Global stability with time-delay of a primal-dual congestion control

This paper concerns network congestion control, focusing on a recently proposed "primal-dual" control law that has been shown to give local stability and desirable equilibrium properties for networks of arbitrary capacity and a fixed bound on delay. In this paper we study global stability for these non-linear, delay differential equations, focusing for simplicity on the scenario of a single flow and bottleneck link. We first provide bounds on the state variables that hold for any choice of parameters. Then we give results regarding global stability, based on Lyapunov-Razumikhin methods and singular perturbation theory.