Flow reliability of a probabilistic capacitated-flow network in multiple node pairs case

Abstract

This article mainly generalizes the flow (or transportation) reliability problem for a directed capacitated-flow network in which the capacity of each arc ai has the values 0<1<2<⋯<Mi from s (source) to t (sink) case to a multiple node pairs case. Given the demands for all specified node pairs simultaneously in the network, a simple algorithm is proposed first to find out the family of all lower boundary points for such demands in terms of minimal paths. The flow reliability, the probability that the system allows the flow satisfying the demands simultaneously, can be calculated in terms of such lower boundary points. The overall-terminal flow reliability, one source to multiple sinks flow reliability and multiple sources to one sink flow reliability can be calculated as special cases.