1. A Queuing Theory Approach to Network Path Parameter Estimation Péter Hága Krisztián Diriczi Gábor Vattay István Csabai Attila Pásztor Darryl Veitch

2. CNL - Network Performance Measurement Group 2 Packet pair methods SenderReceiver Sender Monitor:Receiver Monitor: Goal: estimate network parameters (available bandwidth, physical bandwidth, cross traffic, etc.) with end-to-end methods

3. CNL - Network Performance Measurement Group 3 Packet pair methods fluid model – the asymptotic behaviour is correct, but unable to describe the transition region new analytic description of the transition region  t 2 -t 1  ’  t 2 * -t 1 *

4. CNL - Network Performance Measurement Group 4 Outline The average of the output spacing Explicit solution for M/D/1 Validation with packet level simulation Parametrization with the granularity Estimating the network parameters Laboratory and Internet Experiments Conclusion

5. CNL - Network Performance Measurement Group 5 Output spacing Assuming stationarity, the distribution of the output spacing is related to the conditional probability F(w,t|w 0 ) of having queue length w at time t assuming the queue length is w 0 at t = 0. In our case t = , w = w 2, w 0 = w 1 +p. Cross traffic model – M/G/1 packet with size of P i arrive with Poisson rate i

6. CNL - Network Performance Measurement Group 6 Output spacing where P p (t) is the probability that the queue is not empty at time t: Takács integrodifferential equation:

7. CNL - Network Performance Measurement Group 7 Explicit solution for M/D/1 Simplest M/G/1 type case is an M/D/1 queue: fixed cross traffic packet size: P Poisson rate:

8. CNL - Network Performance Measurement Group 8 Explicit solution for M/D/1

9. CNL - Network Performance Measurement Group 9 Validation with packet level simulation M/D/1 queue P=12000 bits

10. CNL - Network Performance Measurement Group 10 Validation with packet level simulation Trimodal packet size distribution

11. CNL - Network Performance Measurement Group 11 Validation with packet level simulation Uniform packet sizes between [0:12000] bits

12. CNL - Network Performance Measurement Group 12 Parametrization with the granularity

13. CNL - Network Performance Measurement Group 13 Parametrization with the granularity exact form of the CT packet size distribution is not neccessary; the value of the granularity is enough. Granularity – the effective CT packet size:

14. CNL - Network Performance Measurement Group 14 Parametrization with the granularity M/D/1 curves for: fixed packet size, P=800 bits – P g = 800 bits, uniform dist, [0:12000] bits – P g = 4272 bits, trimodal dist, real Internet params – P g = 9786 bits

15. CNL - Network Performance Measurement Group 15 Parametrization with the granularity M/D/1 curves for: fixed packet size P=9786 bits– P g = 9786 bits, uniform dist [7200:12000] bits – P g = 9786 bits, trimodal dist, real Internet params– P g = 9786 bits

16. CNL - Network Performance Measurement Group 16 Estimating the network parameters

17. CNL - Network Performance Measurement Group 17 Laboratory experiments bottleneck link 10 Mbps, cross traffic bandwidth was 4 Mbps, Pg=12000bits. fitted parameters: C = 10 Mbps, Cc = 3.7 Mbps Pg = 12000 bits, while 100 packet pairs were averaged. bottleneck link 100 Mbps, average cross traffic bandwidth was 22 Mbps, Pg=12000 bits. fitted parameters: C = 100 Mbps, Cc = 22.5 Mbps Pg = 15000 bits.

18. CNL - Network Performance Measurement Group 18 Internet measurements www.ETOMIC.org ETOMIC nodes located in Birmingham, UK and Salzburg, Austria. estimated parameters: C = 1.7 Mbps, Cc = 0.1 Mbps and Pg = 15000 bits. ETOMIC nodes located in Pamplona, Spain and Budapest, Hungary. estimated parameters: C = 100 Mbps, Cc = 58.2 Mbps and Pg = 9000 bits.

19. CNL - Network Performance Measurement Group 19 Laboratory and Internet measurements Comparision to existing tools: - pathload - pathChirp data for our method - modified pathChirp tool.

20. CNL - Network Performance Measurement Group 20 Summary new theoretical approach new framework based on the Takács equation exact formula for the average output spacing granulatiry parameter = effective packet size, the third important parameter in describing packet pair measurements confidence surfaces of the estimated parameters (C,Cc,Pg) validation in real measurements in our testlab validation in the ETOMIC infrastructure

21. CNL - Network Performance Measurement Group 21 Thank you for your attention! This work was partially supported by the National Office for Research and Techonolgy (NKFP 02.032.04).