Stability and Hopf bifurcation of a class of TCP/AQM networks

In this paper, the local dynamics around the equilibrium of a class of TCP/AQM networks with proportional feedback is investigated, and the effect of the communication delay on the stability is addressed. It is found that the Internet system keeps stable if the delay is not large, and it exhibits good performance only for proper delay in the stable interval, NOT the case as expected: the smaller the better. In addition, a Hopf bifurcation occurs after the equilibrium loses its stability, and the method of multiple scales (MMS) is used to calculate the bifurcated periodic solution, the direction of the bifurcation, and the stability of the periodic motion resulting from the bifurcation. The method of multiple scales involves easy computation and yields prediction on the bifurcated periodic solution in very good agreement with numerical results.