Parameterizing PI Congestion Controllers

1. Parameterizing PI Congestion Controllers Ahmad T. Al-Hammouri, Vincenzo Liberatore, Michael S. Branicky Case Western Reserve University Stephen M. Phillips Arizona State University April 3, 2006 Support by: NSF CCR-0329910, Department of Commerce TOP 39-60-04003, NASA NNC04AA12A, and an OhioICE Training grant

2. Contributions of the Paper • Complete stability region for PI • Presents examples that show • Different stable PI parameters exhibit widely different control performance • Neglecting delays in control design leads to unstable systems Parameterizing PI Congestion Controllers FeBID’06

3. TCP-AQM Control Loop Plant P(s)= [Hollot et al 2001] x(t)=cwnd/RTT On Ack cwnd += 1/cwnd On loss cwnd /= 2 f(q(t)) q`=Σx(t) - C p(t) ControllerG(s) q(t) tf tb Parameterizing PI Congestion Controllers FeBID’06

4. PI AQM [Hollot et al 2001] q0 q(s) e u G(s) P(s) _ + • PI vs RED • Control signal: • . • Frequency transfer fn: • . Integral term eliminates the steady-state error P PI Parameterizing PI Congestion Controllers FeBID’06

5. Parameterizing PI AQM • Problem: • Determine the entire region of stabilizing kp and ki values • Objectives: • Stable closed-loop system • Enhanced closed-loop performance • Steady-state error, convergence time, overshoot • Challenges: • Delays Parameterizing PI Congestion Controllers FeBID’06

6. Contributions of the Paper • Complete stability region for PI • Presents examples that show • Different stable PI parameters exhibit widely different control performance • Neglecting delays in control design leads to unstable systems Parameterizing PI Congestion Controllers FeBID’06

7. Complete Stability Region SR [Silva et al 2005] • SR = (S0 \ SN) \ SL • S0 : • Stability region for the delay-free system • P0(s) = • SN : • . S0 S0 \ SN Parameterizing PI Congestion Controllers FeBID’06

8. Determination of SL • Set of kp and ki’s that destabilizes the closed-loop for delays less than d0 • For given kp and ki • Find d that gives the blue curve • If (d ≤ d0), (kp,ki ) SL • Else, (kp,ki ) SL • Sweep(kp,ki ) S0 Nyquist Plot of G(s)P(s) Im{s} -1 Re{s} x d++ Parameterizing PI Congestion Controllers FeBID’06

9. Complete Stability Region SR • SR = (S0 \ SN) \ SL SR S0 \ SN Parameterizing PI Congestion Controllers FeBID’06

10. Contributions of the Paper • Complete stability region for PI • Presents examples that show • Different stable PI parameters exhibit widely different control performance • Neglecting delays in control design leads to unstable systems Parameterizing PI Congestion Controllers FeBID’06

11. Example 1 • N = 75; d0 = 0.15 sec; C = 1250 pkt/sec * [Hollot et al 2001] * Parameterizing PI Congestion Controllers FeBID’06

12. Contributions of the Paper • Complete stability region for PI • Presents examples that show • Different stable PI parameters exhibit widely different control performance • Neglecting delays in control design leads to unstable systems Parameterizing PI Congestion Controllers FeBID’06

13. PIP Controller [Heying et al 2002] u q0 q(s) e G(s) P(s) + _ + _ Kh PI Kh PIP Parameterizing PI Congestion Controllers FeBID’06

14. Example 2 [Heying et al 2002] • N = 60; d0 = 0.22 sec; C = 1250 pkt/sec * [Heying et al 2002] Parameterizing PI Congestion Controllers FeBID’06

15. Future Work • Conduct packet-level simulations (ns-2) • Define a “Networks Performance” objective function • Optimize the objective function over the stability region • Analyze the queue nonlinearity (i.e. truncation) Parameterizing PI Congestion Controllers FeBID’06

16. Thank You • Questions • Comments Parameterizing PI Congestion Controllers FeBID’06