A Survey on Reliability Evaluation of Stochastic-Flow Networks in Terms of Minimal Paths

Many networks in real life such as electric power systems, transportation systems and manufacturing systems can be modeled as a stochastic-flow networks whose arcs and nodes have discrete and multi-valued random capacities. For such a flow network, the system reliability is the probability that the maximum flow of the network is not less than the given demand d. The researchers in this field have presented mainly two kinds of algorithms on the reliability evaluation of stochastic-flow networks: minimal paths (MPs) and minimal cuts (MCs). In this paper, a survey of reliability evaluation of stochastic-flow networks in terms of minimal paths is presented, including the algorithms for the basic stochastic-flow network model and its extended models. Finally a future research direction of the stochastic-flow networks is presented.