Instability of a Tandem network and its propagation under RED

The interaction between a random early detection (RED) gateway and transmission control protocol (TCP) connections has been shown to lead to a rich set of nonlinear phenomena in single bottleneck cases. We extend this work and study the interaction of TCP connections with RED gateways in a simple tandem network, using a nonlinear first-order discrete-time model. We demonstrate that the nonlinear behavior of TCP can result in both smooth and nonsmooth bifurcations, leading to chaos. We show that the instabilities can be induced at both bottlenecks by changing the system parameters only at one of the bottlenecks while fixing the parameters at the other, thus demonstrating the propagation of instability. Moreover, we show that locally sufficient conditions for stability based on single node analysis are not sufficient for global network stability.