Reliability Evaluation of Multi-source Multi- Sink Stochastic-flow Networks under Quickest Path and System Capacity Constraints

A multi-source multi-sink stochastic-flow network consists of a set of nodes, including sources nodes si that supply resources and sink nodes tj where demands are realized, and a set of directed arcs that carry resource flows. This paper presents an algorithm to determine the probability, called system reliability ( T C d ij wj R ), that for each source–sink pair (si, tj), dwj (the demand for resource w at sink node tj) units of data can be sent from si to tj through a valid group of paths on the network under two constraints: the transmission time along each valid path does not exceed a specified upper bound T and the maximal capacity of that path is not less than a specified lower bound Cij (required capacity). Based on the minimal paths, the proposed algorithm generates all the lower boundary points for (dwj, Cij, T), which can be used to calculate T C d ij wj R by applying the inclusion-exclusion rule. Finally, we can calculate the system reliability for the multi-source multi-sink stochastic-flow network.