Abstract—Many real-world systems such as manufacturing systems, transportation systems and logistics/distribution systems that play important roles in our modern society 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;c), i.e., the probability that k different types of commodity can be transmitted from the source node to the sink node such that the demand level is satisfied and the total transmission cost is less than or equal to c, can be evaluated in terms of minimal path vectors to level (d;c) (named (d;c)-MPs here). The main objective of this paper is to present an intuitive algorithm to generate all (d;c)-MPs of such a flow network 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.
Keywords— Reliability, limited-flow network, multicommodity, multistate system, (d;c)-MP.
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