  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. 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
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.
