Hopf bifurcation in TCP/adaptive RED

Conditions in terms of adaptation parameter gamma and low-pass filter parameter omega_q are given for the occurrence of a supercritical Hopf bifurcation of a TCP/adaptive RED model. We show the existence of asymptotically stable limit cycles in the closed-loop nonlinear system. We relate our results to the existing adaptive RED algorithms of (Feng et al., A Self Configuring RED Gateway, Infocom, 1999) and (Floyd et al., Adaptive RED). Predicted theoretical results are confirmed by numerical simulations, carried out by using Simnon and network simulator 2.