AT&T Labs - Research

An Information-Theoretic Approach to Traffic Matrix

Estimation

Yin Zhang, Matthew Roughan, Carsten Lund – AT&T ResearchDavid Donoho – Stanford

Shannon LabShannon Lab

AT&T Labs - Research

Want to know demands from source to destination

Problem

Have link traffic measurements

A

B

C

...

...

...,, CABA xx

TM

AT&T Labs - Research

Approach

Principle *“Don’t try to estimate something

if you don’t have any information about it”

Maximum Entropy Entropy is a measure of uncertainty

More information = less entropy To include measurements, maximize entropy subject to

the constraints imposed by the data Impose the fewest assumptions on the results

Instantiation: Maximize “relative entropy” Minimum Mutual Information

AT&T Labs - Research

Results – Single example

±20% bounds for larger flows Average error ~11% Fast (< 5 seconds) Scales:

O(100) nodes

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Other experiments

Sensitivity Very insensitive to lambda Simple approximations work well

Robustness Missing data Erroneous link data Erroneous routing data

Dependence on network topology Via Rocketfuel network topologies

Additional information Netflow Local traffic matrices

AT&T Labs - Research

Conclusion

We have a good estimation method Robust, fast, and scales to required size Accuracy depends on ratio of unknowns to

measurements Derived from principle

Approach gives some insight into other methods Why they work – regularization Should provide better idea of the way forward

Implemented Used in AT&T’s NA backbone Accurate enough in practice