<title>Nonlinearity of TCP and instability with RED</title>

Abstract

Recently researchers have proposed active queue management (AQM) mechanisms as a means of better managing congestion at the bottlenecks inside the network. Random Early Detection (RED) mechanism has been proposed to control the average queue size at the congested routers. It has been shown that the interaction between an RED gateway and TCP connections can lead to period doubling bifurcation and chaos. In this paper we extend this model and study the interaction of the RED gateway with TCP and UDP connections, using a discrete-time model. First, we show that the presence of UDP traffic does much more than simply taking away the available capacity from the TCP connections. In fact it fundamentally changes the dynamics of the system. Second, with the help of bifurcation diagrams, we demonstrate the existence of nonlinear phenomena, such as oscillations and chaos, as the parameters of the RED mechanism are varied. Further, the presence of UDP traffic tends to stabilize the system in the sense that bifurcations and chaos are delayed in the parameter region. We investigate the impact of various system parameters on the stability of the system, present numerical results, and validate our analysis through ns-2 simulation.