Analysis of Two-Layer Resource Supply Flow Networks

The problem of controlling resource flows in two-level networks with a tree structure simulated by a simplified radial structure at each level is considered. A resource flow vector to end consumers is taken as the maximized functional characteristic. Two flow control strategies are analyzed to obtain a Pareto optimal solution based on a weighted leximin rule. The first strategy, called the equal-share resource allocation, is based on the idea of equalizing the ratio of the delivered resource volume to the maximum possible resource volume for the given node for the given network capacity. The second strategy, which ensures that resources are allocated equally, is based on the idea of equalizing the ratio of the delivered resource volume to the required resource volume. In the case of unknown requirements, it is proposed to focus on the strategy that ensures equal allocation. Both strategies are described in two variants: optimization at the main level with the further additional optimization in each allocation network and direct optimization without an intermediate level. It is shown that the solutions are different. Their properties are studied. The possibility of combining different rules is investigated. A model example is presented.