Congestion Control In The Congestion Control In The Internet Internet JY Le Boudec Fall 2009 1
Plan of This Module Plan of This Module 1. Congestion control: theory 2. Application to the Internet 2
Theory of Congestion Control Theory of Congestion Control What you have to learn in this first part: 1. What is the problem; congestion collapse 2. Efficiency versus Fairness 3. Forms of fairness 4. Forms of congestion control 5. Additive Increase Multiplicative Decrease (AIMD) 3
Inefficiency Inefficiency Network may lose some packets Assume you let users send as they want Example 1: how much will S 1 send to D 1 ? S 2 to D 2 ? S 1 D 1 C 4 = 100 Kb/s C 1 = 100 Kb/s C 3 = 110 Kb/s S 2 C 5 = 10 Kb/s C 2 = 1000 Kb/s D 2 4
Solution Solution Both send 10 kb/s Inefficient ! A better allocation is: S 1 : 100 kb/s S 2 : 10 kb/s The problem was that S 2 sent too much C 4 = 100 Kb/s S 1 C 1 = 100 Kb/s D 1 x 41 = 10 C 3 = 110 Kb/s S 2 x 52 = 10 D 2 C 2 = 1000 Kb/s C 5 = 10 Kb/s 5
Congestion Collapse Congestion Collapse How much can node i send to its destination ? source i node link i i+1 node i link (i-1) link (i+1) 6
Solution Solution source i λ i node link i i+1 node i We can solve in close form the λ i ’ nk (i-1) link (i+1) symmetric case (all links and λ i ’’ sources the same) If λ < c/2 there is no loss: Else: 7
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This is congestion collapse ! Take home message Sources should limit their rates to adapt it to the network condition Otherwise inefficiency or congestion collapse may occur Congestion collapse means: as the offered load increases, the total throughput decreases 10
Tout se complique Tout se complique A network should be organized so as to avoid inefficiency However, being maximally efficient may be a problem Example : what is the maximum throughput ? 11
Solution Solution 12
Take Home Message Take Home Message Efficiency may be at the expense of fairness What is fairness ? 13
Definitions of Fairness Definitions of Fairness In simple cases, fairness means same to all May lead to stupid decisions Example 14
Definitions of Fairness Definitions of Fairness A better allocation, as fair but more efficient, is: This is the max-min fair allocation for this example 15
Max-Min fairness Max-Min fairness We say that an allocation is max-min fair if it satisfies the following criterion: If we start from this allocation and increase the rate of source s, then we must decrease the rate of some other (less rich) source s’ 16
Example Example Are these allocations max-min fair ? X 1 X 2 1. 2. 17
Answer Answer 1. No; I can increase x 1 without modifying anyone 2. Yes; if I try to increase x 0 I must decrease x 2 and x 2 ≤ x 0 if I try to increase x 1 I must decrease x 0 and x 0 ≤ x 1 if I try to increase x 2 I must decrease x 0 and x 0 ≤ x 2 18
The Maths of Max-Min Fairness The Maths of Max-Min Fairness Given a set of constraints for the rates If it exists, the max-min fair allocation is unique There exists one max-min fair allocation if the set of feasible rates is convex (this is the case for networks, we have linear constraints) For a set of feasible rates as in our case (the sum of the rates on every link is upper bounded), the (unique) max min fair allocation is obtained by water-filling 19
Water-Filling Example Water-Filling Example Step 1: Rate t to all sources Increase t until t = c/10 Freeze the values for sources that use a link that is fully used x 0 = c/10 x 2 = c/10 Step 2 Rate t to all non frozen sources x 1 = t Increase t until t = 9c/10 Freeze the values for sources that use a link that is fully used x 1 = 9c/10 20
Proportional Fairness Proportional Fairness Max-min fairness is the most egalitarian, but efficient, allocation Sometimes too egalitarian I sources, n i =1 Max-min fair allocation is x i = c/2 for all For I large, one might think that x 0 should be penalized as it uses more of the network This is what proportional fairness does 21
Definition of Proportional Fairness Definition of Proportional Fairness Two ideas Relative shares matter, not absolute Global effect 22
Example Example Are these allocations proportionnally fair ? X 1 X 2 1. 2. 23
Solution Solution 1. I can increase x 2 alone and the average rate of change is positive. The answer is: No 2. Let us try to decrease x 0 by δ . This allows us to increase x 1 by δ and x 2 by δ /9. For δ small enough ( δ ≤ 0.1), the allocation is feasible. The average rate of change is 24
The Maths of Proportional Fairness The Maths of Proportional Fairness Given a set of constraints for the rates that is convex: The proportionally fair allocation exists and is unique It is obtained by maximizing over all feasible allocations: 25
Example Example 26
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Utility Fairness Utility Fairness One can interpret proportional fairness as the allocation that maximizes a global utility. The utility of an allocation, to source I, is here the log of the rate If we take some other utility function we have what we call a utility fairness Max-min fairness is the limit of utility fairness when the utility function converges to a step function U(x) = ln (x): proportional fairness U(x) = 1- (1/x) m : m large => ~ max min fairness 28
Take Home Message Take Home Message Sources should adapt their rate to the state of the network in order to avoid inefficiencies and congestion collapse This is called “congestion control” A rate adaptation mechanism should target some form of fairness E.g. max-min fairness or proportional fairness 29
How can con How can congestion control be estion control be implemented ? implemented ? 30
Additive Increase Multiplicative Additive Increase Multiplicative Decrease Decrease It is a congestion control mechanism that can be implemented end to end It is the basis for what we have in the Internet We explain it on a simple example 31
A Simple Network Model A Simple Network Model Feedback y(t) Rate x i (t) Network sends a one bit feedback Sources reduce rate if y(t)=1, increase otherwise Question: what form of increase/decrease laws should one pick ? 32
Linear Laws Linear Laws We consider linear laws if y(t) == 1 then x i (t+1) = u 1 x i (t) + v 1 if y(t) == 0 then x i (t+1) = u 0 x i (t) + v 0 We want to decrease when y(t)==1, so We want to increase when y(t)==0, so 33
Example Example u 1 = 0.5, v 1 =0, u 0 = 0, v 0 = 1 (unit: Mb/s) 34
Impact of Fairness Impact of Fairness Does such a scheme converge to a fair allocation ? Here max-min and proportionally fair are the same (i.e. same rate to all) The scheme may not converge as sources may not be stationary But we would like that the scheme increases fairness 35
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Example Example 40
Slow Start Slow Start AIMD’s fairness can be improved if we know that one source gets much less than some other For example, if initial condition is a small value target We can increase more rapidly the rate of a source that we know is below its fair share Slow Start is one algorithm for this Set initial value to the Additive Increase v 0 rate Increase the rate multiplicatively until a target rate is reached or negative feedback is received Apply multiplicative decrease to target rate if negative feedback is received Exit slow start when target rate is received 41
Source 3 3 sources u 1 = 0.5, v 1 =0, u 0 = 0, v 0 = 0.01 (unit: Mb/s) 3 rd source starts with rate v 0 Without Slow Start time Source 1 Source 3 rate (all 3 sources) With Slow Start Source 1 time 42
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Plan of This Module Plan of This Module 1. Congestion control: theory 2. Application to the Internet 44
Congestion Control in the Internet is in TCP Congestion Control in the Internet is in TCP TCP is used to avoid congestion in the Internet in addition to what was shown: a TCP source adjusts its window to the congestion status of the Internet (slow start, congestion avoidance) this avoids congestion collapse and ensures some fairness TCP sources interprets losses as a negative feedback use to reduce the sending rate UDP sources are a problem for the Internet use for long lived sessions (ex: RealAudio) is a threat: congestion collapse UDP sources should imitate TCP : “TCP friendly” 45
TCP Congestion Control is based on AIMD TCP Congestion Control is based on AIMD TCP adjusts the window size (in addition to offered window ie credit mechanism) W = min ( cwnd , OfferedWindow ) Principles of TCP Congestion Control negative feedback = loss, positive feedback = ACK received Additive Increase (1 MSS), Multiplicative Decrease (0.5) Slow start with increase factor = 2 Reaction to loss depends on nature of loss detection Loss detected by timeout => slow start Loss detected by fast retransmit or selective Ack => no slow start 46
A Trace A Trace Bytes twnd B C A 60 cwnd 30 0 0 1 2 3 4 5 6 7 8 9 seconds created from data from: IEEE Transactions on Networking, Oct. 95, “TCP Vegas”, L. Brakmo and L. Petersen 47
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