The window sizes and slow start thresholds of each TCP session evolves like independent dynamical systems coupled by the RED mechanism. Here we introduce a mean-field approximation to one such RED system as the number of flows tends to infinity. The
deterministic limiting system is described by a transport equation. The numerical solution of the limiting system is found to provide a good description of the of the evolution of the distribution of the window sizes, the average queue size, the average loss rate per connection and the total throughput. We see that TCP with RED or tail-drop may exhibit limit cycles and this causes unnecessary packet delay variation and variable loss rates. The root cause of these limit cycles is the hysteresis due to the round trip time delay in reacting to a packet loss.