Congestion Control In The Internet

JY Le BoudecFall 2009

1

Plan of This Module

1. Congestion control: theory 2. Application to the Internet

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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)

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Inefficiency

Network may lose some packetsAssume you let users send as they wantExample 1: how much will S1 send to D1 ? S2 to D2 ?

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S1C1 = 100 Kb/s

S2C2 = 1000 Kb/s

D1

D2

C3 = 110 Kb/s

C4 = 100 Kb/s

C5 = 10 Kb/s

Solution

Both send 10 kb/sInefficient ! A better allocation is:

S1: 100 kb/sS2: 10 kb/s

The problem was that S2 sent too much

5

S1

S2

D1

D2

x41 = 10

x52 = 10

C1 = 100 Kb/s

C2 = 1000 Kb/s

C3 = 110 Kb/s

C4 = 100 Kb/s

C5 = 10 Kb/s

Congestion Collapse

How much can node i send to its destination ?

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link (i-1)

link i

link (i+1)node i

nodei+1

source i

Solution

We can solve in close form the symmetric case (all links and sources the same)

If λ < c/2 there is no loss:

Else:

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nk (i-1)

link i

link (i+1)node i

nodei+1

source iλi

λi’

λi’’

8

9

0

2

4

6

8

10

12

1 7 13 19 25 31 37 43 49 55 61 67 73 79 85 91 97

This is congestion collapse !

Take home messageSources should limit their rates to adapt it to the network conditionOtherwise inefficiency or congestion collapse may occurCongestion collapse means: as the offered load increases, the total throughput decreases

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Tout se complique

A network should be organized so as to avoid inefficiencyHowever, being maximally efficient may be a problemExample : what is the maximum throughput ?

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Solution

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Take Home Message

Efficiency may be at the expense of fairnessWhat is fairness ?

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Definitions of Fairness

In simple cases, fairness means same to allMay lead to stupid decisionsExample

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Definitions of Fairness

A better allocation, as fair but more efficient, is:

This is the max-min fair allocation for this example

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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’

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Example

Are these allocations max-min fair ?

1.

2.

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X1 X2

Answer

1. No; I can increase x1 without modifying anyone2. Yes;

if I try to increase x0 I must decrease x2 and x2 ≤ x0

if I try to increase x1 I must decrease x0 and x0 ≤ x1

if I try to increase x2 I must decrease x0 and x0 ≤ x2

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The Maths of Max-Min Fairness

Given a set of constraints for the ratesIf it exists, the max-min fair allocation is uniqueThere 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

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Water-Filling Example

Step 1:Rate t to all sourcesIncrease t until t = c/10Freeze the values for sources that use a link that is fully used

x0 = c/10x2 = c/10

Step 2 Rate t to all non frozen sourcesx1 = tIncrease t until t = 9c/10Freeze the values for sources that use a link that is fully used

x1 = 9c/10

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Proportional Fairness

Max-min fairness is the most egalitarian, but efficient, allocationSometimes too egalitarian

I sources, ni=1Max-min fair allocation is xi= c/2 for allFor I large, one might think that x0 should be penalized as it uses more of the networkThis is what proportional fairness does

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Definition of Proportional Fairness

Two ideasRelative shares matter, not absolute

Global effect

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Example

Are these allocations proportionnally fair ?

1.

2.

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X1 X2

Solution

1. I can increase x2 alone and the average rate of change is positive. The answer is: No

2. Let us try to decrease x0 by δ. This allows us to increase x1 by δ and x2 by δ/9. For δ small enough (δ ≤ 0.1), the allocation is feasible.

The average rate of change is

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The Maths of Proportional Fairness

Given a set of constraints for the rates that is convex:The proportionally fair allocation exists and is uniqueIt is obtained by maximizing over all feasible allocations:

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Example

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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

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U(x) = ln (x): proportional fairness

U(x) = 1- (1/x)m: m large => ~ max min fairness

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 fairnessE.g. max-min fairness or proportional fairness

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How can congestion control be implemented ?

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Additive Increase Multiplicative Decrease

It is a congestion control mechanism that can be implemented endto endIt is the basis for what we have in the InternetWe explain it on a simple example

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A Simple Network Model

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 ?

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Rate xi(t)

Feedback y(t)

Linear Laws

We consider linear lawsif y(t) == 1 then xi(t+1) = u1 x

i(t) + v1

if y(t) == 0 then xi(t+1) = u0 xi(t) + v0

We want to decrease when y(t)==1, so

We want to increase when y(t)==0, so

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Example

u1 = 0.5, v1 =0, u0 = 0, v0 = 1 (unit: Mb/s)

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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 stationaryBut we would like that the scheme increases fairness

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36

37

38

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Example

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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 valueWe can increase more rapidly the rate of a source that we know is below its fair share

Slow Start is one algorithm for thisSet initial value to the Additive Increase v0

Increase the rate multiplicatively until a target rate is reached or negative feedback is receivedApply multiplicative decrease to target rate if negative feedback is receivedExit slow start when target rate is received

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target

rate

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3 sourcesu1 = 0.5, v1 =0, u0 = 0, v0 = 0.01 (unit: Mb/s)

3rd source starts with rate v0

Source 1

Source 1

With Slow Start

Without Slow Starttime

time

rate (all 3 sources)Source 3

Source 3

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Plan of This Module

1. Congestion control: theory 2. Application to the Internet

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Congestion Control in the Internet is in TCPTCP 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 feedbackuse to reduce the sending rate

UDP sources are a problem for the Internetuse for long lived sessions (ex: RealAudio) is a threat: congestion collapse

UDP sources should imitate TCP : “TCP friendly”

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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 Controlnegative 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 detectionLoss detected by timeout => slow start

Loss detected by fast retransmit or selective Ack => no slow start

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A Trace

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created from data from: IEEE Transactions on Networking, Oct. 95, “TCP Vegas”, L. Brakmo and L. Petersen

twnd

cwnd

A B C

0 1 2 3 4 5 6 7 8 9

60

30

0

Bytes

seconds

A Trace

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created from data from: IEEE Transactions on Networking, Oct. 95, “TCP Vegas”, L. Brakmo and L. Petersen

twnd

cwnd

congestion avoidanceslowstart congestion avoidance

A B C

B C

0 1 2 3 4 5 6 7 8 9

60

30

0

Bytes

seconds

How AIMD is ApproximatedMultiplicative decrease (on loss detection by timeout)

twnd = 0.5 × current_window

twnd = max (twnd, 2 × MSS)

Additive increasefor each ACK received

twnd = twnd + MSS × MSS / twnd This is equivalent in packets to

twnd = min (twnd, max-size) (64KB)

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twnd=

1 MSS

32 4

How multiplicative increase (Slow Start) is approximated

non dupl. ack received during slow start ->

cwnd = cwnd + MSS (in bytes) (1)if cwnd = twnd then transition to congestion avoidance

(1) is equivalent in packets to

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32 5cwnd = 1 seg 4 6 7 8

AIMD and Slow Start are Implemented as a Finite State Machine

“Congestion Avoidance” = phase of additive increase“Slow start” = phase of slow start, as according to theoryMultiplicative decrease is implemented as a state transition

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additive increaseadditive increase

multiplicative decrease

slow start

loss

loss

Congestion avoidance Congestion avoidance

Slow Start and Congestion Avoidance

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exponential increase for cwnd until cwnd = twnd

Slow Start

additiveincrease for twnd, cwnd = twnd

CongestionAvoidance

cwnd = twnd

retransmissiontimeout:

- multiplicative decrease for twnd- cwnd = 1 seg

retransmissiontimeout:

- multiplicative decrease for twnd- cwnd = 1 seg

connection opening: twnd = 65535 Bcwnd = 1 seg

notesthis shows only 2 states out of 3twnd = target window

Fast Recovery

Slow start used when we assume that the network condition is newinitial phase, major change

guessed by timeout expiration

In all other packet loss detection events, slow start is not used, but “fast recovery” is used instead

target window is halved

but temporary window size increase is allowed to help recover losseswhen a loss occurs, the sending rate is no longer approximated by the W/RTT

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Fast Retransmit

Fast Retransmit triggers Fast Recovery at time t1assume cwnd = 4 when P4 is sent

fast recovery increases window and allows to send P7

at time t2, cwd is set to 2

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×

P1 P2 P3 P4 P5 P6 P3 P7

A1 A2 A2 A2 A2 A?

t1 t2

Fast Recovery Details

Multiplicative decreasetwnd = 0.5 × current-sizetwnd = max (twnd, 2 × MSS)

Fast Recoverycwnd = twnd + 3 × MSS (exp. increase)cwnd = min (cwnd, 64K)retransmission of the missing segment (n)

For each duplicated ACKcwnd = cwnd + MSS (exp. increase)cwnd = min (cwnd, 64K)send following segments

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Fast Recovery Example

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twnd

cwnd0 1 2 3 4 5 6

60

30

0

Bytes

secondsE F

A B C D E F

A-B, E-F: fast recoveryC-D: slow start

TCP Congestion Control Has Three States

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Slow Start

- exponentialincrease

CongestionAvoidance

- additiveincrease

FastRecovery

- exponential increase

beyond twnd

new connection:

retr. timeout:

cwnd = twnd:

retr. timeout:

retr. timeout: expected ack received:

fast retransmit:

fast retransmit:

Fairness of TCP

TCP implements some approximation of AIMDAIMD is designed to be approximately fair in a single link scenarioQ: what happens in a network ? Does TCP distribute rates according to max-min fairness or proportional fairness ?

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Fairness of TCP

A: TCP tends to distribute rate so as to maximize utility of source given by

with xi = rate, τi = RTT for source i(proof: see lecture notes)

Assume all sources have same RTT. For rates that are not too small and not too large, this is close to proportional fairness (but a little closer to max-min fairness)

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TCP Bias Against Large RTTs

TCP tends to distribute rate so as to maximize utility of source given by

For sources with different RTTs, there is a bias

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Fairness of TCP

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Example network with two TCP sourceslink capacity, delaylimited queues on the link (8 segments)

NS simulation

routerdestination

10 Mb/s, 20 ms 1 Mb/s 10 ms

10 Mb/s, 60 ms 8 seg. 8 seg.

S1

S2

Throughput in time

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time

ACK numbersS1

S2

Bias of TCP Against Large RTTs

A source that uses many hops obtains less becauseit uses more resources (≈ proportional fairness) – desired bias

it has a longer RTT – undesired bias

Cause is additive increase is one packet per RTT

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AQM

By default. routers drop packets when buffers are fullthis is called “Tail Drop”

Issuesbuffers fill, then drop -> buffers are full most of the time

produces large average delayslarge queuing delay => large RTT => smaller TCP throughput

also: produces very irregular behaviour

but buffers are needed to amortize bursts

Solutionactive queue management (AQM)

drop packets before buffer is full, based on estimation of traffic load

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RED (Random Early Detection)

RED is the first AQM scheme proposed today, the only one in usePrinciples

queue estimates its average queue length avg ← a × measured + (1 - a) × avgincoming packet is dropped with a probability that depends on avgroughly speaking. drop proba is read from the curve below + uniformization procedure

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avgth-min th-maxmax-p

1

q

Example network for RED

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Example network with three TCP sourcesdifferent link delayslimited queues on the link (20 packets)

routerdestination

2 Mb/s, 10 ms

2 Mb/s 100 ms2 Mb/s, 60 ms

2 Mb/s, 100 ms20 seg. 20 seg.

S1

S3

S2

Throughput vs Time, with Tail Drop

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time

ACK numbersS1

S2

S3

Throughput vs Time, with RED

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time

ACK numbers S1

S2

S3

RED makes the buffer closer to a fluid queuing system

TCP Loss - Throughput Formula

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Consider a large TCP connection (many bytes to transmit)Assume we observe that, in average, a fraction q of packets is lost (or marked with ECN)Can we say something about the expected throughput for this connection ?

TCP Loss - Throughput Formula

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TCP connection with RTT Tsegment size Laverage packet loss ratio qconstant C = 1.22

Transmission time negligible compared to RTT, losses are rare, time spent in Slow Start and Fast Recovery negligible

Example

Q. Guess the ratio between the throughputs θ1 and θ2 and of S1 and S2

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routerdestination

10 Mb/s, 20 ms 1 Mb/s 10 ms

10 Mb/s, 60 ms 8 seg. 8 seg.

S1

S2

solution

TCP Friendly Applications

All TCP/IP applications that generate long lived flows should mimic the behavior of a TCP source

RTP/UDP flow sending video/audio data

Adaptive algorithmapplication determines the sending rate

feedback - amount of lost packets, loss ratio

sending rate = rate of a TCP flow experiencing the same loss ratio

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Facts to remember

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TCP performs congestion control in end-systemssender increases its sending window until loss occurs, then decreases

additive increase (no loss) multiplicative decrease (loss)

TCP states slow start, congestion avoidance, fast recovery

Negative bias towards long round trip timesUDP applications should behave like TCP with the same loss rate

Congestion Control: SummaryCongestion control aims at avoiding congestion collapse in the networkWith TCP/IP, performed in end-systems, mainly with TCPTCP Congestion control summaryPrinciple: sender increases its sending window until losses occur, then decrease

target window: additive increase (no loss), multiplicative decrease (loss)3 phases:slow start: starts with 1, exponential increase up to twnd

congestion avoidance:additive increase until loss or no increasefast recovery: fast retransmission of one segmentslow start entered at setup or after retransmission timeoutfast recovery entered at fast retransmit

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additive increase additive increasemultiplicative decrease

slow start

lossloss

Solutions

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Example

Q. Guess the ratio between the throughputs θ1 and θ2 and of S1 and S2

A. If processing time is negligible and router drops packets in the same proportion for all flows, then throughput is proportional to 1/RTT, thus

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routerdestination

10 Mb/s, 20 ms 1 Mb/s 10 ms

10 Mb/s, 60 ms 8 seg. 8 seg.

S1

S2

time

ACK numbers S1

S2

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