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Network Tomography on Correlated Links

École Polytechnique Fédérale de Lausanne. Network Tomography on Correlated Links. Denisa Ghita Katerina Argyraki Patrick Thiran. IMC 2010, Melbourne, Australia. Network Tomography. Internet Service Provider. Network tomography infers links characteristics from path measurements.

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Network Tomography on Correlated Links

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  1. ÉcolePolytechniqueFédérale de Lausanne Network Tomography on Correlated Links DenisaGhita KaterinaArgyraki Patrick Thiran IMC 2010, Melbourne, Australia

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

  3. Current TomographicMethods assume Link Independence

  4. Current TomographicMethods assume Link Independence Links can be correlated!

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

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

  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!

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

  9. Our Main Contribution P( link faulty) =… P( link faulty) = ? P( link faulty) = ? P( link faulty) =… P( link faulty) = ? P( link faulty) =… P( link faulty) = ? 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.

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

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

  12. Our Condition A C Identifiable B D E Subset of a Correlation Set Covered Paths eAB eBC eBD eBC, eBD eEB

  13. The Gist behind the Algorithm A C B D E P( PAC good ) = P(eAB good) P(eBC good) Solvable! 3 equations 4 unknowns P( PAD good ) = P(eAB good) P(eBD good) P( PED good ) = P(eEB good) P(eBD good)

  14. The Gist behind the Algorithm A C B D E P( PAC good ) = P(eAB good) P(eBC good) P( PAD good ) = P(eAB good) P(eBD good) P( PED good ) = P(eEB good) P(eBD good) P( PAC , PAD good ) = P(eAB good) P(eBD ,eBC good) ≠ P(eBDgood)P(eBC good)

  15. The Gist behind the Algorithm A C B D E P( PAC good ) = P(eAB good) P(eBC good) Solvable ! 5 unknowns 5 equations P( PAD good ) = P(eAB good) P(eBD good) P( PED good ) = P(eEB good) P(eBD good) P( PAC , PAD good ) = P(eAB good) P(eBD ,eBC good) P( PAD , PED good ) = P(eAB good) P(eEB good)P(eBD good)

  16. The Gist behind the Algorithm A C B D E P( PAC good ) = P(eAB good) P(eBC good) Solvable ! 5 unknowns 5 equations P( PAD good ) = P(eAB good) P(eBD good) P( PED good ) = P(eEB good) P(eBD good) P( PAC , PAD good ) = P(eAB good) P(eBD ,eBC good) P( PAD , PED good ) = P(eAB good) P(eEB good)P(eBD good) Correlation set of 40 links -> 240 unknowns !!!

  17. The Gist behind the Algorithm A C B Consider only sets of paths that do not cover correlated links ! D E P( PAC good ) = P(eAB good) P(eBC good) Solvable ! 5 unknowns 5 equations P( PAD good ) = P(eAB good) P(eBD good) P( PED good ) = P(eEB good) P(eBD good) P( PAC , PAD good ) = P(eAB good) P(eBD ,eBC good) P( PAD , PED good ) = P(eAB good) P(eEB good)P(eBD good) Correlation set of 40 links -> 240 unknowns !!!

  18. The Gist behind the Algorithm A C B Consider only sets of paths that do not cover correlated links ! D E Solvable! 4 unknowns 4 equations P( PAC good ) = P(eAB good) P(eBC good) P( PAD good ) = P(eAB good) P(eBD good) P( PED good ) = P(eEB good) P(eBD good) P( PAC , PAD good ) = P(eAB good) P(eBD ,eBC good) P( PAD , PED good ) = P(eAB good) P(eEB good)P(eBD good)

  19. Simulations – Domain Level Tomography Actual Topology Measured Topology

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

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

  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. • Ourtomographic algorithm determines accurately the probabilities that links are faulty in a variety of congestion scenarios.

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

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