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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%