Shannon Lab

1. Shannon Lab An Information-Theoretic Approach to Traffic Matrix EstimationYin Zhang, Matthew Roughan, Carsten Lund – AT&T ResearchDavid Donoho – Stanford AT&T Labs - Research

2. Problem Have link traffic measurements Want to know demands from source to destination B C A AT&T Labs - Research

3. 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

4. Results – Single example • ±20% bounds for larger flows • Average error ~11% • Fast (< 5 seconds) • Scales: • O(100) nodes AT&T Labs - Research

5. 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

6. 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 AT&T Labs - Research