Reliability evaluation for a multi‐commodity flow model under budget constraint

This paper is mainly to extend the multi‐commodity minimum cost flow problem from deterministic cases to stochastic cases. Under budget constraint, we propose an approach to calculate the probability that the required amount of multiple commodities can be transported simultaneously through a stochastic flow network. Such a probability is called system reliability. An algorithm is proposed first to find out all lower boundary points for the requirement in terms of minimal paths. The system reliability can then be calculated in terms of such lower boundary points.