In order to mitigate Internet congestion, this work is among the first ones to use a 20 years old modeling via a nonlinear differential equation with a variable delay, where a new flatness-like property is encountered: the delay is a flat output. Combining flatness-based open-loop control and closed-loop control via the intelligent proportional controller deduced from model-free control yields easily implementable and convincing computer experiments which display a remarkable robustness with respect to large uncertainties on the number of TCP connections.

The above nonlinear modeling has mainly been employed until today to derive time-invariant linear delay approximate systems, which are quite popular, not only for investigating queue management but also for computer experiments. The flatness-like property of the nonlinear model shows that freezing the delay implies that all other system variables, including the control one, are kept constant. The validity of the linear approximations is therefore questioned, from a control standpoint as well as for digital simulations.

Joint work with H. Mounier (Université Paris-Sud), C. Join (Université de Lorraine), E. Delaleau (École Nationale d’Ingénieurs de Brest)