“On Designing Improved Controllers for AQM Routers

Supporting TCP Flows”

The PI Controller

Presented by Bob Kinicki

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OutlineOutline

Introduction Background

– TCP Analytic Model– Brief Control Theory

Proportional Controller Proportional Integral (PI) Controller ns Simulation Results Conclusions

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Control Theoretic Analysis of REDControl Theoretic Analysis of REDVariable Definitions:

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Block diagram of a TCP connectionBlock diagram of a TCP connection

ttR1

N

21

1 W W q q

p

__

__

C

ttR1

ttR1Time Delay

Rtt

TCP window control

TCP load factor

congested queue

Control law(e.g. RED)

Vishal Misra’s Slide

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Linearized TCP Connection

Linearized TCP Connection

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AQM Feedback ControlAQM Feedback Control

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Linearized AQMLinearized AQM

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RED ControllerRED Controller

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Proportional ControllerProportional 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.

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Preliminary Simulation with Proportional Controller

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.

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Comparison of RED and PCComparison of RED and PC

ProportionalController hasbetter response

ProportionalController hasbetter response

Time varying dynamics Time varying dynamics

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Comparison of RED and PCComparison of RED and PC

When RTT’s areDoubled, RED hasa large overshoot!

When RTT’s areDoubled, RED hasa large overshoot!

Time varying dynamics Time varying dynamics

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Limitations of PCLimitations of PC

Under certain network conditions, the operating point p can be above the pmax 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 qref regardless of the load.

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PI ControllerPI Controller

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PI AlgorithmPI Algorithm

Executed once per sampling period:{

p = a ( q – q_ref)

– b (q_old – q_ref) + p_old

p_old = p

q_old = q

}

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ns Experimental Parameters

ns Experimental Parameters

Sampling frequency = 160 Hz. a = 1.822 (10)-5 ; b = 1.816 (10)-5

qref = 200 packets Buffer size = 800 packets RED parameters (defined by stability):

– pmax = 0.1– minth = 150– maxth = 700– wq = 1.33 (10)-6

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Experiment 3Experiment 3

PI “relatively”insensitive to loadPI “relatively”insensitive to load

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Experiment 4Experiment 4

PI Controller hasfaster responsetime.

PI Controller hasfaster responsetime.

Time varyingdynamics removed

Time varyingdynamics removed

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Experiment 5Experiment 5

180 FTP flows and360 HTTP flows

PI Controller ismore robust forhigher loads.

180 FTP flows and360 HTTP flows

PI Controller ismore robust forhigher loads.

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Experiment 6Experiment 6

16 FTP flows and180 HTTP flows

Under lighter load,RED oscillates.

16 FTP flows and180 HTTP flows

Under lighter load,RED oscillates.

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Experiment 7Experiment 7

400 FTP flows and180 HTTP flows

The heavy load haspushed the operatingqueue length beyondthe buffer size forRED and PC.

400 FTP flows and180 HTTP flows

The heavy load haspushed the operatingqueue length beyondthe buffer size forRED and PC.

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Experiment 8Experiment 8

Time varying settingsof Experiment1 withpropagation delaysreduced to 40 ms.

Time varying settingsof Experiment1 withpropagation delaysreduced to 40 ms.

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PI – Delay-Utilization Tradeoff

PI – Delay-Utilization Tradeoff

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RED - Delay-Utilization Tradeoff

RED - Delay-Utilization Tradeoff

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ConclusionsConclusions 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.

Thanks!

rek@cs.wpi.edu