Abstract. The reliability problem of the quickest path deals with the transmission of a message of sizeσ from a source to a destination with both the minimum end-to-end delay and the reliability of the path over a network with bandwidth, delay, and probability of fault free on the links. For any value of message sizeσ , we present algorithm to compute all-pairs most-reliable quickest paths each with time complexity O(n 2 m), where n and m are the number of nodes and the number of arcs or links in the network, respectively.