In dynamic networks, the quickest time is the least possible time required to transmit specified data from the source to the sink. When arcs in dynamic networks are independently subjected to failures, the quickest time is a random variable. Although previous studies have already explored the reliability of the quickest path, this work presents an algorithm that computes the probability distribution of the quickest time from the viewpoint of the quickest flow that contains all possible joint and disjoint paths. For moderate dynamic networks, the proposed algorithm can be easily modified to approximate the quickest time distribution with a trade-off between accuracy and running time. The performance and properties of the exact and modified algorithms are explored through computational experiments, which are conducted on 10 randomly generated networks. The exact algorithm is also compared with the exhaustive method which examines all state vectors.
