References

[Single flow] F.Baccelli, D.Hong TCP is Max-Plus Linear,TCP is Max-Plus Linear, Sigcomm 00

[Competition of N flows] F.Baccelli, D.Hong AIMD, AIMD, Fairness and Fractal Scaling of TCP traffic, Fairness and Fractal Scaling of TCP traffic, Infocom 02[TCP on Network] F.Baccelli, D.Hong Interaction of TCP Interaction of TCP Flows as Billiards, Flows as Billiards, INRIA Report 02

[TCP pacing] D.Hong FTCP, FTCP, Internet Draft, March 02: www.ietf.org/internet-drafts/draft-hong-ftcp-00.txt

http://www.di.ens.fr/~trec/aimd

Impact of SynchronizationImpact of Synchronization

Caltech, CA02/07/2002

D. HongINRIA-ENS

on Performance

OutlineOutline

I. AIMD modelII. Link/Router levelIII. Packet bursty

I. AIMD model

Model: fluid dynamic

0

2

4

6

8

10

12

14

16

18

pkts

sources

destinations

10 Mbps

Model: to get an idea

sources

destinations

10 Mbps

Congestion!Congestion!

The model includes… N parallel sources

data transfer: ftp, http… Network extension

Downstream, Upstream, RTT coupling Non linear model

queueing impact: RTT(t) QM: DropTail, RED, … Policy: FIFO, WFQ, Min Rate…

Priority flows: real time constraint voice over IP, video broadcast, video on demand, game

on line

II. Synchronization at Router

AIMD interaction equation : 1 link

2

n(i)n

(i)1n

(i)1n R

X γ X

N

1i

(i)n2

n X - C R

1nn1n1n BXA X

Evolution equation:

Affine map representation:

vector of size N matrix NxN

(Xn + n / R2) = C

Steady state solution

XXnn = B = Bnn + A + AnnBBn-1n-1 + A + AnnAAn-1n-1BBn-2n-2 + + A AnnAAn-1n-1AAn-2n-2BBn-3n-3 + +

…… Variance, covariance, autocorrelation:

var(X) =

cov(X) =

Corr(X0,Xn) =

b)ρ(aa1

ρb)b)(1(acb

N

C2

2

b)ρ(aa1

b)ρb(acb

N

C2

2

ρJ)Xcov()Xvar(γk

Performance formula

Square root formula:

Throughput = loss

0

pRTT

c

losspRTT

p/4)-2(1

241.1c22.12/3 0

With synchronization:

Throughput =

Synchronization (main) effect:

Impact on Performance

Whatever

- C, B, N, RTT, QM, Service Policy

if « input rate >= C » at congestion epoch: Synchronization impact is

Impact on performanceImpact on performance: up to 25%

III. Packet bursty

AIMD by fluid model:

If W=10,

1 RTT

Packet bursty: intuition

1 RTT

time

1/10 RTT

Packet bursty: example

100 Pkts/s

10 sources 10 destinations

RTT = 1 s

Packet bursty: example

RTT

10 flows

Packet bursty: example

In mean, each flow shouldget: C/10 = 10 pkts/s

1 flow : congestion with input rate = C/102 flows collision : congestion with input rate = C/203 flows collision : congestion with input rate = C/30

In fluid model, input rate = C !!!input rate = C !!!

Packet bursty: input rate at Congestion

C

Fluid Discrete

t

real input rate

Packet bursty: impact

Multiplexing effect ??

proba. of no collision =0,00036

Collision increases collision probability ! increase also synchronization

Huge Impact !!

about 90% loss on perf

Conclusion

C=100 Mbps synchronizatio

n effect

Burstiness in

RTT

Total

Goodput

75-100 75-100 MbpsMbps ~10 ~10 MbpsMbps

What to do ?

optimal AQM control ?gain up to 30%

use FTCP ?(tcp pacing)gain up to 900%