Hopf bifurcation control of congestion control model in a wireless access network

The main purpose of this paper is to analyze the problem of Hopf bifurcation control for a congestion control model in a wireless access network with time delay. By choosing communication delay as a bifurcation parameter, it is shown that when delay passes through a critical value, the Hopf bifurcation occurs. The bifurcation behavior may cause heavy oscillation and induce network instability. In order to control the undesirable Hopf bifurcation, a hybrid control strategy is proposed. By using a linear stability analysis, we show that adjusting the control parameters of the hybrid control strategy properly, the Hopf bifurcation can be delayed or even eliminated completely without changing the equilibrium point of the system. Therefore, this method can effectively control the Hopf bifurcation for the TCP/AQM wireless network model. Theoretical analysis and numerical simulation results show that this method is effective in controlling Hopf bifurcation of congestion control model in wireless network.