A simple stability condition for RED using TCP mean-field modeling
  Congestion on the Internet is an old problem but still a subject of intensive research. The TCP protocol with its AIMD (Additive Increase and Multiplicative Decrease) behavior hides very challenging problems; one of them is to understand the interaction between a large number of users with delayed feedback. This article will focus on two modeling issues of TCP which appeared to be important to tackle concrete scenarios when implementing the model proposed in [Baccelli McDonald Reynier 02] firstly the modeling of the maximum TCP window size: this maximum can be reached quickly in many practical cases; secondly the delay structure: the usual Little-like formula behaves really poorly when queuing delays are variable, and may change dramatically the evolution of the predicted queue size, which makes it useless to study drop-tail or RED (Random Early Detection) mechanisms. Within proposed TCP modeling improvements, we are enabled to look at a concrete example where RED should be used in FIFO routers instead of letting the default drop-tail happen. We study mathematically fixed points of the window size distribution and local stability of RED. An interesting case is when RED operates at the limit when the congestion starts, it avoids unwanted loss of bandwidth and delay variations. 
Julien Reynier (INRIA Rocquencourt)