A family of multi-path congestion control algorithms with global stability and delay robustness

The goal of traffic management is to efficiently allocate network resources via adjustment of source transmission rates and routes selection. Mathematically, it aims to solve a traditional utility maximization problem in a fair and distributed manner. In this paper, we first develop a generalized multi-path utility maximization problem which features a weighted average of the classical Kelly's formulation and the Voice's model. Next, we design from this broader framework a family of multi-path dual congestion control algorithms whose equilibrium point can both achieve a desired bandwidth utilization and preserve a notion of fairness among competing users. Global stability can be guaranteed for the proposed schemes in the absence of delays by use of a totally novel Lyapunov function. Moreover, when heterogeneous propagation delays are taken into account, we establish decentralized and scalable sufficient conditions for robust global stability by constructing a reasonable Lyapunov-Krasovskii functional candidate. These conditions give estimates for the maximum admissible delays that the controller can tolerate without losing stability. Finally, we verify the results through simulation.