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A Queuing Theory Approach to Estimating Network Path Parameters Using Packet Pair Methods

This paper presents a novel analytical framework for estimating key network parameters such as available bandwidth, physical bandwidth, and cross traffic using packet pair methods. We explore the asymptotic behavior and transition region through fluid models and derive explicit solutions for M/D/1 queues. Our results include validation against packet-level simulations and multiple laboratory and Internet experiments. Key insights include a new parameter, granularity, which characterizes effective packet sizes. Comprehensive results are provided, comparing our method to existing tools, highlighting its efficacy in real-world scenarios.

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A Queuing Theory Approach to Estimating Network Path Parameters Using Packet Pair Methods

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  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!

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