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Analysis of the Increase and Decrease Algorithms
for Congestion Avoidance in Computer Networks
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Analysis of the Increase and Decrease Algorithms
for Congestion Avoidance in Computer Networks

• by Dah-Ming Chiu and Raj Jain, DEC
• Computer Networks and ISDN Systems
• 17 (1989), pp. 1-14

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Motivation (1)

• Internet is heterogeneous
• Different bandwidth of links
• Different load from users
• Congestion control
• Help improve performance after congestion has
  occurred
• Congestion avoidance
• Keep the network operating off the congestion

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Motivation (2)

• Fig. 1. Network performance as a function of the
  load.

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Power of a Network

• The power of the network describes this
  relationship of throughput and delay
• Power Goodput/Delay
• This is based on M/M/1 queues ( 1 server and a
  Markov distribution of packet arrival and
  service).
• This assumes infinite queues, but real networks
  the have finite buffers and occasionally drop
  packets.
• The objective is to maximize this ration, which
  is a function of the load on the network.
• Ideally the resource mechanism operates at the
  peak of this curve.

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Power Curve
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Motivation (2)

• Power Goodput/Response Time

• Fig. 1. Network performance as a function of the
  load.

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Relate Works

• Centralized algorithm
• Information flows to the resource managers and
  the decision of how to allocate the resource is
  made at the resource Sanders86
• Decentralized algorithms
• Decisions are made by users while the resources
  feed information regarding current resource usage
  Jaffe81, Gafni82, Mosely84
• Binary feedback signal and linear control
• Synchronized model
• What are all the possible solutions that converge
  to efficient and fair states

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Control System
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Linear Control (1)

• 4 examples of linear control functions
• Multiplicative Increase/Multiplicative Decrease
• Additive Increase/Additive Decrease
• Additive Increase/Multiplicative Decrease
• Additive Increase/ Additive Decrease

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Linear Control (2)

• Multiplicative Increase/Multiplicative Decrease
• Additive Increase/Additive Decrease
• Additive Increase/Multiplicative Decrease
• Multiplicative Increase/ Additive Decrease

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Criteria for Selecting Controls

• Efficiency
• Closeness of the total load on the resource to
  the knee point
• Fairness
• Users have the equal share of bandwidth
• Distributedness
• Knowledge of the state of the system
• Convergence
• The speed with which the system approaches the
  goal state from any starting state

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Responsiveness and Smoothness of Binary Feedback
System

• Equlibrium with oscillates around the optimal
  state

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Vector Representation of the Dynamics
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Example of Additive Increase/ Additive Decrease
Function
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Example of Additive Increase/ Multiplicative
Decrease Function
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Convergence to Efficiency

• Negative feedback
• So
• If y0
• If y1
• Or

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Convergence to Fairness (1)

• where ca/b (6)

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Convergence to Fairness (2)

• cgt0 implies
• Furthermore, combined with (3) we have

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Distributedness

• Having no knowledge other than the feedback y(t)
• Each user tries to satisfy the negative feedback
  condition by itself
• Implies (10) to be

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Truncated Case

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Important Results

• Proposition 1 In order to satisfy the
  requirements of distributed convergence to
  efficiency and fairness without truncation, the
  linear increase policy should always have an
  additive component, and optionally it may have a
  multiplicative component with the coefficient no
  less than one.
• Proposition 2 For the linear controls with
  truncation, the increase and decrease policies
  can each have both additive and multiplicative
  components, satisfying the constrains in
  Equations (16)

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Vectorial Representation of Feasible conditions
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Optimizing the Control Schemes

• Optimal convergence to Efficiency
• Tradeoff of time to convergent to efficiency te,
  with the oscillation size, se.
• Optimal convergence to Fairness

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Optimal convergence to Efficiency

• Given initial state X(0), the time to reach Xgoal
  is

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Optimal convergence to Fairness

• Equation (7) shows faireness function is
  monotonically increasing function of ca/b.
• So larger values of a and smaller values b give
  quicker convergence to fairness.
• In strict linear control, aD0 gt fairness
  remains the same at every decrease step
• For increase, smaller bI results in quicker
  convergence to fairness gt bI 1 to get the
  quickest convergence to fairness
• Proposition 3 For both feasibility and optimal
  convergence to fairness, the increase policy
  should be additive and the decrease policy should
  be multiplicative.

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Practical Considerations

• Non-linear controls
• Delay feedback
• Utility of increased bits of feedback
• Guess the current number of users n
• Impact of asynchronous operation

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Conclusion

• We examined the user increase/decrease policies
  under the constrain of binary signal feedback
• We formulated a set of conditions that any
  increase/decrease policy should satisfy to ensure
  convergence to efficiency and fair state in a
  distributed manner
• We show the decrease must be multiplicative to
  ensure that at every step the fairness either
  increases or stays the same
• We explain the conditions using a vector
  representation
• We show that additive increase with
  multiplicative decrease is the optimal policy for
  convergence to fairness