An Approach for System Reliability of Two- Commodity Stochastic-Flow Networks with Budget Constraints

Many physical systems such as transportation systems and logistics systems can be regarded as flow networks in which arcs have independent and multi-valued random capacities. Such a flow network is a multistate system with multistate components. For such a flow network with two different types of commodity, it is very desirable to compute its system reliability for level, i. e. , the probability that two 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, can be computed in terms of minimal path vectors to level (named here). The main objective of this article is to present an intuitive algorithm to generate all of such a flow network for each level in terms of minimal pathsets. An example is given to illustrate how all are generated by our algorithm and the system reliability is then computed.