Local and Global Stability of Delayed Congestion Control Systems

Abstract—Stability proofs of nonlinear congestion control systems under heterogeneous feedback delays are usually difficult and involve a fair amount of effort. In this paper, we show that there exist a class of congestion control methods that admit very simple proofs of asymptotic stability and allow control equations to be delay-independent. This is in contrast to most previous work, which requires that each flow (and sometimes each router) adapt its control-loop constants based on the feedback delay and/or the length of the corresponding end-to-end path. Our new congestion control method, which we call Max–Min Kelly Control (MKC), builds upon Kelly’s original work in [3] and allows end-flows to be stable and fair regardless of network feedback delays or the number of hops in their end-to-end paths. Using basic matrix algebra and discrete control theory, we show MKC’s local asymptotic stability under heterogeneous, directional feedback delays. We also offer a simple proof of its global asymptotic stability assuming constant feedback delay. Index Terms—Asymptotic stability, congestion control, delay. I