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

1
A State Feedback Control Approach to Stabilizing
Queues for ECN-Enabled TCP Connections

• Yuan Gao and Jennifer Hou
• IEEE INFOCOM 2003,
• San Francisco, April 2003
• Presented by Bob Kinicki

2
Outline

• Introduction
• Enhanced TCP model
• Analyze the Interaction between TCP and AQM
• Details of the State Feedback Controlled AQM
• Related Work
• Simulations
• Conclusions

3
Introduction

• 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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Introduction

• 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)/ t ?2p/ 2 t
• where ? current cwnd size and
• t is the round-trip time (RTT).

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Introduction

• They claim other models only model gradual
  decrease in ?2p/ 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).

6
Outline

• 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 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 model

• Big deal claim the expected cwnd change is
  calculated over one RTT and not over the interval
  between two ACKs.
• Namely,
• E (? ?) / t
• is used as the cwnd rate change.

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Enhanced TCP model

• TCP behavior is modeled in terms of cycles that
  are approximately one RTT to yield equation 1
• E (? ?) fcn (?, ?, b, p) 1
• where
• b allows for modeling of delayed ACKs
• ? is the size of cwnd one RTT in past.

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Enhanced TCP model

• Using the assumption, p is small and that
• ?p ltlt 1, yields equation 4
• d E(?) / 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 between 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 between TCP and AQM

• Homogeneous All TCP connections are assumed to
  have the same RTT.
• q - the queue length on the bottleneck
  link
• ? Each connection has the same connection
  window size.

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Dynamic System Equations

• dq/dt g(?(t), q) N?/ t - C
• d?/dt f(?(t), ?(t - t), 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 Approximation

• Since the system model is non-linear, the system
  is approximated with its small-deviation
  linearized model around an operating point (?0
  ,p0) to analyze its local stability. This yields
  the following set of differential equations
• dq/dt Nd?/ t
• d?/dt - (p0 2b?0p0)d?/ 2bt
• - dp(t-t)/btp0

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Utilizing 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 systems state
  (i.e., characterized by q and ?), can be taken to
  a desirable equilibrium point.

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State Feedback Controller

• Based on state feedback control theory, the
  authors design an AQM controller under the
  linearized model.
• Stabilize (in this context) makes dq and d? as
  close to zero as possible!

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State Feedback Controller

• Reasons for state feedback controller
• Using average queue length brings sluggishness
  into a delay system.
• A state feedback controller can be easily
  implemented and it can respond quickly to system
  dynamics.

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Block 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 Regions

• The stable region for k2 is bounded by N/ tC.
• Based on Figure 2 , the stable region is
  characterized in terms of Nmin and tmax .
• After the value of k2 is determined, k1 can be
  determined and the relationship is graphed in
  Figure 3.

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Sample Settings

• Given
• C 10Mbps
• average packet size 1000 bytes
• Nmin 300
• tmax 0.6 sec.
• b 2
• Then k2 0.2 and k1 0.0005

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SFC Algorithm
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AQM Taxonomy
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Schemes 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 thresholds
• BRED
• Extends FRED and imposes three thresholds.

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Schemes that decouple congestion 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 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 instantaneous 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 Simulations
10 Mbps, 40 ms
10 Mbps, 40 ms
10 Mbps, 20 ms
router
router
10 Mbps, 40 ms
10 Mbps, 40 ms
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200 TCP flows
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200 TCP flows
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200 TCP flows
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System Response
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Dynamic Traffic Changes
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Throughput Robustness
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Loss Rate Robustness
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Multiple Bottleneck Simulations
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Instantaneous Queue Length
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Link Utilization
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Packet Loss Rate
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Conclusions

• Paper 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.

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Criticisms

• What did they not do?
• Other issues?