Departmental Papers (ESE)


Fair resource allocation in high-speed networks, such as the Internet, can be viewed as a constrained optimization program. Kelly et al. 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 explicit 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 seperate systems which are stable individually, and we show that under certain assumptions the entire system is semiglobally stable and converges fast to the equilibrium point exponentially.

Document Type

Journal Article

Date of this Version

June 2002


Copyright 2002 IEEE. Reprinted from IEEE Transactions on Automatic Control, Volume 47, Issue 6, June 2002, pages 882-894.
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Adaptive virtual queue, congestion control, explicit congestion notification (ECN) marking, Internet, singular perturbations



Date Posted: 20 November 2004

This document has been peer reviewed.