A novel algorithm to evaluate the performance of stochastic transportation systems

Network analysis is a usual approach to evaluate the performance of real-life systems such as transportation systems. We construct a multicommodity stochastic flow network with weighted capacity allocation to model the transportation systems. Each arc with cost attribute has several possible capacities. The capacity weight, the consumed quantity of arc capacity by per commodity, varies with the arcs and types of commodity. Nevertheless, the system capacity is not appropriate to be treated as the maximal sum of the commodity. We define the system capacity as a demand vector d if the system fulfills at most d. The main problem of this work is to measure the quality level of a transportation system. We propose a performance index, the probability that the upper bound of the system capacity equals a demand vector d subject to the budget constraint. A novel algorithm based on minimal cuts is presented to generate all maximal capacity vectors meeting exactly the demand d under the budget B. The performance index can then be evaluated in terms of such vectors.