As an enhancement mechanism for the end-to-end congestion control, AQM (Active Queue Management) can keep smaller queuing delay and higher throughput by purposefully dropping the packets at the intermediate nodes. Comparing with RED algorithm, although the PI (Proportional-Integral) controller for AQM designed by C. Hollot improves the stability, it seems unscientific to tune the controller parameters through trial-error, moreover the transient performance of the PI controller is not perfect, such as the regulating time is too long. In order to overcome this drawback, in this paper, the PID (Proportional-Integral-Differential) controller is proposed to speed up the responsiveness of AQM system. The controller parameters are tuned based on the determined gain and phase margins. The simulation results show that the integrated performance of the PID controller is obviously superior to that of the PI controller.

For a real Schur polynomial, estimates are derived for a Schur stability margin in terms of matrix entries or tableau entries in some stability test methods. An average size of the zeros of the polynomial is also estimated. These estimates enable us to obtain more information than stability once a polynomial is tested to be stable via the established Schur stability criterion for real polynomials.