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

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 Ahmad Al-Hammouri Parameterizing PI Congestion Controllers FeBID’06

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

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

Parameterizing PI Congestion Controllers 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 Ahmad Al-Hammouri Parameterizing PI Congestion Controllers FeBID’06

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 Ahmad Al-Hammouri Parameterizing PI Congestion Controllers FeBID’06

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

Parameterizing PI Congestion Controllers 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++ Ahmad Al-Hammouri Parameterizing PI Congestion Controllers FeBID’06

Complete Stability Region SR SR = (S0 \ SN) \ SL SR S0 \ SN Ahmad Al-Hammouri Parameterizing PI Congestion Controllers FeBID’06

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 Ahmad Al-Hammouri Parameterizing PI Congestion Controllers FeBID’06

Parameterizing PI Congestion Controllers Example 1 N = 75; d0 = 0.15 sec; C = 1250 pkt/sec * [Hollot et al 2001] * Ahmad Al-Hammouri Parameterizing PI Congestion Controllers FeBID’06

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 Ahmad Al-Hammouri Parameterizing PI Congestion Controllers FeBID’06

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

Parameterizing PI Congestion Controllers Example 2 [Heying et al 2002] N = 60; d0 = 0.22 sec; C = 1250 pkt/sec * [Heying et al 2002] Ahmad Al-Hammouri Parameterizing PI Congestion Controllers FeBID’06

Parameterizing PI Congestion Controllers 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) Ahmad Al-Hammouri Parameterizing PI Congestion Controllers FeBID’06

Parameterizing PI Congestion Controllers Thank You Questions Comments Ahmad Al-Hammouri Parameterizing PI Congestion Controllers FeBID’06