Stop: a fast procedure for the exact computation of the performance of complex probabilistic systems

A new set-theoretic method for the exact and efficient computation of the probabilistic performance of complex systems has been developed. The core of the method is a fast algorithm for disjointing a collection of product sets which is intended for systems with more than 1000 components and 100,000 cut sets. The method is based on a divide-and-conquer approach, in which a multidimensional problem is progressively decomposed into lower-dimensional subproblems along its dimensions. The method also uses a particular pointer system that eliminates the need to store the subproblems by only requiring the storage of pointers to those problems. Examples of the algorithm and the divide-and-conquer strategy are provided, and comparisons with other significant methods are made. Statistical complexity studies show that the expected time and space complexity of other methods is O(me/sup n/), but that our method is O(nm3 log(m)). Problems which would require days of Cray-1 computer time with present methods can now be solved in seconds. Large-scale systems that can only be approximated with other techniques can now also be evaluated exactly