congestion control 2 talks

8/18/2019 Congestion Control 2 Talks

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TCP Congestion Control:Algorithms and Analysis

Simon S. Lam

The University of Texas at Austin

Little’s Law

Avera e o ulation= (average delay) x

(throughput)

where N is number of departures

where T is duration of observation

N1average delay delayiN i 1

throughput N/T

avera e o ulation to be defined

2

Try homework problem athttp://www.cs.utexas.edu/users/lam/cs356/homework/hw2.html

TCP Congestion Control (Simon Lam)


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i n s y s

t e m

n ( t )

Time t

N u m b e r

3

T dt t n

T 0)(1 populationaverage


Sliding Window Protocol

Consider an infinite array, Source, at thesender, and an infinite array, Sink, at thereceiver.

0 1 2 a–1 a s–1 s

send window

acknowledged unacknowledged

Source:

P1Sender

0 1 2 r

received

delivered receive window

r + RW – 1

Sink:P2

Receiver

next expected

RW receive window sizeSW send window size (s - a SW)

4TCP Congestion Control (Simon Lam)


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Sliding Windows in Action

Data unit r has just been received by P2 Receive window slides forward

2 sen s cumu ative ac wit sequencenumber it expects to receive next (r+3)

unacknowledged

0 1 2 a–1 a s–1 s

send window

acknowledged

Source:

P1Sender

0 1 2 r


r + RW – 1Sink:

P2Receiver

next expected

r+3


Sliding Windows in Action

P1 has just received cumulative ack withr+3 as next expected sequence number Send window slides forward

0 1 2 a–1 a s–1 s

send window

acknowledged

Source:

P1Sender

0 1 2 r


r + RW – 1Sink:

P2Receiver

next expected



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Window Flow Control

RTT

timeSource

Destination

1 2 W

1 2 W

1 2 W

data ACKs

1 2 W

7

~ W packets per RTT when no loss

Lost packet detected by missing ACK(note: timeout value T O > RTT)

me


Throughput (send rate) Limit the number of unacked transmitted

packets in the network to window size W

Throughput packets/sec

= bytes/sec

W

RTT

W MSS

RTT

8

Where did we apply Little’s Law?Answer: Consider send buffer



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Clarifications Average number in the send buffer is typically

less than W unless packet arrival rate to sendbuffer is infinite -> previous formula provides a

If each packet may be lost with rate p, then theaverage delay is

Since T O > RTT, actual throughput is smaller. With loss, goodput is

(1 )O p RTT p T

9

Note: in some papers and other context (e.g., randomaccess protocols), goodput is called throughput . To avoidconfusion, throughput is called send rate

p roug pu


Effect of Congestion W too big for each of many flows -> congestion

Packet loss -> transmissions on links prior to packet

Congestion collapse due too many retransmissionsand too much waste

October 1986, Internet had its first congestioncollapse

goodput

10

loadTCP Congestion Control (Simon Lam)


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TCP Window Control

Receiver flow control

rwnd: receiver (advertised) window Receiver sends rwnd to sender

Network congestion control Sender tries to avoid overloading network It infers available network capacity from “loss

11

n cat ons cwnd: congestion window

Sender sets W = min (cwnd, rwnd)


Receiver Flow Control

Receiver advertises rwnd with each packet it

Size of rwnd indicates available space inreceive buffer decreased when data is received from IP layer and

ack’d

increased when data is consumed b a lication

12

process



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Network Congestion Control

Sender calculates cwnd from indications ofnetwork congestion

timeout (loss) dupACK (loss likely) queueing delaymark (needs ECN)

TCP algorithms to calculate cwnd

13

Tahoe, Reno, Vegas, …

Link algorithms: RED, REM …


TCP & AQM

pl(t)

xi(t)

Con estion measures t for distributed feedback control of x t

14

loss and dupACK (DropTail)

queueing delay (Vegas)

with the help of active queue management (AQM)

queue length (RED)

price (REM)TCP Congestion Control (Simon Lam)


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TCP Congestion Control Tahoe (Jacobson 1988)

Slow Start Congestion Avoidance

as e ransm

Reno (Jacobson 1990) Fast Recovery Its variants: NewReno, SACK

Vegas (Brakmo & Peterson 1994) New Congestion Avoidance

AQM

15

RED (Floyd & Jacobson 1993)• Probabilistic marking or dropping

REM (Athuraliya & Low 2000)

• Clear buffer, match rate Others…


Slow Start Start with cwnd = 1 On each successful ACK, increment cwnd

+ Exponential growth of cwnd

each RTT: cwnd 2 x cwnd

Enter CA when cwnd >= ssthresh

For initial slow start, ssthresh is set to a ver lar e

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value (e.g., 65 Kbytes)

Note: for clarity, cwnd, rwnd, and ssthresh arecounted in packets (segments) rather than in bytes



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Slow Start

receiversendercwnd

data packet

ACK 1 RTT

2

34

17

56

78

cwnd cwnd + 1 (for each ACK)TCP Congestion Control (Simon Lam)

Congestion Avoidance

CA starts whencwnd

receiversender

On each successfulACK:

cwnd cwnd + 1/cwnd

2

3

1 RTT

data packet

ACK

18

Linear growth of cwnd

each RTT:

cwnd cwnd + 14



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Packet Loss

Assumption: loss indicates congestion

ac e oss e ec e y Retransmission timeout (RTO timer)

Duplicate ACKs (at least 3)

Packets

19

1 2 3 Acknowledgements

3 3 3


Fast Retransmit

A timeout is quite long (> RTT)

U on receivin 3 du ACKs immediatelretransmit without waiting for timeout

Adjusts ssthresh

ssthresh max(flightsize/2, 2)

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w ere g s ze s num er o ou s an ng ac e s,which may be less than W = min(rwnd, cwnd)

Enter Slow Start (cwnd = 1)



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TCP Tahoe (Jacobson 1988)

cwnd

21

SSme

(in RTTs)CA

SS: Slow StartCA: Congestion Avoidance


Successive Timeouts When there is another timeout, double the

timeout value-

retransmission Exponential backoff up to

max timeout value equalto 64 times initial timeoutvalue

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Note: red line in figure denotes a loss indication



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Summary: Tahoe

Basic ideas Probe network for spare capacity during SS andCA and increase send rate

Drastically reduce rate on congestion indication Self-clocking Error recovery by retransmission Round trip time estimation (to get T O value)

for every ACK {

if W < ssthresh then W++ SS

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else W += 1/W (CA)

}

for every loss indication {ssthresh = W/2

W = 1

} TCP Congestion Control (Simon Lam)

TCP Tahoe (Jacobson 1988)

cwnd

time

24

SS CA

SS: Slow Start

CA: Congestion Avoidance



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TCP Reno (Jacobson 1990)

cwnd

time

25

SS CA

SS: Slow Start

CA: Congestion Avoidance Fast retransmission/fast recovery


TCP Reno (another scenario)

TO

halved

3 dupACKscwnd

26

Initial slow startt

Slow start until cwndreaches ssthresh



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Fast recovery (in detail)

Idea: each dupACK represents a packet. ,

very drastic action

Enter FR/FR after 3 dupACKs Set ssthresh max(flightsize/2, 2)

Retransmit lost packet

Set cwnd ssthresh + #dupACKs (window inflation)

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= ,new packet(s)

On non-dup ACK (1 RTT later), set cwnd ssthresh

(window deflation)

Enter CA


9

Example: FR/FR

timeS 1 2 3 4 5 6 87 1 10 11

94

0 0

Above scenario: Packet 1 is lost, packets 2, 3, and

timeR 8

cwnd 8ssthresh

74

0 0 0

Exit FR/FR

44

411

00

28

are rece ve ; up s w t seq. no. returne Fast retransmit

Retransmit on 3 dupACKs

Fast recovery Inflate window such that new packets 9, 10, and 11 can be

sent while repairing lossTCP Congestion Control (Simon Lam)


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Summary: Reno

Basic ideas

dupACKs: fast retransmit + fast recovery

Timeout: fast retransmit + slow start

congestion

dupACKs

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slow start retransmit

avoidance FR FR

timeout


AIMD in steady statemultiplicative decrease:

cut cwnd in half after3 dupACKs

additive increase:increase cwnd by 1MSS every RTT in the

16 Kbytes

24 Kbytes

congestionwindow

a sence o any ossevent

30

8 Kbytes

time

Long-lived TCP connectionTCP Congestion Control (Simon Lam)


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TCP throughput (send rate)

We derived the approximate formula

throughput = packets/sec

W changes with the arrival of eachcongestion indication

W

RTT

31

To ca cu ate average sen rate, we neethe average value of W

Q: W is a function of what parameter?


First approximationM. Mathis, et al., “The Macroscopic Behavior of the TCP CongestionAvoidance Algorithm,”ACM Computer Communicatons Review , 27(3), 1997.

No slow-start, no timeout, long-lived TCPconnection

Independent identically distributed “periods” Each packet may be lost with probability p



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Geometric DistributionAve. no. of transmissions to get first loss

1

1 1

(1 )iii i

n ib i p p

1

1

1 0

2

(1 )

(1 ) (1 )

1 1

i

i

i i

i i

p i p

d d p p p p

dp dp

d p p

33

1/ p

Similarly, ave. no. of transmissions to get first success is1/(1- p )


First approximation (cont.)

8

3W

p

Average number ofpackets delivered in

2 2

21 3

2 2 2 8

W W W

2

send rate (in packets/sec)

3no. of packets/period 8

time per period

W

W RTT

one saw-tooth)

Average number of

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1 / 1 3

22

3

p

RTT p RTT

p

pac ets sent per perio(incl. loss at the end) is1/ p

Equating the two andsolving for W , we get



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TCP ACK generation [RFC 1122, RFC 2581]

Event at Receiver TCP Receiver action

Arrival of in-order segment with

expected seq #. All data up to

expected seq # already ACKed

Arrival of in-order segment with

expected seq #. One other

segment has ACK pending

Delayed ACK. Wait up to 500ms

for next segment. If no next segment,

send ACK

Immediately send single cumulative

ACK, ACKing both in-order segments

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- -

higher-than-expect seq. # .

Gap detected

Arrival of segment that

partially or completely fills gap

,

indicating seq. # of next expected byte

Immediate send ACK, provided that

segment starts at lower end of gap


Receiver implements Delayed ACKs

Receiver sends one ACK for every two packetsreceived -> each saw-tooth is WxRTT wide-> area under a saw-toot is

Send rate is

One ACK for every b packets received -> send rate

23

4

W

1 3

4 RTT p

36

s

1 3

2 RTT bp



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o e ng roug pu : mp eModel and its Empirical Validation,

Proc. ACM SIGCOMM , 1998

Jitendra Padhye, Victor Firoiu,

on ows ey, an m urose

Motivation

Previous formulas not so accurate when

TCP traces show that there are more lossindications due to timeouts (TO) than dueto triple dupACKs (TD)



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Objectives

More accurate steady-state throughput

by also accounting for TO behavior of aTCP connection

Formula applicable over a wider range ofloss rates

Explicit statements of assumptions and

39

approx mat ons use n er vat on othroughput formula

Formula to include the impact of a smallrwnd


Many assumptions andapproximations

A1. TCP sender is saturated, i.e., source

send when send window has space available i.e., bulk transfer application

A2. Slow Start not modeled

A3. Time to send all packets in a window is

40

i.e.,transmission rate is not too low



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A3. Time to send W packets isless than RTT

•ACK receptionmarks the end ofcurrent round and

time

beginning of nextround.

•Approximation: Forb > 1, ACK is notreceived

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End of round

space

one RTT, but it is soassumed in theanalysis


AIMD evolution of Window Size over time

Each TD period is ended by a TD loss indication.

TDP eriod has duration A rounds

42

A4. Duration of a round (RTT) is independent ofwindow size approximation (poor for a slow line)

A5. No window inflation in Fast Recovery approximation



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Markov regenerative assumption

For the i- th TD period, Wi is window size atthe end of the period, Yi is the number ofpackets sent in the period

A6. Assume {Wi} to be a Markovregenerative process with rewards {Yi}

Given A6, the steady-state TCP throughputis

43

lim lim[ ] [ ]

t it

t t

i

B Bt E A E A


Consider i -th TD period

when ACK oflast packet is

received

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One ACK after receiving b packets (b = 2 in abovefigure) -> linear increase has a slope of 1/b packet perRTT

Number of rounds is X i +1

i is the first packet lost in i -th TD periodTCP Congestion Control (Simon Lam)


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Loss assumptions

A7. Losses in different rounds are

approximation

A8. Losses within the same round arecorrelated as follows: If a packet is lost,all remaining packets transmitted until theend of that round are also lost

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approx mat on – ursty oss e av or ut on ywithin the same round

all lost packets in the same round are countedas a single loss indication when estimating p


AIMD throughput derivation (1)seq. no. of first loss

r round trip time

Y no. of packets sent

[ ] 1/

[ ]

E p

E r RTT

W window size

X no. of rounds

A time duration of a period1

[ ] [ ] [ ] 1 1 [ ]

From , we have2

[ ] [ ]2

i ii

E Y E E W E W p

W X W

b

b E X E W

46


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AIMD throughput derivation (2)Another way to

compute E[Y]/ 1 10

( )2

i X bi

i i

k

W Y k b


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AIMD throughput (4)

To get a simple formula, collect terms that are o(1/sqrt(p))

[ ] (1/ )3

2[ ] [ ] (1/ )

2 3

1/ (1/ ) 1 3

E W o pbp

b b E X E W o p

p

p o p

49

22

(1/ )3

RTT bpb RTT o p

p


AIMD with TO

Let n i denote the number of TD periods within a

c cle endin in i -th TO eriod R denote no. of

50

,retransmissions in i -th TO period A10. {n i } form an i.i.d. sequence, independent of

{Yij} and {Aij}



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Throughput of AIMD with TO (1)[ ] [ ] [ ] [ ]

[ ] [ ] [ ] [ ]TO

E M E n E Y E R

E S E n E A E Z

Assumption of

Markovregenerative

send rate[ ] [ ] [ ] [ ]

[ ] [ ]

[ ] [ ]

1where

TO

TO

n B

E S E n E A E Z

E Y Q E R B

E A Q E Z

Q

process again.

51

1[ ]

1

with and [ ] to be determined TO

n

E R p

Q E Z


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Approximate solution for Q (cont.)


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Throughput of AIMD with TO (2)1

[ ] (1 ) for 1, 2,...(2 1) for 6

k

k

k O

P R k p p k L T k


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Impact of receiver’s rwnd limitation

Full model Eq. (31)

if E[W]


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Summary data from traces (1 hour)

Saturated TCPsender

from dividingtotal no. of lossindications bytotal number ofpackets sent

RTT and T O

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averaged overentire 1-hourtrace


Summary data from 100s traces

60

Each row represents results of 100 traces each of100 seconds in duration for same S-D pair

Totals are cumulative over 100 traces

RTT and T O are average values over 100 traces forsame S-D pair



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Experimental comparison (1)

61

Each point represents number of packets in 100s interval of trace T0 ~ single TO, T1 ~ at least 1 double TO in trace, etc. “TD Only” is analytic model by Mathis et al. Note: Wmax is only 6 in Figure 7 TCP Congestion Control (Simon Lam)


62

Wmax = 33 Wmax=44



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63

Wmax=8 Wmax=48


Accuracy of approximate model

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Figure 18: manic to spiff, with predictions by both full andapproximate models (Wmax=32)



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Average errors

65

ave. error no. of observations

predicted observed

observations observed

N N

N


Conclusions A much more rigorous analysis than the one by

Mathis et al.

Numerous assumptions and approximations used

Large amount of experimental measurements onthe Internet to validate accuracy of the full model(less for the approximate model)

Throughput formula accounts for loss indicationsdue to TO as well as rwnd restriction

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s ng t e ormu a requ res accurate measurements oloss rate and RTT values (which could be tricky)

For TCP Reno and drop-tail router

Accuracy (like beauty) is in the eye of thebeholder. What do you think?



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TCP Throughput limited by loss rate

TCP average throughput (approximate) interms of loss rate, L :

Example: 1500-byte segments, 100ms RTT,to get 10 Gbps throughput, loss rate needsto be very low

.

RTT p

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p = x -

New version of TCP needed for connections

with high-delay bandwidth product addressed in paper by Katabi’s et al


The End


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