Farsighted Congestion Controllers Milan Vojnović Microsoft Research Cambridge, United Kingdom...
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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
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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
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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
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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
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Compare with TCP
Window
Time
w w + 1/ww w – ½ w
+ ack- ack
high congestion
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Roadmap
Optimality Properties Rate adaptation Protocol & verification Conclusion
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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
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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
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Problem
l ql
qulUuRr
rr uxCuxV ))(()()( ,
0)(uxr
maximize
over
SYSTEM:
Rrxr , optimal if it solves SYSTEM
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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:
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With long-run throughput optimizers
l qlqul
Uu
Frrr
Mrrr
uxCu
xUuxUu
))(()(
)())(()(
,
0)(uxr
maximize
over
• No separation
• Long-run throughput optimizers = “farsighted”
SYSTEM:
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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
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Roadmap
Optimality Properties Rate adaptation Protocol & verification Conclusion
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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”
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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
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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)
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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
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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
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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
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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
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Roadmap
Optimality Properties Rate adaptation Protocol & verification Conclusion
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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
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Farsighted
))(( 'rrrrrdt
d xUa
1
)(
rl
lrrrdtd qkx
Fast timescale (RTT)
Slow timescale
ar small r)('rr xU
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Roadmap
Optimality Properties Rate adaptation Protocol & verification Conclusion
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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
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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)
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“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
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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
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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
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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
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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)
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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
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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
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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
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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)
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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
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More
http://research.microsoft.com/~milanv/farsighted.htm
& Thanks!