A Mp-based Algorithm for a Multicommodity Stochastic-flow Network with Capacity Weights

This paper proposes an efficient algorithm to evaluate system reliability for many real-life systems such as manufacturing, telecommunication and computers systems. A multicommodity stochastic-flow network is constructed to model a manufacturing system in which each node stands for a machine station, and each arc stands for a transmission medium (shipping machine or conveyor). Four characteristics are considered: 1) both nodes and arcs have multiple possible capacities and may fail; 2) each component (arc/node) has both capacity and cost attributes; 3) multicommodity are proceed; and 4) the capacity weight varies with arcs, nodes, and types of commodity. We study the possibility that multicommodity can be transmitted through this network simultaneously under the budget constraint. Such a possibility is named the system reliability. The MP (minimal path) plays the role of describing the relationship among flow vectors and capacity vectors. Subsequently, an efficient algorithm in terms of MP is proposed to evaluate the system reliability.