Two-commodity reliability evaluation for a stochastic-flow network with node failure

This paper considers a stochastic-flow network, in which each node as well as each arc has several capacities and may fail, which allows each commodity to be transmitted from the source to the sink. Given the demand for each commodity, the evaluation of the system reliability to fulfill the demand is performed. At first, a simple algorithm is proposed to generate all lower boundary points for the demand, and then the system reliability can be calculated in terms of such points. An example is shown to illustrate the solution procedure.