In a communication network, a multiroute channel is more reliable than is an ordinary channel against link or terminal failures. An m-route flow coresponds to a set of m-route channels, where m is the number of disjoint paths the m-route channel passes through. The max-flow min-cut theorem of the m-route flow has been proved by Kishimoto and Takeuchi. We show how to obtain the maximum m-route flow between two vertices. First, we evaluate the maximum value of m-route flows between two vertices by at most m times calculations of the maximum value of ordinary flows. Then, we construct the m-route flow with the maximum value. The correctness of this method gives another proof of Kishimoto and Takeuchi's max-flow min-cut theorem. The maximum value of m-route flows corresponds to the maximum capacity by m-route channels between two terminals.
