Farsighted Congestion Controllers

Milan Vojnović

Microsoft Research

Cambridge, United KingdomCollaborators:Dinan Gunawardena (MSRC), Peter Key (MSRC), Shao Liu (UIUC), Laurent Massoulié (MSRC)

MIT, 09 Nov 05

2

Problem

Applications concerned with long-run throughput Indifferent to short-timescale throughput Ex. peer-to-peer file sharing

Goal: Optimize long-run throughput Share bandwidth fairly with TCP

Data transfer

WebWeb Internet

3

0 0.5 1 1.5 2

x 104

0

1

2

3

4

5

6

x 106

time

rates

rates over time, FAR and TCP

FAR

TCP

Solution

Number ofconnections

Farsighted TCP

TCPTCP

Rat

e (M

b/s)

Internet

Time

4

Solution: farsighted controller

w w + 1/ww max(w – 1/(ww0)

+ ack- ack

-m

Window

Time

high congestion

• Two-timescale control• = parameter learned on-line at slow timescale

w0

5

Compare with TCP

Window

Time

w w + 1/ww w – ½ w

+ ack- ack

high congestion

6

Roadmap

Optimality Properties Rate adaptation Protocol & verification Conclusion

7

Setup

Network state fluctuates over a set of phases U

Ex. single link phase = number of competing flows

(u) = fraction of time phase is u Cl,u(x) = cost of link l with arrival rate x

Network

8

Setup (cont’d)

Vr(x) = utility for rate x = (x(u), uU)

User r

Uu

rrrr uxUuxV ))(()()(

rrr xxU / const )(

)()( rrrr xUxV

Uu

rr uxux )()(

TCP-like Long-run throughput optimizer

9

Problem

l ql

qulUuRr

rr uxCuxV ))(()()( ,

0)(uxr

maximize

over

SYSTEM:

Rrxr , optimal if it solves SYSTEM

10

TCP-like only

l ql

qulRr

rr uxCuxUu

))(())(( ,

0)(uxr

maximize

over

• Separation into independent problems

• Traditional controllers are “myopic”• Optimize rates “independently over time”

SYSTEM u:

11

With long-run throughput optimizers

l qlqul

Uu

Frrr

Mrrr

uxCu

xUuxUu

))(()(

)())(()(

,

0)(uxr

maximize

over

• No separation

• Long-run throughput optimizers = “farsighted”

SYSTEM:

12

Formally: multi-path problem

phase 1 phase 2 phase 3 phase N. . .

rxr(1) xr(2) xr(3) xr(N)

Studied by Gibbens & Kelly 02

But our setup in phase spacePath is not spatial path present at all times “Paths come and leave over time”Time (not space) diversity

13

Roadmap

Optimality Properties Rate adaptation Protocol & verification Conclusion

14

Price equalization

Farsighted user r pr(u) = price when phase is u (price = loss event rate)

rr

rrr

pup

pupux

)( else,

)( ,0)( If

)(' rrr xUp

“good phase”

“bad phase”

“reference price”

15

Special: single link

farsightedmyopic 1

u

Phase u = u competing myopic flows

xF(u)xM(u)

else

)()(

0

1 uuuxuxF

else)(

u

uuxuxM 1

)),max()(()( '' u

FM uxuUxU 01

1 uxu : integer largest

capacity = 1

16

Farsighted users are conservative

A flow said r to be conservative iff

= average user-perceived price

)(1'

rrr pUx

rp

ur

urr

r uxu

uxupup

)()(

)()()(

Seen as throughput maximizers under a “TCP-friendly” constraint

“TCP-friendly”

If TCP lossthroughput(C)

Farsighted user: “=“ in (C)

17

Throughput comparison

Consider a farsighted user F and a myopic user M

Both with same utility functions Both competing for same set of links

MF xx Result

18

Diminishing returns with switching to farsighted n flows k farsighted, n-k myopic flows use same routes = throughput of farsighted flow for given k

kkxF withdecreases )(

)(kxF

Result

19

Can be made “low-priority”

One link characterized by increasing, convex function

Strictly concave utility functions f farsighted flows (0) = fraction of time no myopic flow on the link

Result

0 all ),()( ')0(' xxUxU MfF

“low-priority” iff

20

File transfer time Short-lived flows:

Poisson arrivalsExponential file sizes

short lived

long lived myopic

S1:

short lived

long lived farsighted

S2:

21 TT Result Ti = mean file transfer time in Si

21

Roadmap

Optimality Properties Rate adaptation Protocol & verification Conclusion

22

Traditional myopic

))()(( ' dtNxdtxUxkdx rrrrrrr 212

))(( '

rl

lrrrrdtd qxUkx ql = price at link l

Fast time scale (RTT)

TCP:• 0 or 1• 1 with rate

rllr qx

const

rl

lq)('rr xU

23

Farsighted

))(( 'rrrrrdt

d xUa

1

)(

rl

lrrrdtd qkx

Fast timescale (RTT)

Slow timescale

ar small r)('rr xU

24

Roadmap

Optimality Properties Rate adaptation Protocol & verification Conclusion

25

Back to the solution

w w + 1/ww w – 1/(w

+ ack- ack

-m

Window

Time

high congestion

• Two-timescale control• = parameter learned on-line at slow timescale

26

Sensing phase

vcwnd vcwnd + 1/w0

vcwnd vcwnd – 1/(w0+ ack- ack

-m

Time

w0

Sequential hypothesis testing: p In fact, optimal for Poi(pw0) losses (CUSUM)

Know how to set m so false positives are rare and control is responsive (reflected random walk)

27

“Reference price”: initial guess Want be almost constant Solution: small gain for adaptation But need to converge to equilibrium Solution:

Initial guess = current loss rate

gain

number of iterates

g_min

g_max

n0 n1

loss rate

g_max = 0.005g_min = 0.0001

28

Verification by simulation Scenario 1:

1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

phases

flow

num

ber

Pyrimid Topology, 2-6 flows

1 period has 9 phasesu = (2,3,4,5,6,5,4,3,2)

RED, 6 Mb/sLong-lived farsightedLong-lived TCP

Phase duration = 800 sec

29

Send rate

0 1000 2000 3000 4000 5000 6000 7000

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

x 106 Rate vs time, FAR and TCP

time

rate

FAR

TCP

Time (sec)

Sen

d ra

te (

Mb/

s)

FAR

TCP

30

Loss rate

0 1000 2000 3000 4000 5000 6000 70000

1

2

3

4

5

6

7

8

x 10-3 Loss event probabilities of FAR and TCP and xi of FAR

time

Pro

bability

FAR

TCPxi

Loss

rat

e

Time (sec)

FAR

TCPReference loss rate

31

Per phase rate averages

2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 70

0.5

1

1.5

2

2.5

3

3.5

4

4.5x 10

6Phase average rate: Theoretical Vs Measurement, Farsighted and TCP

Phases

Pha

se a

ve ra

tes

Far measured

Far theoreticalTCP measured

TCP theoretical

The 7th phase is theaverage value over allphases

Phase FAR (Mbps) TCP (Mbps)

2 4.38/4.24 1.61/1.73

3 2.77/2.46 1.61/1.77

4 1.15/1.20 1.61/1.58

5 0/0.62 1.50/1.33

6 0/0.23 1.20/1.11

Avg rate

1.61/1.73 1.53/1.53

Phase

FAR theory

FAR simulation

TCP simulations

TCP theory

Total Avg

Ave

rage

sen

d ra

te (

Mb/

s)

32

Scenario 2

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

x 104

2

3

4

5

6

7

8

time

flow

num

ber

inclu

din

g p

ers

iste

nt

flow

s

flow number over time

0 0.5 1 1.5 2

x 104

0

1

2

3

4

5

6

x 106

time

rate

s

rates over time, FAR and TCP

FAR

TCP

1 2 3 4 5 6 7 80

1

2

3

4

5

6

7x 10

6 Phase average rate: Theoretical Vs Measurement, Far and TCP

phases

phas

e av

e ra

te

FAR measurement

FAR theoreticalTCP measurement

TCP theoretical

The last phase is for theaverage of all phases

Time (sec)

Num

ber

of F

low

sS

end

Rat

e (b

/s)

Ave

rage

sen

d ra

te (

Mb/

s)

Time (sec)Phase

FAR theory

FAR simulation

TCP simulations

TCP theory

Total Avg

33

File transfer time

RED, 6 Mb/s

TCPTCP

RED, 6 Mb/s

FARTCP

Fn ~ Exp()

Tn = Poi()

S1:

S2:

= 0.11/ = 10 MB

S1 S2

Avg Flow Number 8.7139 8.1679

Avg file transfer time (sec) 179 173

Avg link bandwidth (Mb/s) 10.80 10.82

Per connection avg rate (Mb/s) TCP = 1.3405

TCP = 1.3472

FAR = 1.3642

TCP = 1.3262

34

Benefits to other flows?

Ex. same as earlier slide But 10 long-lived flows: either all TCP or all FAR

= 0.051/ = 20 MB

10 FAR 10 TCP

Avg Flow Number 6.92 12.84

Avg Transfer Time (sec) 349 470

35

More realistic traffic

Synthetic web (UNC, Jeffay+) Requests, responses,

idle times drawn from empirical distributions

S1: 1 persistent TCP S2: 1 persistent FAR

Both S1 & S2: number of web users = 1

0 100 200 300 400 500 6000

100

200

300

400

500

600

TCP

FAR

File transfer time for FAR and TCP

TCP: File transfer time (sec)

FA

R:

File

tra

nsfe

r tim

e (s

ec)

36

Conclusion

Farsighted Congestion Control Solution for long-run throughput optimization

Decentralized control No special feedback required

(standard TCP sender modif) Not a heuristic hack

Microeconomics rationale Benefits to other flows On-going:

Further simulations Experimental implementation in MS Vista Real-word experiments

37

More

http://research.microsoft.com/~milanv/farsighted.htm

& Thanks!