Communication Networks with Simultaneous Flow Requirements

This paper considers the analysis and synthesis of communication networks with constant branch capacities, subject to a set of simultaneous flow requirements which are, in general, time-varying. Since the maxima of different flow requirements usually do not occur at the same time, savings in total capacity or total cost are possible through reassignments of flow paths. A set of necessary and sufficient conditions for a communication network to satisfy a given set of simultaneous time-dependent flow requirements is obtained. This set of conditions, when applied to the case of constant simultaneous flow requirements, is shown to be more conpact than those previously known. A synthesis procedure is then derived which enables one to obtain a communication network realization of minimum total branch capacity subject to the constraint that the network must assume a tree configuration.