On Global Stability of Internet Congestion Control

In this paper, we address the question of global asymptotic stability of TCP/AQM congestion control protocols. We analyze a well-known model, whose dynamics were previously shown to be locally stable via analysis of its linearization. We show that in fact the nonlinear dynamics are globally stable, and explicitly account for the effects of both nonlinearities and time-delays in the dynamics. These results hold in the case of a single link with sources of identical fixed delay, and global stability holds under the same conditions that local stability does. The dynamic model analyzed is nonlinear, nonsmooth, and contains a delay, and the proof is based on the theory of integral-quadratic constraints.