index for stochastic network simulation. The index is particularly appropriate for identifying the importance of activities for project scheduling. The index is computed following the theory and definitions given by earlier authors, and particularly Dodin and Elmaghraby. Here, the criticality index of an activity is defined as the sum of the critical indices of the paths containing it, and the criticality index of a path is the probability that the duration of the path is the largest among all the paths through the network. One of the purposes of this paper is to show that this definition leads to questionable conclusions in practice. An alternative definition is proposed for the critical index of activities. Here, the criticality index of an activity is defined as the probability that the activity has no total slack. This avoids many of the problems associated with the earlier definition.