Local in-flows control in regular resource networks with a low resource

A. V. Evseenko, V. A. Skorokhodov

Institute of Mathematics, Mechanics and Computer Science of the Southern Federal University, 8a Milchakov Street, 344090 Rostov-on-Don, Russia

Abstract: The paper is devoted to solving the problem of local in-flows control in regular resource networks with a low resource. For such networks, a set of controlled vertices is specified. The local control problem is to determine such capacities of arcs entering the controlled vertices that the unique limit state of regular resource network $Q^*$ is the closest to the given state $Q'$. Conditions for the unreachability of the limit state that coincides with the state $Q'$ are obtained. Various configurations of resource networks with respect to the distribution of controlled vertices in them are considered. It is shown that if the conditions for the unreachability of the limit state are not satisfied, then there is such a set of capacities of arcs entering the controlled vertices for which the limit state $Q^*$ is equal to the given state $Q'$. Illustr. 2, bibliogr. 21.

Keywords: flows in networks, resource network, limit state, limit flow, flow control.

UDC: 519.1

Received: 11.12.2024
Revised: 15.01.2025
Accepted: 22.03.2025

DOI: 10.33048/daio.2025.32.823