On a multicommodity stochastic-flow network with unreliable nodes subject to budget constraint

From the quality management and decision making view point, reliability and unreliability are important indices to measure the quality level for a stochastic-flow network. In a multicommodity stochastic-flow network with unreliable nodes, the branches and nodes all have several possible capacities and may fail. Different types of the commodity, which are transmitted through the same network simultaneously, compete the capacities of branches and nodes. In this paper we first define the system capacity as a vector for a multicommodity stochastic-flow network with unreliable nodes. Then we design a performance index which is the probability that the upper bound of the system capacity is a given pattern subject to the budget constraint. It can be applied to evaluate the quality level for such a network. A simple approach based on minimal cuts is thus presented to evaluate the performance index.