1. References TCP is Max-Plus Linear, [Single flow] F.Baccelli, D.Hong TCP is Max-Plus Linear, Sigcomm 00 AIMD, Fairness and Fractal Scaling of TCP traffic, [Competition of N flows] F.Baccelli, D.Hong AIMD, Fairness and Fractal Scaling of TCP traffic, Infocom 02 Interaction of TCP Flows as Billiards, [TCP on Network] F.Baccelli, D.Hong Interaction of TCP Flows as Billiards, INRIA Report 02 FTCP, [TCP pacing] D.Hong FTCP, Internet Draft, March 02 : www.ietf.org/internet-drafts/draft-hong-ftcp-00.txt http://www.di.ens.fr/~trec/aimd

2. Impact of Synchronization Caltech, CA 02/07/2002 D. Hong INRIA-ENS on Performance

3. Outline I. AIMD model II. Link/Router level III. Packet bursty

4. I. AIMD model

5. Model: fluid dynamic

6. sources destinations 10 Mbps Model: to get an idea

7. sources destinations 10 Mbps Congestion!

8. 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

9. II. Synchronization at Router

10. AIMD interaction equation : 1 link Evolution equation: Affine map representation: vector of size N matrix N x N  (X n +  n / R 2 ) = C

11. Steady state solution X n = B n + A n B n-1 + A n A n-1 B n-2 + A n A n-1 A n-2 B n-3 + … Variance, covariance, autocorrelation: var(X) = cov(X) = Corr(X 0,X n ) =

12. Performance formula Square root formula: Throughput = With synchronization: Throughput = Synchronization (main) effect:

13. Impact on Performance Whatever - C, B, N, RTT, QM, Service Policy if « input rate >= C » at congestion epoch: Synchronization impact is Impact on performance Impact on performance: up to 25%

14. III. Packet bursty

15. AIMD by fluid model: If W=10, 1 RTT

16. Packet bursty: intuition 1 RTT time 1/10 RTT

17. Packet bursty: example 100 Pkts/s 10 sources 10 destinations RTT = 1 s

18. Packet bursty: example RTT 10 flows

19. Packet bursty: example In mean, each flow should get: C/10 = 10 pkts/s 1 flow : congestion with input rate = C/10 2 flows collision : congestion with input rate = C/20 3 flows collision : congestion with input rate = C/30 In fluid model, input rate = C !!!

20. Packet bursty: input rate at Congestion C Fluid Discrete t real input rate

21. 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

22. Conclusion C=100 Mbps synchronization effect Burstiness in RTT Total Goodput 75-100 Mbps ~10 Mbps What to do ? optimal AQM control ? gain up to 30% use FTCP ? (tcp pacing) gain up to 900%