Competition of Cluster Flows in Multiuser Network Systems under Capacity Constraints. I. The Problem of Fair Cluster Flow Control

For multicommodity networks with node flow clusters, the problem of a fair distribution of deficit resources of edge capacity among these clusters is formulated. Solution methods and properties are analyzed. Some differences in the use of the leximin rule are revealed depending on the system network structure. Game-theory models are designed to describe the competition of the cluster owners for resources under leximin flow control and equilibria conditions are found.