A Simple Algorithm to Find All Minimal Path Vectors to Demand Level d in a Stochastic-Flow Network

Many real-life systems such as manufacturing, telecommunication and transportation systems may be regarded as a stochastic-flow network whose arcs have independent integer-value random capacities. System reliability of such a system can be computed in terms of minimal path vectors to demand level d, called d-MinPaths (d-MPs) or minimal cut vectors to demand level d, called d-MinCuts (d-MCs). This paper proposes a simple algorithm merely in accordance with the definition of d-MP for finding all the d-MPs in a stochastic-flow network. The proposed algorithm is demonstrated to be more efficient than some other existing algorithms, by computing its time complexity. An example is used to show how the algorithm finds all the d-MPs. Finally, the system reliability of the example is computed by the inclusion-exclusion method.