An algorithm to evaluate the system reliability for multicommodity case under cost constraint

System reliability evaluation for flow networks is an important issue in our modern society. This paper studies the system reliability that a given amount of multicommodity can be transmitted through a stochastic-flow network, in which each are has several capacities, under the cost constraint. A simple algorithm is proposed to generate all (d1, d2,…, dp; C)-MPs where di is the demand of commodity i. The system reliability can then be calculated in terms of (d1, d2,…, dp; C)-MPs.