Reliability of a stochastic-flow network with unreliable nodes and cost constraints

This paper concentrates on a stochastic-flow network in which nodes as well as branches have several possible capacities. The possibility is evaluated that a given amount of messages can be transmitted through the Such stochastic-flow network under the budget constraint. Such a possibility is named the system reliability. A minimal path, an order sequence of nodes & branches from the source to the sink without cycles, is used to assign the flow to each branch and node. A lower boundary point for (d, C) is a minimal capacity vector which enables the system to transmit d messages under the budaet C. Based on minimal paths, an efficient algorithm is proposed to generate all lower boundary points for (c C). The system reliability can then be calculated in terms of all lower boundary points by applying the inclusion-exclusion rule.