“…When data are transmitted through a flow network, it is desirable to adopt the shortest path, the least cost path, the largest capacity path, the shortest delay path, or some combination of multiple criteria [1,4,13], which are all variants of the shortest path problem. For the network with a time attribute, it is an important task to reduce the transmission time from the viewpoint of QoS [5,14,15,17,21,23,35]. Hence, Chen and Chin [10] proposed a version of the shortest path problem called the quickest path problem that finds a path with minimum transmission time to send a given amount of data through the network.…”