Global stability of TCP/RED with many-flows: a numerical approach

We study the global stability of TCP/RED under the many flows regime. The traditional approach based on Lyapunov functions is not suitable for a system with many flows due to its complexity. In this paper, we present a normalized model to capture the essential system dynamics. Based on this normalized model, we find its equilibrium point and local stability criterion, which closely match the existing results. This, in turn, reinforce the correctness of our normalized model. We then proceed with a numerical analysis to obtain the global stability. Our results show that by properly choosing RED parameters, we can always make the TCP/RED system globally stable. In addition, our numerical results also show that any locally stable TCP/RED system is mostly globally stable as long as the number of flows is large.