network tomography on correlated links
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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
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Network tomography infers links characteristics from path measurements.
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Current Tomographic Methods assume Link Independence
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Current Tomographic Methods assume Link Independence
Links can be correlated!
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Can we use network tomography when links are correlated?
Yes, we can!
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All
Link Correlation Model
links are independent.Some
possibly correlated
independent
Independence among correlation sets!
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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!
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The Probability that a Link is Faulty
link is faultyP( ) = ?
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Our Main Contribution
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.
P( link faulty) =…
P( link faulty) =…
P( link faulty) =…
P( link fa
ulty) =…
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Our ConditionEach subset of a correlation set must be covered by a different set of paths!
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A
B
Identifiable
Our Condition
Subset of aCorrelation Set Covered Paths
eAB eBC eBD eBC, eBD
Each subset of a correlation set must be covered by a different set of paths!
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?
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Our ConditionA
B
C
D
Identifiable
ESubset of aCorrelation Set
eAB eBC eBD eBC, eBD
Covered Paths
eEB
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The Gist behind the Algorithm
Solvable!3 equations 4 unknowns
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)
BC
DE
A
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The Gist behind the Algorithm
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)
BC
DE
A
P( PAC , PAD good ) = P(eAB good) P(eBD ,eBC good)
P(eBDgood)P(eBC good)≠
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The Gist behind the Algorithm
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)
BC
DE
A
P( PAC , PAD good ) = P(eAB good) P(eBD ,eBC good)
P( PAD , PED good ) = P(eAB good) P(eEB good) P(eBD good)
Solvable !5 unknowns5 equations
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The Gist behind the Algorithm
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)
BC
DE
A
P( PAC , PAD good ) = P(eAB good) P(eBD ,eBC good)
P( PAD , PED good ) = P(eAB good) P(eEB good) P(eBD good)
Solvable !5 unknowns5 equations
Correlation set of 40 links -> 240 unknowns !!!
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The Gist behind the Algorithm
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)
BC
DE
A
P( PAC , PAD good ) = P(eAB good) P(eBD ,eBC good)
P( PAD , PED good ) = P(eAB good) P(eEB good) P(eBD good)
Solvable !5 unknowns5 equations
Correlation set of 40 links -> 240 unknowns !!!
Consider only sets of paths that do not cover correlated links !
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The Gist behind the Algorithm
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)
BC
DE
A
P( PAC , PAD good ) = P(eAB good) P(eBD ,eBC good)
P( PAD , PED good ) = P(eAB good) P(eEB good) P(eBD good)
Consider only sets of paths that do not cover correlated links !
Solvable!4 unknowns 4 equations
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Simulations – Domain Level Tomography
Actual Topology Measured Topology
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Simulations – Domain Level Tomography
absolute error between the actual probability that a link is faulty, and the probability inferred by the algorithm.
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Simulations – Domain Level Tomography
absolute error between the actual probability that a link is faulty, and the probability inferred by the algorithm.
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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.
