Express Analysis and Aggregated Representation of the Set of Reachable Flows for a Multicommodity Network System

Abstract

Within the formalism of the mathematical model of transferring a multicommodity flow, the reachability set of multiuser network systems is studied. A method is proposed for constructing an internal supporting frame based on the vectors of the maximum flows that can be transferred between all pairs of nodes in exclusive and limited exclusive modes of flow control. Using the obtained limit values, we construct a polyhedron of a simpler structure (frame) belonging to the set of reachable multi-flows and a cone of possible directions for the generation of boundary points. Methods for obtaining various multicriteria evaluations of the functional capabilities of a transmission network are considered. The developed approach can be used for the a priori analysis of the set of reachable multiflows, including quickly obtaining estimates and acceptable options for the fair distribution of the limited capacity of the transmission network.