Delay-independent stability and performance of distributed congestion control

Recent research efforts to design better Internet transport protocols combined with scalable Active Queue Management (AQM) have led to significant advances in congestion control. One of the hottest topics in this area is the design of discrete congestion control algorithms that are asymptotically stable under heterogeneous feedback delay and whose control equations do not explicitly depend on the RTTs of end-flows. In this paper, we first prove that single-link congestion control methods with a stable radial Jacobian remain stable under arbitrary feedback delay (including heterogeneous directional delays) and that the stability condition of such methods does not involve any of the delays. We then extend this result to generic networks with fixed consistent bottleneck assignments and max-min network feedback. To demonstrate the practicality of the obtained result, we change the original controller in Kelly et al.'s work ["Rate Control for communication networks: Shadow prices, proportional fairness and stability," Journal of the Operational Research Society, vol. 49, no. 3, pp. 237-252, March 1998] to become robust under random feedback delay and fixed constants of the control equation. We call the resulting framework Max-min Kelly Control (MKC) and show that it offers smooth sending rate, exponential convergence to efficiency, and fast convergence to fairness, all of which make it appealing for future high-speed networks.