1. École Polytechnique Fédérale de Lausanne Network Tomography on Correlated Links Denisa Ghita Katerina Argyraki Patrick Thiran IMC 2010, Melbourne, Australia

2. Network Tomography Internet Service Provider 2 Network tomography infers links characteristics from path measurements.

3. Current Tomographic Methods assume Link Independence 3

4. 4 Links can be correlated!

5. Can we use network tomography when links are correlated? 5 Yes, we can!

6. All Link Correlation Model links are independent. Some possibly correlated independent Independence among correlation sets! 6

7. How to find the Possibly Correlated Links? Links in the same local-area network may be correlated! Links in the same administrative domain may be correlated! 7

8. The Probability that a Link is Faulty link is faulty P(P( ) = ? 8

9. Our Main Contribution P ( link faulty) = ? Theorem that states the necessary and sufficient condition to identify the probability that each link is faulty when links in the network are correlated. P ( link faulty) =… 9

10. Our Condition Each subset of a correlation set must be covered by a different set of paths! 10

11. A B Identifiable Our Condition Subset of a Correlation Set Covered Paths e AB e BC e BD e BC, e BD Each subset of a correlation set must be covered by a different set of paths! 11 C D 1.Define the subsets of the correlation sets. 2.Find the paths that cover each subset. 3.Are any subsets covered by the same paths?

12. Our Condition A B C D Identifiable E Subset of a Correlation Set e AB e BC e BD e BC, e BD Covered Paths e EB 12

13. The Gist behind the Algorithm Solvable! 3 equations 4 unknowns P ( P AC good ) = P (e AB good) P (e BC good) P ( P AD good ) = P (e AB good) P (e BD good) P ( P ED good ) = P (e EB good) P (e BD good) B C D E A 13

14. The Gist behind the Algorithm P ( P AC good ) = P (e AB good) P (e BC good) P ( P AD good ) = P (e AB good) P (e BD good) P ( P ED good ) = P (e EB good) P (e BD good) B C D E A 14 P ( P AC, P AD good ) = P (e AB good) P (e BD,e BC good) P (e BD good) P (e BC good) ≠

15. The Gist behind the Algorithm P ( P AC good ) = P (e AB good) P (e BC good) P ( P AD good ) = P (e AB good) P (e BD good) P ( P ED good ) = P (e EB good) P (e BD good) B C D E A 15 P ( P AC, P AD good ) = P (e AB good) P (e BD,e BC good) P ( P AD, P ED good ) = P (e AB good) P (e EB good) P (e BD good) Solvable ! 5 unknowns 5 equations

16. The Gist behind the Algorithm P ( P AC good ) = P (e AB good) P (e BC good) P ( P AD good ) = P (e AB good) P (e BD good) P ( P ED good ) = P (e EB good) P (e BD good) B C D E A 16 P ( P AC, P AD good ) = P (e AB good) P (e BD,e BC good) P ( P AD, P ED good ) = P (e AB good) P (e EB good) P (e BD good) Solvable ! 5 unknowns 5 equations Correlation set of 40 links -> 2 40 unknowns !!!

17. The Gist behind the Algorithm P ( P AC good ) = P (e AB good) P (e BC good) P ( P AD good ) = P (e AB good) P (e BD good) P ( P ED good ) = P (e EB good) P (e BD good) B C D E A 17 P ( P AC, P AD good ) = P (e AB good) P (e BD,e BC good) P ( P AD, P ED good ) = P (e AB good) P (e EB good) P (e BD good) Solvable ! 5 unknowns 5 equations Correlation set of 40 links -> 2 40 unknowns !!! Consider only sets of paths that do not cover correlated links !

18. The Gist behind the Algorithm P ( P AC good ) = P (e AB good) P (e BC good) P ( P AD good ) = P (e AB good) P (e BD good) P ( P ED good ) = P (e EB good) P (e BD good) B C D E A 18 P ( P AC, P AD good ) = P (e AB good) P (e BD,e BC good) P ( P AD, P ED good ) = P (e AB good) P (e EB good) P (e BD good) Consider only sets of paths that do not cover correlated links ! Solvable! 4 unknowns 4 equations

19. Simulations – Domain Level Tomography Actual TopologyMeasured Topology 19

20. Simulations – Domain Level Tomography absolute error between the actual probability that a link is faulty, and the probability inferred by the algorithm. 20

21. Simulations – Domain Level Tomography absolute error between the actual probability that a link is faulty, and the probability inferred by the algorithm. 21

22. Conclusion We study network tomography on correlated links. We formally prove under which necessary and sufficient condition the probabilities that links are faulty are identifiable. Our tomographic algorithm determines accurately the probabilities that links are faulty in a variety of congestion scenarios. 22

23. Thank you! denisa.ghita@epfl.ch 23