A State Feedback Control Approach to Stabilizing Queues for ECN-Enabled TCP Connections

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A State Feedback Control Approach A State Feedback Control Approach to Stabilizing Queues for ECN-to Stabilizing Queues for ECN-

Enabled TCP ConnectionsEnabled TCP Connections

Yuan Gao and Jennifer Hou

IEEE INFOCOM 2003,

San Francisco, April 2003

Presented by Bob Kinicki

Advanced Computer Networks : (SFC)

State Feedback Controller2

OutlineOutline

Introduction Enhanced TCP model Analyze the Interaction between TCP and

AQM Details of the State Feedback Controlled

AQM Related Work Simulations Conclusions



IntroductionIntroduction

Authors put their research in the category where network behavior is modeled with AQM routers as controllers and TCP traffic as plants in an automatic control theory scheme.

Analytic models can then be used to provide insight on designing better AQM controllers.



IntroductionIntroduction Generally, these models describe the main

dynamics of TCP in congestion avoidance phase where AIMD is used to adjust cwnd.

Rate of change in size of cwnd is expressed as:

(1-p)/ τ – ω2p/ 2 τ

where ω current cwnd size and

τ is the round-trip time (RTT).



IntroductionIntroduction They claim other models only model gradual

decrease in ω2p/ 2 instead of sudden halving of cwnd.

Their model is more realistic in that cwnd decreases faster.

Paper analyzes the stability of its linearized model with the use of state feedback control theory. Hence their AQM controller is called the state feedback controller (SFC).



OutlineOutline

Introduction Enhanced TCP model Analyze the Interaction between TCP and

AQM Details of the State Feedback Controlled

AQM Related Work Simulations Conclusions



Enhanced TCP modelEnhanced TCP model

Assumptions

(A1) TCP connections only operate in congestion avoidance phase.

(A2) The change in packet dropping/marking probability is insignificant in one RTT.

(A3) All packets are marked independently.




Big deal claim :: the expected cwnd change is calculated over one RTT and not over the interval between two ACKs.

Namely,

E (Δ ω) / τ

is used as the cwnd rate change.




TCP behavior is modeled in terms of “cycles” that are approximately one RTT to yield equation 1

E (Δ ω) = fcn (ω, ω’, b, p) [1]

where

b allows for modeling of delayed ACKs

ω’ is the size of cwnd one RTT in past.




Using the assumption, p is small and that

ωp << 1, yields equation 4:

d E(ω) / dt = … [4]

The important idea being :: this model (when compared to others) has the congestion window size decreasing faster the impact of the dropping/marking probability on cwnd change is larger than other models predict.



Analysis of the Interaction Analysis of the Interaction between TCP and AQMbetween TCP and AQM

The authors use partial differential equations to describe the dynamic system used to analyze the interaction between TCP and an AQM.

The system consists of N homogeneous TCP connections traversing a single bottleneck link with bandwidth C.



Analysis of the Interaction Analysis of the Interaction between TCP and AQMbetween TCP and AQM

Homogeneous :: All TCP connections are assumed to have the same RTT.

q - the queue length on the bottleneck link

ω – Each connection has the same connection window size.



Dynamic System EquationsDynamic System Equationsdq/dt = g(ω(t), q) = Nω/ τ - C

dω/dt = f(ω(t), ω(t - τ), p)

The first differential equation states that the queue length is an integral of the difference between the packet arrival rate and the link capacity.

The second differential equation describes the dynamic behavior of the TCP window developed in the enhanced TCP model.



Linear Differential ApproximationLinear Differential Approximation

Since the system model is non-linear, the system is approximated with its small-deviation linearized model around an operating point (ω0 ,p0) to analyze its local stability. This yields the following set of differential equations:

δq/dt = Nδω/ τ

δω/dt = - (p0 + 2bω0p0)δω/ 2bτ

- δp(t-τ)/bτp0



Utilizing Control TheoryUtilizing Control Theory

The authors convert the linear differential equations to a matrix form where the matrix [D AD] is full ranked.

This implies this system is controllable and by using the proper control law, the system’s state (i.e., characterized by q and ω), can be taken to a desirable equilibrium point.



State Feedback ControllerState Feedback Controller

Based on state feedback control theory, the authors design an AQM controller under the linearized model.

Stabilize (in this context) makes δq and δω as close to zero as possible!



State Feedback ControllerState Feedback Controller

Reasons for state feedback controller:

1. Using average queue length brings “sluggishness” into a delay system.

2. A state feedback controller can be easily implemented and it can respond quickly to system dynamics.



Block DiagramBlock Diagram

Letting p(t) = K x(t) allows parameter characterization in terms of k1 and k2.

The control theory then permits determination of the stable region for k1 and k2.



Stable RegionsStable Regions

The stable region for k2 is bounded by N/ τC.

Based on Figure 2 , the stable region is characterized in terms of Nmin and τmax .

After the value of k2 is determined, k1 can be determined and the relationship is graphed in Figure 3.



Sample SettingsSample SettingsGiven:

C = 10Mbps;

average packet size =1000 bytes;

Nmin = 300;

τmax = 0.6 sec.;

b = 2;

Then k2 = 0.2 and k1 = 0.0005



SFC AlgorithmSFC Algorithm



AQM TaxonomyAQM Taxonomy



Schemes that aim to achieve fairnessSchemes that aim to achieve fairness

FRED – monitors both global average queue length

and also average queue length for queue for each flow.

– Requires two min and max thresholdsBRED

– Extends FRED and imposes three thresholds.



Schemes that decouple congestion Schemes that decouple congestion index from the performance index.index from the performance index.

These AQM schemes aim for high utilization and low delay.

The decoupling accomplished by calculating p using an additional measure than queue length.

BLUE– Uses instantaneous queue length and link

utilization as traffic load indices.



Schemes that decouple congestion Schemes that decouple congestion index from the performance index.index from the performance index.

REM– Defines a “price function” in terms of rate

difference and queue mismatch.AVQ

– Only uses input rate and maintains a virtual queue.



Schemes that stabilize the Schemes that stabilize the instantaneous queue lengthinstantaneous queue length

SRED– Estimates value of N and uses estimate in

determining p.PI

– aims to stabilize instantaneous queue size using fluid model.

Scalable control scheme– Uses link price and virtual capacity.



Single Bottleneck SimulationsSingle Bottleneck Simulations

router router

10 Mbps, 40 ms

10 Mbps, 40 ms

10 Mbps, 40 ms

10 Mbps, 40 ms10 Mbps, 20 ms



200 TCP flows200 TCP flows









System ResponseSystem Response



Dynamic Traffic ChangesDynamic Traffic Changes



Throughput RobustnessThroughput Robustness



Loss Rate RobustnessLoss Rate Robustness



Multiple Bottleneck Multiple Bottleneck Simulations Simulations



Instantaneous Queue LengthInstantaneous Queue Length



Link UtilizationLink Utilization



Packet Loss RatePacket Loss Rate



ConclusionsConclusionsPaper developed enhanced model to

characterize TCP.Designed SFC as AQM controller

designed to stabilize the queue at the router.

Simulations show SFC outperforms other schemes with respect to queue length, utilization, and packet loss.



CriticismsCriticisms

What did they not do?Other issues?

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A State Feedback Control Approach to Stabilizing Queues for ECN-Enabled TCP Connections

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