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

AT&T Labs - Research Approach Principle * Dont try to estimate something if you dont have any information about it zMaximum Entropy yEntropy is a measure of uncertainty xMore information = less entropy yTo include measurements, maximize entropy subject to the constraints imposed by the data yImpose the fewest assumptions on the results zInstantiation: Maximize relative entropy yMinimum Mutual Information

AT&T Labs - Research Results – Single example z±20% bounds for larger flows zAverage error ~11% zFast (< 5 seconds) zScales: yO(100) nodes

AT&T Labs - Research Other experiments zSensitivity yVery insensitive to lambda ySimple approximations work well zRobustness yMissing data yErroneous link data yErroneous routing data zDependence on network topology yVia Rocketfuel network topologies zAdditional information yNetflow yLocal traffic matrices

AT&T Labs - Research Conclusion zWe have a good estimation method yRobust, fast, and scales to required size yAccuracy depends on ratio of unknowns to measurements yDerived from principle zApproach gives some insight into other methods yWhy they work – regularization yShould provide better idea of the way forward zImplemented yUsed in AT&Ts NA backbone yAccurate enough in practice