A Queuing Theory Approach to Network Path Parameter Estimation

Péter Hága

Krisztián Diriczi

Gábor Vattay

István Csabai

Attila Pásztor

Darryl Veitch

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Packet pair methods

Sender Receiver

Sender Monitor: Receiver Monitor:

Goal: estimate network parameters (available bandwidth, physical bandwidth, cross traffic, etc.) with end-to-end methods

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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

*

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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

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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 = , w = w2, w0 = w1+p.

Cross traffic model – M/G/1packet with size of Pi arrive with Poisson rate i

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Output spacing

where Pp(t) is the probability that the queue is not empty at time t:

Takács integrodifferential equation:

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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:

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Explicit solution for M/D/1

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Validation with packet level simulation

M/D/1 queue

P=12000 bits

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Validation with packet level simulation

Trimodal packet size distribution

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Validation with packet level simulation

Uniform packet sizes between [0:12000] bits

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Parametrization with the granularity

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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:

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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

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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

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Estimating the network parameters

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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.

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Internet measurements www.ETOMIC.org

ETOMIC nodes located 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.

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Laboratory and Internet measurements

Comparision to existing tools: - pathload- pathChirp

data for our method - modified pathChirp tool.

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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 pairmeasurements

• confidence surfaces of the estimated parameters (C,Cc,Pg)• validation in real measurements in our testlab• validation in the ETOMIC infrastructure

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Thank you for your attention!

This work was partially supported by the National Office for Research and Techonolgy (NKFP 02.032.04).