Instability of a tandem network and its propagation under RED

Random early detection (RED) mechanism has been proposed to control the average queue size at the bottlenecks inside the network. It has been shown that the interaction between a RED gateway and TCP connections can lead to a rich set of nonlinear phenomena in single bottleneck cases. In this paper we extend this model 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, using bifurcation diagrams, that the nonlinear behavior of TCP can result in both smooth and non-smooth bifurcations, leading to chaos. We show that the instabilities can be induced at both 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.