Reliability evaluation of network flows with stochastic capacity and cost constraint

This paper addresses flow networks whose arcs have finite and independent random capacities. The reliability of such a system, that is the probability that d units of flow can be transmitted from the source node to the sink node with total cost at most equal to c , can be computed in terms of Minimal Path Vectors, named as ( d , c )-MPs. In this paper, first, a method for computing the upper and lower bounds of the capacity cost of the system is proposed. The presented method shows how to compute a ( d , c )-MP with the minimum capacity cost. Subsequently, we develop an algorithm, based on the computed bounds, to generate all ( d , c )-MPs and then, the system reliability is calculated in terms of such ( d , c )-MPs. The computational complexity of the proposed algorithm is also presented. At the end the solution procedure is illustrated by an example.