Analysis of the virtual rate control algorithm in TCP networks

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Analysis of the virtual rate control algorithm in
TCP networks

• IEEE Globecom 2002
• Nov 20, 2002
• E.-C. Park, H. Lim, K.-J. Park, and C.-H. Choi
• School of Electrical Engineering Computer
  Science
• Seoul National University, Korea

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Contents

• Introduction
• VRC algorithm
• Stability analysis
• Simulation results
• Conclusion

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1. Introduction

• What is congestion?
• Senders present a larger aggregate traffic than
  intermediate nodes in the network can process.
• Congestion control scheme
• Sender-based control (TCP)
• Router-supported control (AQM)

Intermediate node (router)
receiver
sender
packet
packet
packet dropping/marking
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TCP Congestion Control

• Window-based transmission control
• AIMD Control Scheme
• On detection of congestion
• Multiplicative decrease in cwnd (MD)
• Cooperate to resolve congestion
• Otherwise
• Additive increase in cwnd (AI)
• Probe available excess bandwidth
• ?Best-effort service

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• TCP with drop-tail queue
• Detect congestion only after packet loss due to
  buffer overflow
• Large loss rate
• Global synchronization of sources
• Relying on only sender (e.g.,TCP) is not
  sufficient to resolve congestion
• At the intermediate node (router), congestion
  should be controlled before buffer overflow
• Active Queue Management

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Various AQM schemes

• Random Early Detection (RED)
• Floyd and Jacobson 1993
• Pros
• Detect congestion early before overflow
• Drop/mark packets randomly with increasing
  probability as average queue length increases
• ? Reduce loss rate, avoid global sync.
• Cons
• Difficulty of appropriate parameter setting for
  different network conditions
• Sensitive queueing delay and throughput to the
  traffic load and to parameters
• proportional control of average queue length

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• Proportional-Integral (PI)control
• Hollot et al. 2001
• Control-theoretic approach
• Introduce target rate and add integral control
• Regulate queue length to qt regardless of
  traffic load
• However, cause slow response and overshoot

Proportional control
Integral control
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• Random Exponential Marking (REM)
• Athuraliya et al. 2001
• Introduce price , as congestion measure

match rate
clear buffer

• Similar to PI
• Cf. PI

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• Adaptive Virtual Queue (AVQ)
• Kunniyur and Srikant 2001
• Utilize virtual queue and virtual capacity
• Make input rate (r(t)) achieve desired
  utilization
• that is slightly smaller than actual link
  capacity ( )
• Keep small queue length
• Virtual Rate Control algorithm (VRC)
• proposed by authors (IEE Elec. Letters, Aug,
  2002)

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• Contributions
• Analyze stability of VRC algorithm with TCP
  dynamics
• Derive parametric range for stability
• Confirm validity of analysis
• Evaluate performance of VRC

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2. VRC Algorithm

• Objective
• Regulate queue length with small variation
• Achieve high link utilization and small packet
  loss rate
• Adapt to the dynamic traffic load rapidly
• Excess input rate over output link capacity
  affects queue length and possibly leads to buffer
  overflow
• Queue occupancy rate should be controlled as well
  as queue length
• Rate-based control
• Achieve rapid response to traffic fluctuations
• Cf. RED, PI, REM queue-length-based control

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Motivation

• Consider proportional rate control with adaptive
  target rate (rt)
• Fast response to input rate changes
• Adaptive target rate
• If q(t)ltqt ? more room to accommodate packets,
  target rate increases
• Otherwise, as q(t) exceeds qt, target rate
  decreases
• This proportional rate control in TCP networks
  can not ensure r(t) matches C
• Sending rate of TCP is self-adaptive
• ? Incorporate source (TCP) behavior

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Virtual Rate Control

• Consider steady-state behavior of TCP and rate
  control by a graphical method
• Assume Sending rate of TCP rTCP(p) is a
  decreasing function of loss rate p
• Equilibrium point is at the intersection of
  control function and TCP sending rate function

• Discrepancy between input rate and link capacity
  in steady-state

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• Introduce virtual target rate
• Compensate for the rate error
• Updated to minimize the difference between input
  rate and target rate
• Easy to implement
• Simple and low overhead

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3. Stability Analysis

• Convergence of input rate
• Theorem 1 Assuming that the throughput of
  TCP is a strictly decreasing function of loss
  rate, i.e., , the input rate of VRC
  converges to the target rate at the steady-state
• Proof can be performed without resorting to any
  TCP dynamic model
• Derivation of stability condition
• Adopt fluid-based TCP dynamic model
• Represented in terms of control parameters

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System Dynamic Model

• (1) TCP dynamics
• Fluid-flow analysis Misra2000
• Modeling window size (W(t)) as AIMD
• (2) Router queue dynamics
• Integrator of queue occupancy rate, i.e.,
  difference between r(t) and C
• (3) AQM(VRC) as congestion controller
• Represented in terms of queue length error
  (e(t)q(t)-qt)

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Stability Condition of TCP/VRC

• Obtain stability condition
• (1) Linearize the dynamic model around
  equilibrium point
• (2) Obtain characteristic equation using Laplace
  Transform
• (3) Approximate time delay using Padé first-order
  lag
• (4) Apply Routh-Hurwitz stability criterion
• Closed-form stability condition
• Theorem 2 The approximated system is stable
  
• if the control parameters KD , KP , and KI
  satisfy

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• Used as an effective design guideline for control
  parameter setting
• If the system parameters are given
• Provide the maximum or minimum bound of system
  parameters
• If VRC is already designed

• Stability region decreases
• when delay(R) and capacity(C) increase
• when number of connection(N) decreases

Fig. Stability region of R,C,N at fixed control
parameters The region below the curve is stable
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4. Simulation Results

• Simulation Environment
• ns-2 network simulator
• Simple bottleneck topology
• TCP/Reno, average packet size 1Kbyte
• qt50, qmax100 packets
• Control parameters

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Confirmation of analysis validity

• Find maximum delay bound using analysis
  results for given control parameters (
  )
• Compare input rate and queue length for two RTTs
• ( )

? Performance is degraded significantly if the
system does not satisfy stability condition
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• Compare analysis and simulation results
• Maximum delay bound
• Parametric range for system stability

Maximum delay bound
? Show validity of analysis results
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Evaluation of VRC performance

• Responsiveness to dynamic traffic
• At t100s, one half of the connections (50) are
  dropped,
• and another 100 connections are
  established at t200s

Input rate matches to link capacity ? Show fast
response

• Queue length is stabilized well
• ? Not load-dependent
• controllable queuing delay
• by adjusting qt

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• Performance comparison of VRC with other AQMs
• Robustness to the traffic load
• Change N from 20 to 200

VRC(), RED(), PI(x), REM(?), and AVQ(?)
VRC shows consistent average queue length with
small variation
VRC keeps high utilization and small loss rate
Performance of VRC is almost immune to traffic
load
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5. Conclusion

• Analyze stability of VRC algorithm
• Convergence of input rate to link capacity
• Derivation of stability condition
• Provide effective design guideline of parameter
  setting for system stability
• Simulation results
• Confirm validity of analysis
• Evaluate the performance of VRC
• Regulate queue length with small variation
• High utilization and small loss
• Robust performance to different network
  conditions and dynamic traffic changes