A simple algorithm for reliability evaluation of a stochastic-flow network with node failure

Abstract

This paper addresses a stochastic-flow network in which each arc or node has several capacities and may fail. Given the demand d, we try to evaluate the system reliability that the maximum flow of the network is not less than d. A simple algorithm is proposed firstly to generate all lower boundary points for d, and then the system reliability can be calculated in terms of such points. One computer example is shown to illustrate the solution procedure. Scope and purpose The maximum flow problem is a standard problem in operations research and network analysis (Ford and Fulkerson, Flows in networks. NJ: Princeton University Press, 1962). This paper discusses the maximum flow problem for a stochastic-flow network in which arcs and nodes all have several capacities and may fail. We can evaluate the probability (named system reliability here) that the maximum flow is not less than a given demand, and then treat such a reliability as a system performance index. The purpose of this paper is to provide such a performance index for many real-world systems such as computer systems, telecommunication systems, logistics systems, etc.