Simultaneous Flows Through a Communication Network

This paper presents a generalization of the results of Elias, Feinstein, and Shannon, and Ford and Fulkerson on the maximum rate of information flow through a communciation network. The problem which is considered is the following: suppose a fixed rate of flow of information is being maintained between a pair of stations and of a communication network, then 1) what is the maximum rate of flow of information between another pair of stations and of the same communication network, and 2) how can one allocate, among the channels, the original load on the communciation network to obtain the maximal flow between stations and . It is shown that within certain determinable limits the sum of these two rates of flow remains a constant. A technique for attaining the maximal flow between stations and based upon the linear programming is described. A solution of the generalization of this problem to the case of simultaneous flows is also presented.