1 a state feedback control approach to stabilizing queues for ecn- enabled tcp connections yuan gao...
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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)
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OutlineOutline
Introduction Enhanced TCP model Analyze the Interaction between TCP and
AQM Details of the State Feedback Controlled
AQM Related Work Simulations Conclusions
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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.
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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).
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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).
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OutlineOutline
Introduction Enhanced TCP model Analyze the Interaction between TCP and
AQM Details of the State Feedback Controlled
AQM Related Work Simulations Conclusions
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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.
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Enhanced TCP modelEnhanced TCP model
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.
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Enhanced TCP modelEnhanced TCP model
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.
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Enhanced TCP modelEnhanced TCP model
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.
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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.
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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.
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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.
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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
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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.
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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!
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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.
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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.
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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.
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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
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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.
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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.
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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.
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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.
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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
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Dynamic Traffic ChangesDynamic Traffic Changes
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Throughput RobustnessThroughput Robustness
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Loss Rate RobustnessLoss Rate Robustness
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Multiple Bottleneck Multiple Bottleneck Simulations Simulations
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Instantaneous Queue LengthInstantaneous Queue Length
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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.