System reliability for joint minimal paths under time constraint

The quickest path in a transmission problem for a multistate flow network is considered in this article. In this problem, a given amount of data is transmitted to the destination through multiple minimal paths (MPs) simultaneously, and the probability of complete transmission within a time constraint is of interest. In particular, the MPs are joint such that a constriction occurs. An algorithm is developed by applying Monte Carlo simulation to find the system reliability. Furthermore, the proposed algorithm can be used to manage situations with either joint or disjoint MPs. Although the system reliability obtained from this algorithm is an approximate value, the experiments and inference statistics indicate that the expected value is very close to the actual system reliability.