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A family of multi-path congestion control algorithms with global stability and delay robustness. (English) Zbl 1309.93127

Summary: 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 formulation and the voice 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.

MSC:

93D20 Asymptotic stability in control theory
90B18 Communication networks in operations research
93B35 Sensitivity (robustness)
93D09 Robust stability
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