An Information-Theoretic
Approach to Traffic Matrix
Estimation
Yin Zhang, Matthew Roughan, Carsten Lund – AT&T Research
David Donoho – Stanford
Shannon Lab
AT&T Labs - Research
Problem
Have link traffic measurements
Want to know demands from source to destination
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AT&T Labs - Research
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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
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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
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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
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