Analysis of the Increase and Decrease Algorithms for Congestion Avoidance in Computer Networks - PowerPoint PPT Presentation

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

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


1
Analysis of the Increase and Decrease Algorithms
for Congestion Avoidance in Computer Networks
CS7701 Research Seminar on Networking http//arl.
wustl.edu/jst/cse/770/
  • Paper by
  • Dah-Ming Chiu (Digital Equipment Corporation)
  • Raj Jain (Digital Equipment Corporation)
  • Published in
  • Computer Networks and ISDN Systems (1989)
  • Presented by
  • Max Podlesny
  • Discussion Leader
  • Michela Becchi

2
Outline
  • Problem
  • Linear Controls
  • Optimizing the Control Schemes
  • Nonlinear Controls
  • Conclusion

3
Problem
  • Mismatch of arrival and service rates
  • Increased queuing in a buffer of a router
  • Packet drops
  • Does TCP congestion control scheme have a
    theoretical basis?

4
What is congestion?
5
Criteria for selecting controls
  • Distributedness
  • Efficiency
  • Fairness
  • Convergence

6
Control system model
  • n users share the resource
  • Time is divided into small slots
  • The i-th users load is xi(t) at time slot t

7
Control system model
  • The total load at the bottleneck resource is ?
    xi(t)
  • The state of the system is characterized by
  • x(t)x1(t), x2(t), , xn(t)
  • Xgoal is the desired load level

8
Control system model
  • Users receive the same feedback
  • Users receive feedback at the same time

9
Control system model
  • Binary feedback y(t),
  • xi(t1) xi(t) f(xi(t), y(t))

10
Control system model
User 1
x1
x2
?xi gt Xgoal ?
User 2
?

xn
User n
y
11
Control functions
  • MIMD (Multiple Increase/Multiple Decrease)
  • bI gt 1, 0 lt bD,lt 1
  • AIAD (Additive Increase/Additive Decrease)
  • aI gt 0, aD,lt 0

12
Control functions
  • AIMD (Additive Increase/Multiple Decrease)
  • aI gt 0, 0 lt bD,lt 1
  • MIAD (Multiple Increase/Additive Decrease)
  • bI gt 0, aD,lt 0

13
Distributedness
  • System does the minimum amount of feedback
  • The following information is assumed to be
    unknown
  • The desired load level
  • The number of users sharing the resource

14
Efficiency
  • X(t) gt Xgoal or X(t) lt Xgoal are considered to be
    inefficient

15
Fairness
  • 1/nltF(x)lt1
  • Independent of scale(unit measurement)
  • A continuous function
  • Equal sharing by k users of n users, k-n users do
    not receive any resource, F(x)k/n

16
Convergence
  • Time taken till the system approaches the goal
    state from any starting state
  • Characterized by
  • Responsiveness
  • Smoothness
  • Tradeoff between responsiveness and smoothness

17
Vector representation
  • 2 users, so n2
  • x0 x10, x20
  • The fairness at any point (x1, x2) is equal to

Fairness Line
x0

User 2s allocation
Efficiency Line
User 1s allocation
18
AIAD
Fairness Line
User 2s allocation
x0
x2
Efficiency Line
User 1s allocation
x1
19
AIMD
x1
Fairness Line
User 2s allocation
x0
x2
x2
Efficiency Line
User 1s allocation
x1
20
How to find control function?
  • Convergence to efficiency
  • The principle of negative feedback
  • if y(t) 0 then ?xi(t1) gt ? xi(t)
  • if y(t) 1 then ?xi(t1) lt ? xi(t)
  • Convergence to fairness
  • F(x(t)) ? 1 as t ? ?, so
  • F(x(t1)) F(x(t)) (1-F(x(t))) ? (1- ? xi2(t)
    / ? (cxi(t))2), where c a/b
  • Distributedness
  • if y(t) 0 then xi(t1) gt xi(t) ? i
  • if y(t) 1 then xi(t1) lt xi(t) ? i

21
Requirements for control function
  • The linear increase policy should have an
    additive component, and optionally, a
    multiplicative component
  • aI gt 0
  • bI ? 1
  • The linear decrease policy should be
    multiplicative
  • aD 0
  • 0 ? bD lt 1

22
Optimal Convergence to Efficiency
  • Given
  • n states for n users, i.e. xi(t1) a bxi(t),
  • i 1, 2, , n.
  • State of the system X(t) ?xi(t)
  • X(0) - initial state
  • Xgoal optimal state
  • One can calculate
  • te - responsiveness
  • se - smoothness
  • te, se are decreasing functions of a and b

23
Optimal Convergence to Fairness
  • F(x(t1)) F(x(t)) is a monotonically increasing
    function of c a/b
  • aD 0, so decrease steps have no affect on
    Fairness
  • The optimal value of bI is its minimum value,
    i.e. bI 1

24
Linear control conditions
  • Increase policy should be additive
  • Decrease policy should be multiplicative

Fairness Line
x0
x2
Efficiency Line
x1
25
Nonlinear Controls
  • Control function
  • A lot of complexity

26
Conclusion
  • Best control condition is AIMD within the
    described model
  • AIMD is used in TCP congestion control
  • It is not the case in real networks
  • MIMD can also be a good decision

27
Questions?
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