Metric evaluations of the angular points of the set of attainable internodal flows of multiuser network

The paper considers a model of a multiuser communication network in which information flows of various types are simultaneously transmitted between all pairs of correspondent nodes. The results of computational experiments for evaluation of the metric characteristics of a convex set of attainable interstitial flows and angular points located on the faces are analyzed. The angular points of intersection of the outer boundary of the set with the coordinate axes, each of which corresponds to the maximum internodal flow of a certain type, are considered as basic-point. To determine the coordinates of the support-angular-points, the values of permissible internodal flows are calculated, with simultaneous transmission of which the maximum load of all network edges is achieved. The coordinates of the bench-mark-point at which the sum of the internodal flows reaches the maximum possible value on the attainable set are also calculated. The norm of vectors corresponding to the coordinates of angular points is estimated in conditional units of flows during the computational experiments. Comparative diagrams of conditional distances between the bench-mark and support-angular points are provided. Computational experiments make it possible to write an explicit form of the vectors of internodal flows, the convex combination of which can be used to guarantee the evaluation of the functional characteristics of the network at the maximum load of all edges. When forming the basic vectors of the support frame, the problem of the maximum flow and the minimum cut is repeatedly solved. The resulting computational costs are estimated by a polynomial function of the total number of network nodes.