Two-commodity reliability evaluation for a stochastic-flow network with node failure

Abstract This paper considers a stochastic-flow network, in which each node as well as each arc has several capacities and may fail, which allows each commodity to be transmitted from the source to the sink. Given the demand for each commodity, the evaluation of the system reliability to fulfill the demand is performed. At first, a simple algorithm is proposed to generate all lower boundary points for the demand, and then the system reliability can be calculated in terms of such points. An example is shown to illustrate the solution procedure. Scope and purpose Assuming that the arcs of a flow network are deterministic, the multicommodity maximum flow (MMF) problem is a standard one in network analysis and operations research. The purpose of this paper is to extend the MMF problem to a stochastic-flow network in which arcs and nodes all have several capacities and may fail. We evaluate the probability (named system reliability here) that the system satisfies the demand for each commodity simultaneously. Such a probability can be treated as a performance index for many supply–demand systems such as computer systems, telecommunication systems, logistics systems, etc.