Global stability of a dual congestion control under time-varying queueing delays

This paper concerns the global dynamics of a certain “dual” network congestion control, for which the feedback signal measures a queueing delay at congested links. Earlier studies of this kind of protocol have shown attractive properties of local stability scalable to arbitrary networks, and also global stability results under more restrictive assumptions. All of these have, however, relied on the assumption of fixed, time-invariant network delays. For protocols that build real queues and therefore introduce a time-varying delay in the feedback signal, the dynamics are significantly more complex. In this paper we study a single link and source network under these conditions, and give a global stability theorem for the resulting nonlinear, time-varying, time-delay system.