A simple algorithm to generate all (d,B)-MCs of a multicommodity stochastic-flow network

Both minimal paths and minimal cuts are important media to evaluate the performance indexes, the system reliability or unreliability, for a single-commodity stochastic-flow network. This paper concentrates on a multicommodity stochastic-flow network in which each arc has both the capacity and cost attributes. Different from the single-commodity case, the system capacity is a pattern for multicommodity case. Since the traditional performance indexes are not suitable for multicommodity case, we propose a new performance index, the probability that the system capacity is less than or equal to a given pattern under the budget constraint. A simple algorithm based on minimal cuts is presented to generate all (d,B)-MCs that are the maximal capacity vectors meeting the demand d and budget B. The proposed performance index can be evaluated in terms of (d,B)-MCs.