Analysis and Design of Controllers for AQM Routers Supporting TCP Flows. C. V. Hollot, V. Misra, D. Towsley and W. Gong

Transcription

1 A Study Group Presentation Analysis and esign of Controllers for AQM outers Supporting TCP Flows C. V. Hollot, V. Misra,. Towsley and W. Gong Presented by: Tan Chee-Wei Advisors: Professor Winston Chiu, Professor John Lui The Chinese University of Hong Kong

2 Contents Introduction The AQM Control Problem AQM Using andom Early etection AQM Using Proportional Control AQM Using Proportional-Integral Control elated Work Conclusion

3 Introduction TCP is a protocol that sits between application and network The Internet is powered by TCP/IP TCP characteristics: Acknowledgement etransmission Flow control Congestion avoidance

4 TCP Window ynamics Additive Increase eceiver Time Time Sender

5 TCP Window ynamics Multiplicative ecrease eceiver Time Packet rop Time Sender

6 What Are The Factors Affecting TCP Throughput Number of TCP Sessions ound Trip Time Link Capacity of Network Buffer Capacity of Network

7 Why Active Queue Management Passive Queue Management has only two states No packet drop No early congestion warning packet drop All senders back off Goal of AQM is to avoid the above problems Characteristics of AQM andom packet drop is performed before buffer is full The probability of packet drop increases with congestion level

8 A Single Bottlenecked Queue

9 Contents Introduction The AQM Control Problem AQM Using andom Early etection AQM Using Proportional Control AQM Using Proportional-Integral Control elated Work Conclusion

10 The ole Of Buffer-based AQM Introduction TCP Queue elay secs AQM

11 ', * - ' ' ' ), ' ' ' #" A Fluid-flow Model of TCP Behavior Windows dynamic Queue dynamic probability of packet mark trip time round (secs) link capacity (packets/sec) propagation delay (secs) number of TCP sessions average queue length (packets) average TCP time window size (packets) +* ( $ % &!

12 TCP Congestion Avoidance Mode / delay 8 7 8

13 : ' : ' : TCP Model Is Non Linear First step: Simplify TCP model Employ small signal linearization about steady state operating points Perturbed variables about operating point ' Second step: Concentrate only on nominal dynamic behavior

14 : ) 8 : ) < )=< > < > A@ B 6 : < > Linearalized TCP Connection First step: Simplify TCP model

15 : 8 : > < F HG B ) < 6 : C Linearized TCP ynamic And High Frequency Parasitic Second step: Concentrate only on nominal dynamic behavior Isolate high frequency parasitic C

16 . I K J I Negative Feedback Control Loop eference signal Output signal Stable plant Controller I 8 K L J stable The case of a regulator with disturbance rejection,

17 M AQM As Feedback Control Plant model consists of Window and Queue dynamics : N24 : C P(s) > AQM control law

18 : 8 6 : > 01E24 AQM As Feedback Control esign a that stabilizes M > and gain-stabilizes P(s) C(s) C C

19 P M M Nyquist Stability Criterion Assume does not encircle the point in the clockwise direction in the complex plane, then the system is asymptotically stable. and are stable. If the Nyquist plot of O

20 S Q elative Stability Frequency domain performance specifications Phase Margin Close Loop System Bandwidth

21 Z C P T P P T P T.U ) VXW Y B U Stabilizing AQM Control Laws V(s) Using Small Gain Theorem, will not encircle -1 for all frequencies. Z\[ C C

22 Z T b C C M a _^ `, ] - AQM Proposition 1 Given feasible network parameters, the linearized AQM control system is stable if * and operating point stabilizes the delayed nominal plant > the high frequency parasitic i.e.,, P P Z [ is gain stabilized,.

23 F, * f f f f e B < d f k BY k k, then stabilizes the perturbed plant Z P M P ) - i j * g f f f g a f f f ] f and operating - f B * f, f d< a ` ] stabilizes the delayed nominal plant - M > g. k c < V W M > c < V W BY AQM Proposition 2 Given feasible network parameters, assume Further, for feasible network parameters point, suppose that If is stable, -, ^ `hg., is monotonically nonincreasing and. where., j ( ^, and operating point *

24 Contents Introduction The AQM Control Problem AQM Using andom Early etection AQM Using Proportional Control AQM Using Proportional-Integral Control elated Work Conclusion

25 vu tsr xwr nvm,op q Tuning E E takes an average measure of the queue length and randomly drop packets that are within a threshold between and minl maxl OGradient uv ropping probability 1 p_max 0 Average queue length min_th max_th

26 O {z ~} AQM Using E The low pass filter pole yis a function of the averaging weight and sampling frequency Transfer function of V W c < nvm O z B.z.e d< ~} Y B Select ysuch that it lies outside the loop s bandwidth or less than corner frequencies of Mthe. Let pole ydominates the system s transient response.

27 S j S z O ƒ AQM Using E Evaluate system at unity gain cross-over frequency Phase response of P must satisfy arctan y(queue averag- A tradeoff between ing) (Speed of response) and Using the general relationship j For a desired phase margin, an increase in queue averaging leads to smaller system bandwidth

28 Š - ˆ An Example Of Using E Consider the network parameters and 0.246s. pkts/s, flows Plant have poles at < ' y & 'min % ' ' ' ) ' ' and Take rads To satisfy phase constraint, we get ominant pole is too near to Imaginary Axis.

29 Contents Introduction The AQM Control Problem AQM Using andom Early etection AQM Using Proportional Control AQM Using Proportional-Integral Control elated Work Conclusion

30 y Œ S AQM Using Proportional Control E results in small Sluggish performance emove the low pass filter in E to improve transient response c < V W B.e O d< Ž Y B U y Under the likely case O, phase response of P ' ˆ Guarantees Close Loop Stability Using previous example, we have rads which is almost 30 times that of E

31 Contents Introduction The AQM Control Problem AQM Using andom Early etection AQM Using Proportional Control AQM Using Proportional-Integral Control elated Work Conclusion

32 AQM Using Proportional-Integral Control Both E and Proportional Controller results in finite steady state error in queue length Use an Integrator with Proportional Controller to drive steady state error to zero / 5 b constant if and only if.a@ c < V W.. š B.e O d< Ž Y B U y b PI zero to coincide with TCP Window Pole First Order System Given a desired phase margin, select that satisfies arctan

33 j j S j ' j ' ' esigning PI Control Using the previous example, we select rads, and we have a phase margin of and a system bandwidth of Stability margin decreases with increased link capacity ound Trip Time or decreased number of TCP flows, increased Need to avoid integrator windup due to control saturation since dropping probability is

34 Comparing PI Control With E Using NS Simulations Consider 60 TCP flows and 180 HTTP sessions A queue with buffer size 800 packets esire a steady state queue length of 200 packets Load variation At Time, 20 TCP flows drop out At Time, 20 TCP flows return

35 PI egulates Queue Length Independent Of TCP Flow Level

36 Increasing TCP Flow ecreases The System Bandwidth Smaller system bandwidth S dampens system transient response

37 Phase Margin ecreases With Increasing TCP Flows Lower Phase Margin More Oscillations

38 PI Continues To egulate Queue Length At High TCP Load E and Proportional controllers exhibit large steady state errors

39 Contents Introduction The AQM Control Problem AQM Using andom Early etection AQM Using Proportional Control AQM Using Proportional-Integral Control elated Work Conclusion

40 œ elated Work L. Le, J. Aikat, K. Jeffay and F.. Smith, "The Effects of Active Queue Management on Web Performance", ACM SIGCOMM 2003 H. G. Zhang, C. V. Hollot,. Towsley and V. Misra, "A Self-tuning Structure for Adaptation in TCP/AQM Networks", IEEE Globecom 2003 Y. Gao and J. C. Hou, "A State Feedback Control Approach to Stabilizing Queues for ECN-Enabled TCP Connections", IEEE INFO- COM 2003 P. F. Quet and H. zbay, "On the esign of AQM Supporting TCP Flows Using obust Control Theory", IEEE Transactions on Automatic Control, 2004 C. G. Wang, B. Li, Y. T. Hou, K. Sohraby and Y. Lin, "LE: A obust Active Queue Management Scheme Based on Packet Loss atio", IEEE INFOCOM 2004

41 Contents Introduction The AQM Control Problem AQM Using andom Early etection AQM Using Proportional Control AQM Using Proportional-Integral Control elated Work Conclusion

42 Conclusion A model for a single bottlenecked link Apply classical control theory to Internet congestion avoidance A set of design rules for tuning packet dropping probability Queue averaging in E is not recommended Tradeoff between low queueing delay and high link utilization

43 , ), j * - [ - j g ( f f f g Comments Other dynamic behavior Modeling issue Congestion window < is not gradually decreased at a rate of, but suddenly halved upon receipt of congestion Model assumes only long-lived TCP connections (Elephants). Ignores short-lived HTTP connections (Mice) and UP connections

44 What s Next More robust and adaptive AQM schemes for "Elephants" and "Mice" Multiple bottlenecks in network Exploit traffic characteristic, e.g., Long ange ependence, for predictive control Feasibility of implementation of discretized PI controller in Today s high-speed routers