System reliability for a multistate flow network with multiple joint minimal paths under time constraint

The uncertainty of transmission time for a multistate flow network is the main issue when the quickest path problem is applied to such a network. A variant of quickest path problem focusing on the probability of complete transmission instead of finding the quickest path is studied in this paper. In transmission process, a congestion phenomenon may happen when there are joint arcs in minimal paths (MPs). That is, the some arcs are shared by some of MPs. Based on Monte Carlo Simulation, an algorithm is developed to assign the flows through MPs for evaluating the system reliability, the probability that the data can be sent within a time constraint. Experiments are performed to verify the approximate system reliability value obtained from the proposed algorithm is close to the real one. Furthermore, the experiments about CPU time of the algorithm and the characteristics of the variants of quickest path problem are also displayed.