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.
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