Reliability Evaluation of a Multicommodity Capacitated-Flow Network in Terms of Minimal Pathsets

[[abstract]]Many real-world systems such as transportation systems, logistics/distribution systems, and manufacturing systems can be regarded as multicommodity flow networks whose arcs have independent, finite and multi-valued random capacities. Such a flow network is a multistate system with multistate components and its reliability for level d = (d1, d2, . . . , dk), i.e., the probability that k different types of commodity can be transmitted from the source node to the sink node in the way that the demand level d = (d1, d2, . . . , dk) is satisfied, can be computed in terms of minimal path vectors to level d (named d-MPs here). The main objective of this paper is to present a simple algorithm to generate all d-MPs of such a flow network for each level d = (d1, d2, . . . , dk) in terms of minimal pathsets. Three examples are given to illustrate how all d-MPs are generated by our algorithm and then the reliability of one example is computed