A Queuing Theory Approach to Network Path Parameter Estimation

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

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

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 =t2-t1 ’=t2*-t1*

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. Output spacing Assuming stationarity, the distribution of the output spacing is related to the conditional probability F(w,t|w0) of having queue length w at time t assuming the queue length is w0 at t = 0. In our case t = d, w = w2, w0 = w1+p. Cross traffic model – M/G/1packet with size of Pi arrive with Poisson rate li

6. where Pp(t) is the probability that the queue is not empty at time t: Output spacing Takács integrodifferential equation:

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: l

8. Explicit solution for M/D/1

9. Validation with packet level simulation M/D/1 queue P=12000 bits

10. Validation with packet level simulation Trimodal packet size distribution

11. Validation with packet level simulation Uniform packet sizes between [0:12000] bits

12. Parametrization with the granularity

13. Parametrization with the granularity Granularity – the effective CT packet size: exact form of the CT packet size distribution is not neccessary; the value of the granularity is enough.

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

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

16. Estimating the network parameters

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 was22 Mbps, Pg=12000 bits. fitted parameters:C = 100 Mbps, Cc = 22.5 Mbps Pg = 15000 bits.

18. Internet measurements www.ETOMIC.org ETOMIC nodeslocated in Birmingham, UKand 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. Laboratory and Internet measurements Comparision to existing tools: - pathload- pathChirpdata for our method - modified pathChirp tool.

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. Thank you for your attention!