On a hybrid model for max-min congestion controllers

In this paper we address the congestion control problem in computer networks offering a single class of best effort service. The problem is viewed as a resource allocation problem. The objective is to distribute the available network resources among competitive users in a fair way. The fairness criterion adopted is the max-min criterion. The problem is formulated mathematically and a decentralized, simple to implement algorithm is considered. The resulting feedback system can be realized as an autonomous switched system. The special structure of the system and the fundamental properties resulting from this structure are outlined. Global asymptotic stability is then established for two 2-dimensional network examples. The extension of this stability result to higher dimension networks is currently under investigation.