Stability Properties of Networks with Interacting TCP Flows

The equilibrium distributions of a Markovian model describing the interaction of several classes of permanent connections in a network are analyzed. It has been introduced by Graham and Robert [5]. For this model each of the connections has a self-adaptive behavior in that its transmission rate along its route depends on the level of congestion of the nodes on its route. It has been shown in [5] that the invariant distributions are determined by the solutions of a fixed point equation in a finite dimensional space. In this paper, several examples of these fixed point equations are studied. The topologies investigated are rings, trees and a linear network, with various sets of routes through the nodes.