Improved results on global stability of network congestion control based on iterative bounding

We study a "primal-dual" nonlinear network congestion control law in the presence of time delays, for which a global stability condition has been recently given using singular perturbation analysis. We show that stronger results can be obtained through direct study of the system trajectories. In particular, we first extend earlier results on boundedness of trajectories to general networks. We then proceed to iteratively refine those bounds in the single link case, through iterations that can be proven to be globally contractive, under appropriate parameter conditions, leading to the global stability result.