Analysis of the Increase and Decrease. Congestion Avoidance in Computer Networks

Transcription

1 Analysis of the Increase and Decrease Algorithms for Congestion Avoidance in Computer Networks Dah-Ming Chiu, Raj Jain Presented by: Ashish Vulimiri

2 Congestion Control

3 Congestion Avoidance

4 Congestion Avoidance Congestion control vs congestion avoidance

5 System Model Single shared bottleneck resource Synchronous feedback Control applied by all users Feedback type: binary

6 System Model Feedback mechanism: set signal bit on packets, processed by destination Rejected alternatives: extra signal packets, induce routing changes, signal bit processed by source TCP Tahoe (and derivatives): signal = packet loss

7 Feedback Binary feedback { 0 Increase load y(t) = 1 Decrease load x i (t + 1) = x i (t) + u i (t) u i can be an arbitrary function of x i (t) and y(t) We focus on a linear model { a I + b I x i (t) x i (t + 1) = a D + b D x i (t) if y(t) Increase if y(t) Decrease

8 Criteria

9 Criteria 1 Efficiency: load must be as close to knee point as possible

10 Criteria 1 Efficiency: load must be as close to knee point as possible 2 Fairness In a perfectly fair system, i jx i = x j We use a fairness criterion: F = ( x i ) 2 n ( ) xi 2 F lies between 0 and 1, higher values indicating greater fairness

11 Criteria 1 Efficiency: load must be as close to knee point as possible 2 Fairness In a perfectly fair system, i jx i = x j We use a fairness criterion: F = ( x i ) 2 n ( ) xi 2 F lies between 0 and 1, higher values indicating greater fairness 3 Distributedness Users do not know anything about state of system Resource delivers only binary feedback to limit overhead

12 Criteria 4 Convergence Constant-state convergence unlikely since we use only binary feedback We use two parameters: responsiveness (how quickly the steady state is reached), and smoothness (size of oscillations)

13 Constraints

14 Constraints: Fairness Fairness must improve in at least one of increase and decrease, and not degrade in either This implies: both a I b I and a D b D must be non-negative, and at least one must be positive

15 Constraints: Fairness Fairness must improve in at least one of increase and decrease, and not degrade in either This implies: both a I b I and a D b D must be non-negative, and at least one must be positive

16 Constraints: Efficiency Feedback must be negative

17 Constraints: Efficiency Feedback must be negative

18 Efficiency: Example Consider a 2-user system with x 1 (t) = x 2 (t) = 100

19 Efficiency: Example Consider a 2-user system with x 1 (t) = x 2 (t) = 100 Let y(t) = decrease, a D = 10, b D = 1/2

20 Efficiency: Example Consider a 2-user system with x 1 (t) = x 2 (t) = 100 Let y(t) = decrease, a D = 10, b D = 1/2 Then x 1 (t + 1) = x 2 (t + 1) = 60

21 Efficiency: Example Consider a 2-user system with x 1 (t) = x 2 (t) = 100 Let y(t) = decrease, a D = 10, b D = 1/2 Then x 1 (t + 1) = x 2 (t + 1) = 60 -ve feedback

22 Efficiency: Example Consider a 2-user system with x 1 (t) = x 2 (t) = 100 Let y(t) = decrease, a D = 10, b D = 1/2 Then x 1 (t + 1) = x 2 (t + 1) = 60 -ve feedback Suppose instead x 1 (t) = x 2 (t) = 10

23 Efficiency: Example Consider a 2-user system with x 1 (t) = x 2 (t) = 100 Let y(t) = decrease, a D = 10, b D = 1/2 Then x 1 (t + 1) = x 2 (t + 1) = 60 -ve feedback Suppose instead x 1 (t) = x 2 (t) = 10 Then x 1 (t + 1) = x 2 (t + 1) = 15

24 Efficiency: Example Consider a 2-user system with x 1 (t) = x 2 (t) = 100 Let y(t) = decrease, a D = 10, b D = 1/2 Then x 1 (t + 1) = x 2 (t + 1) = 60 -ve feedback Suppose instead x 1 (t) = x 2 (t) = 10 Then x 1 (t + 1) = x 2 (t + 1) = 15 +ve feedback

25 Constraints: Efficiency + Distributedness Feedback must be negative no matter what the load distribution at the other users This implies a I > 0 b I 1 a D = 0 0 b d < 1 Constraints can be loosened if bounds on X goal and number of users are known

26 Constraints: Efficiency + Distributedness Feedback must be negative no matter what the load distribution at the other users This implies a I > 0 b I 1 a D = 0 0 b d < 1 Constraints can be loosened if bounds on X goal and number of users are known

27 Constraints: Efficiency + Distributedness Feedback must be negative no matter what the load distribution at the other users This implies a I > 0 b I 1 a D = 0 0 b d < 1 Constraints can be loosened if bounds on X goal and number of users are known

28 Combined Constraints Decrease Linear decrease must be purely multiplicative

29 Combined Constraints Increase Increase must have an additive component, and optionally a multiplicative component Multiplicative component 0 for optimal fairness convergence

30 Nonlinear Control Suppose x i (t + 1) = x i (t) + k= α k (x i (t)) k Can derive constraints on α k and k by evaluating the criteria as done for linear feedback Advantage: more flexibility Disadvantage: less robust higher sensitivity to system parameters like X goal and n

31 Unresolved Issues Effect of delayed feedback Utility of non-binary feedback X goal can t be known, but should users attempt to guess n? Asynchronous feedback

32 Other Issues Effect of packet loss due to errors Fault-resillience Can (and should) a scheme tailored to Internet traffic patterns be designed?

33 Other Issues Effect of packet loss due to errors Fault-resillience Can (and should) a scheme tailored to Internet traffic patterns be designed? And...?