A discrete time feedback control system model based on a multi-router network has been presented. The model can be described by a set of recurrence equations. The numerical examples about the bifurcation of average and instantaneous queue size along with the variety of RED control parameter are shown. The simulate experiments about those of the RED control parameters are also presented. All of these results show that instability in TCP-Reno traffic under RED can be induced by the inherent nonlinear behavior of the network.