Shifting Network Tomography Toward A Practical Goal
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1 École Polytechnique Fédérale de Lausanne Shifting Network Tomography Toward A Practical Goal Denisa Ghita, Can Karakus, Katerina Argyraki, Patrick Thiran CoNext 2011, Tokyo, Japan 1
2 The ISP Curious About its Peers Source ISP ISP = Internet Service Provider 2
3 The ISP Curious About its Peers Peer ISP Source ISP ISP = Internet Service Provider 3
4 The ISP Curious About its Peers Peer ISP Source ISP ISP = Internet Service Provider 4
5 The ISP Curious About its Peers Peer ISP Source ISP ISP = Internet Service Provider 5
6 Boolean Inference N. Duffield 06 good congested 6
7 Boolean Inference N. Duffield 06 good congested A path is good if and only if all its links are good. 7
8 Boolean Inference N. Duffield 06 good congested A path is good if and only if all its links are good. congested paths Boolean Inference congested links network topology 8
9 Contributions In the commercial ISP scenario, the information provided by Boolean Inference cannot be computed accurately. We identify the right problem to solve in this scenario, which provides useful accurate information. 9
10 Challenge: Boolean Inference is Ill-Posed A B C F D 10
11 Challenge: Boolean Inference is Ill-Posed A B C If all paths are congested, then the congested links may be: F D 11
12 State-of-the-Art Boolean Inference Algorithms Link Independence Assumption: All links are independent. Link Homogeneity Assumption: All links are equally likely to be congested. Stationarity Assumption: Stationary network dynamics. 12
13 State-of-the-Art Boolean Inference Algorithms Sparsity Duffield 06 Dhamdhere &al. 07 Bayesian Independence Nguyen &al. 07 Bayesian Correlation Ghita &al. 11 Link Independence Assumption: All links are independent. Link Homogeneity Assumption: All links are equally likely to be congested. Stationarity Assumption: Stationary network dynamics. 13
14 Boolean Inference Not Accurate Enough in Our Scenario! best Detection Rate = the fraction of congested links correctly identified as congested generated topology commercial ISP topology False Positives Rate = the fraction of links incorrectly identified as congested best 0.0 Sparsity (Dhamdhere &al. 07) Bayesian-Independence (Nguyen &al. 07) Bayesian-Correlation (Ghita &al. 11) 14
15 Where s the Rub in Boolean Inference? Our topology is sparser than generated topologies. Paths that criss-cross yield more information. The assumptions cannot be verified in practice. Link Independence Assumption: All links are independent. Link Homogeneity Assumption: All links are equally likely to be congested. Stationarity Assumption: Stationary network dynamics. 15
16 Contributions In the commercial ISP scenario, the information provided by Boolean Inference cannot be computed accurately. We identify the right problem to solve in this scenario, which provides useful accurate information. 16
17 Inferring Congestion Frequency congested good few minutes time 17
18 Inferring Congestion Frequency congested P( link is congested) good few minutes time 18
19 Inferring Congestion Frequency congested P( link is congested) good time few minutes congested paths Boolean Inference congested links congested paths Congestion Frequency congestion probability of links +1 network topology congestion status of each link network topology the probability that a set of links is congested +1 few minutes not accurate enough (ill-posed, unverifiable assumptions) tens of minutes accurate + (well-posed, realistic assumption) 19
20 Our Assumption: Correlation Sets possibly correlated independent Independence among correlation sets. 20
21 How to Know the Correlation Sets? source ISP Links in the same administrative domain may be correlated! 21
22 Is Congestion Frequency Well-Posed? A B C F D Each subset of a correlation set must be covered by a different set of paths! Subset of a Correlation Set e AB e BC e BD e BC, e BD Covered Paths e FB 22
23 Is Congestion Frequency Well-Posed? A B C F Each subset of a correlation set must be covered by a different set of paths! Subset of a Correlation Set e AB e BC e BD e BC, e BD D Congestion Frequency e FB 23
24 The Core Idea Each set of paths generates an equation! A B C F D 24
25 The Core Idea Each set of paths generates an equation! A B C F D 25
26 The Core Idea Each set of paths generates an equation! A B C F D 26
27 The Core Idea Each set of paths generates an equation! A B C F D 27
28 The Core Idea A B F C D 28
29 The Core Idea A B F C D The system of equations has a unique solution! 29
30 The Challenge Combinatorial explosion: 1500 paths => equations! 30
31 The Challenge Combinatorial explosion: 1500 paths => equations! Our theorem identifies a large portion of the space that is redundant. 31
32 The Challenge Combinatorial explosion: 1500 paths => equations! Our theorem identifies a large portion of the space that is redundant. Our algorithm efficiently computes the probability that each set of links is congested. 32
33 Key Points of the Algorithm Pick the sets of paths that are most likely to yield useful information (linearly independent equations). Efficiently check if a set of paths yields useful information (a linearly independent equation). 33
34 How to Pick the Most Likely Sets of Paths A B F C D The system of equations has an unique solution! 34
35 How to Pick the Most Likely Sets of Paths A B F C D The system of equations has an unique solution!
36 How to Pick the Most Likely Sets of Paths A B F C D The system of equations has an unique solution! The matrix has full column rank! 36
37 How to Pick the Most Likely Sets of Paths 1. make sure each unknown appears in at least one row A B F C D 1 37
38 How to Pick the Most Likely Sets of Paths 1. make sure each unknown appears in at least one row A B F C D
39 How to Pick the Most Likely Sets of Paths 1. make sure each unknown appears in at least one row 2. augment the matrix with a new linearly independent row A F B C D
40 How to Pick the Most Likely Sets of Paths 1. make sure each unknown appears in at least one row 2. augment the matrix with a new linearly independent row A F B C D path set s.t. is linearly independent with 40
41 How to Pick the Most Likely Sets of Paths 1. make sure each unknown appears in at least one row 2. augment the matrix with a new linearly independent row A F B C D path set s.t. is linearly independent with 41
42 How to Pick the Most Likely Sets of Paths 1. make sure each unknown appears in at least one row 2. augment the matrix with a new linearly independent row A F B C D path set s.t. is linearly independent with 42
43 How to Pick the Most Likely Sets of Paths 1. make sure each unknown appears in at least one row 2. augment the matrix with a new linearly independent row A F B C D path set s.t. is linearly independent with 43
44 How to Pick the Most Likely Sets of Paths 1. make sure each unknown appears in at least one row 2. augment the matrix with a new linearly independent row A F B C D path set s.t. is linearly independent with 44
45 How to Pick the Most Likely Sets of Paths 1. make sure each unknown appears in at least one row 2. augment the matrix with a new linearly independent row A F B C D path set s.t. is linearly independent with Path set must cover link 45
46 How to Pick the Most Likely Sets of Paths 1. make sure each unknown appears in at least one row 2. augment the matrix with a new linearly independent row A F B C D Path set must cover link 46
47 CDF Simulations Correlation-complete (our algorithm) Independence (Nguyen &al. 07 ) 1.0 absolute error between the actual probability that a link is congested, and the probability inferred by the algorithm. 47
48 Conclusions In the commercial ISP scenario, the information provided by Boolean Inference cannot be computed accurately. Boolean Inference is ill-posed. The assumptions made by Boolean Inference algorithms are not verifiable in practice. The right problem to solve which provides useful accurate information is Congestion Frequency. Congestion Frequency is well-posed under certain well-defined conditions, and requires only one realistic assumption. We propose a complete and efficient algorithm which computes the congestion frequencies of links. Future Work Our method gives insights on how to deal with noisy measurements. 48
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