A time scale decomposition approach to adaptive ECN marking

Fair resource allocation in high-speed networks such as the Internet can be viewed as a constrained optimization program. Kelly and his co-workers have shown that an unconstrained penalty function formulation of this problem can be used to design congestion controllers that are stable. In this paper, we examine the question of providing feedback from the network such that the congestion controllers derived from the penalty function formulation lead to the solution of the original unconstrained problem. This can be viewed as the decentralized design of early congestion notification (ECN) marking rates at each node in the Internet to ensure global loss-free operation of a fluid model of the network. We then look at the stability of such a scheme using a time-scale decomposition of the system. This results in two separate systems which are stable individually and we show that under certain assumptions the entire system is semi-globally stable and converges to the equilibrium point exponentially fast.