Study on the system capacity for a multicommodity stochastic-flow network with node failure

For a deterministic flow network, the system capacity in single-commodity case is the maximum value of flow from the source node to the sink node. In a multicommodity stochastic-flow network with node failure (arcs and nodes all have several possible capacities and may fail), different types of commodities are transmitted through the same network simultaneously and compete the capacities. This paper defines the system capacity as a pattern for a multicommodity stochastic-flow network with node failure. And we propose a performance index, the probability that the upper bound of the system capacity is a given pattern, to evaluate the performance for a system. An algorithm based on the properties of minimal cuts is proposed to evaluate such a performance index.