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
AT&T Labs - Research
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