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 , Department of Commerce TOP , 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
Ahmad Al-Hammouri
Parameterizing PI Congestion Controllers
FeBID’06

3. 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

4. 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

5. 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

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
Ahmad Al-Hammouri
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 \ SN S0
Ahmad Al-Hammouri
Parameterizing PI Congestion Controllers
FeBID’06

8. 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

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

11. 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

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
Ahmad Al-Hammouri
Parameterizing PI Congestion Controllers
FeBID’06

13. 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

14. 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

15. 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

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