1. “On Designing Improved Controllers for AQM Routers Supporting TCP Flows” The PI Controller Presented by Bob Kinicki

2. Advanced Computer Networks - PI Controller 2 Outline  Introduction  Background –TCP Analytic Model –Brief Control Theory  Proportional Controller  Proportional Integral (PI) Controller  ns Simulation Results  Conclusions

3. Advanced Computer Networks - PI Controller 3 Control Theoretic Analysis of RED Variable Definitions:

4. Advanced Computer Networks - PI Controller 4 Block diagram of a TCP connection N 1 __ Time Delay R tt TCP window control TCP load factor congested queue Control law (e.g. RED) Vishal Misra’s Slide

5. Advanced Computer Networks - PI Controller 5 Linearized TCP Connection

6. Advanced Computer Networks - PI Controller 6 AQM Feedback Control

7. Advanced Computer Networks - PI Controller 7 Linearized AQM

8. Advanced Computer Networks - PI Controller 8 RED Controller

9. Advanced Computer Networks - PI Controller 9 Proportional Controller  The feedback signal is simply the regulated output, the queue length, multiplied by a gain factor.  In the RED context, this means using the instantaneous queue length instead of the average queue length.  Note – Control Theory emphasizes “stability” which is well-defined mathematically, but this significantly constrains the choices for RED parameters used in this paper.

10. Advanced Computer Networks - PI Controller 10 Preliminary Simulation with Proportional Controller  60 FTP flows, 180 HTTP sessions  C = bottleneck link = 15 Mbps  Propagation delays uniform between 160 and 240 ms.  Packet size = 500 bytes  Time varying dynamics –At t = 100, 20 FTP flows drop out. –At t = 140, the 20 FTP flows start again.

11. Advanced Computer Networks - PI Controller 11 Comparison of RED and PC Proportional Controller has better response Proportional Controller has better response Time varying dynamics

12. Advanced Computer Networks - PI Controller 12 Comparison of RED and PC When RTT’s are Doubled, RED has a large overshoot! When RTT’s are Doubled, RED has a large overshoot! Time varying dynamics

13. Advanced Computer Networks - PI Controller 13 Limitations of PC  Under certain network conditions, the operating point p can be above the p max imposed by buffer size limitations.  This leads to oscillations as seen in Figure 7.  Hence, PI, the Proportional Integral controller is used to clamp the queue size to q ref regardless of the load.

14. Advanced Computer Networks - PI Controller 14 PI Controller

15. Advanced Computer Networks - PI Controller 15 PI Algorithm Executed once per sampling period: { p = a ( q – q_ref) – b (q_old – q_ref) + p_old p_old = p q_old = q }

16. Advanced Computer Networks - PI Controller 16 ns Experimental Parameters  Sampling frequency = 160 Hz.  a = 1.822 (10) -5 ; b = 1.816 (10) -5  q ref = 200 packets  Buffer size = 800 packets  RED parameters (defined by stability): –p max = 0.1 –min th = 150 –max th = 700 –w q = 1.33 (10) -6

17. Advanced Computer Networks - PI Controller 17 Experiment 3 PI “relatively” insensitive to load PI “relatively” insensitive to load

18. Advanced Computer Networks - PI Controller 18 Experiment 4 PI Controller has faster response time. PI Controller has faster response time. Time varying dynamics removed Time varying dynamics removed

19. Advanced Computer Networks - PI Controller 19 Experiment 5 180 FTP flows and 360 HTTP flows PI Controller is more robust for higher loads. 180 FTP flows and 360 HTTP flows PI Controller is more robust for higher loads.

20. Advanced Computer Networks - PI Controller 20 Experiment 6 16 FTP flows and 180 HTTP flows Under lighter load, RED oscillates. 16 FTP flows and 180 HTTP flows Under lighter load, RED oscillates.

21. Advanced Computer Networks - PI Controller 21 Experiment 7 400 FTP flows and 180 HTTP flows The heavy load has pushed the operating queue length beyond the buffer size for RED and PC. 400 FTP flows and 180 HTTP flows The heavy load has pushed the operating queue length beyond the buffer size for RED and PC.

22. Advanced Computer Networks - PI Controller 22 Experiment 8 Time varying settings of Experiment1 with propagation delays reduced to 40 ms. Time varying settings of Experiment1 with propagation delays reduced to 40 ms.

23. Advanced Computer Networks - PI Controller 23 PI – Delay-Utilization Tradeoff

24. Advanced Computer Networks - PI Controller 24 RED - Delay-Utilization Tradeoff

25. Advanced Computer Networks - PI Controller 25 Conclusions  The authors introduced both the Proportional and the PI Controllers for AQM.  Both controllers respond faster than RED.  PI is better with respect to regulating the steady-state queue length.  PI controlled exhibited superior performance to RED in all the ns simulations shown.  Note – At the very end of the paper, the authors advocate the use of ECN (namely, marking) in all AQM’s.

26. Thanks! rek@cs.wpi.edu