“on designing improved controllers for aqm routers supporting tcp flows” the pi controller...
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![Page 1: “On Designing Improved Controllers for AQM Routers Supporting TCP Flows” The PI Controller Presented by Bob Kinicki](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649d365503460f94a0d60e/html5/thumbnails/1.jpg)
“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.