Robust global stability to delays of a multi-path dual congestion control algorithm

Global stability has been shown for network congestion control algorithms in the absence of propagation delays by use of the conventional Lyapunov function method. When heterogeneous delays are taken into account, this problem becomes harder and is partly answered until the latest work of Papachristodoulou et al., where a Lyapunov-Krasovskii functional argument is used to analyze global stability of nonlinear congestion control algorithms, but only applicable to the single-path case. In this paper, we develop a new multi-path extension to the dual algorithm in the presence of delays. By finding a reasonable Lyapunov-Krasovskii functional candidate, usually difficult to do in a constructive way, we establish a new sufficient condition for robust global stability to delays, which includes Papachristodoulou's as a special case. Finally, we verify the results through simulations.