Reliability evaluation of capacitated-flow networks with budget constraints

Many real-world systems such as transportation systems and manufacturing systems can be regarded as flow networks whose arcs have independent, finite and multi-valued random capacities. Such a flow network is indeed a multistate system with multistate components and so its reliability for level (d, c), i.e., the probability that d units of flow can be transmitted from the source node to the sink node such that the total transmission cost is less than or equal to c, can be computed in terms of minimal path vectors to level (d, c) (named (d, c)-MPs here). The main objective of this paper is to present a simple algorithm to generate all (d, c)-MPs of such a system for each level (d, c) in terms of minimal pathsets. Two examples are given to illustrate how all (d, c)-MPs are generated by our algorithm and then the reliability of one example is computed.