Tomo-gravity

How to Compute How to Compute Accurate Traffic Matrices for Accurate Traffic Matrices for your Network in Secondsyour Network in Seconds

Yin Zhang, Matthew Roughan, Carsten Lund, Yin Zhang, Matthew Roughan, Carsten Lund, Nick Duffield, Albert Greenberg, Quynh Nguyen Nick Duffield, Albert Greenberg, Quynh Nguyen

–– AT&T LabsAT&T Labs--ResearchResearch

David David DonohoDonoho –– StanfordStanford

Shannon LabShannon Lab

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Want to know demands from source to destination

ProblemProblemHave link traffic measurements (from SNMP)

A

BC

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Example App: reliability analysisExample App: reliability analysisUnder a link failure, routes change

want to predict new link loads

A

BC

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Network EngineeringNetwork Engineering

What you want to doReliability analysisTraffic engineeringCapacity planning

What do you need to knowNetwork and routing Prediction and optimization techniques

? Traffic matrix

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Solution: Solution: TomoTomo--gravitygravity

Computes traffic matricesinput: SNMP, topology, routing policies

AdvantagesToday’s data no special instrumentationFast: a few seconds Accurate: average 12% errorScales: hundreds of nodesRobust: copes easily with data glitchesFlexible: can incorporate more detailed data

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TomographyAstronomySeismologyMedical imaging ⌧CAT in CATSCAN

TomoTomo--gravitygravity

Gravity modelingEconometricsTransportation ⌧planes, trains,

automobiles

Foundation: Information Theory

+

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TomoTomo--gravity in a Nutshellgravity in a Nutshell

tomographic constraints(from link measurements)

1. gravity solution

2. tomo-gravity solution

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TomoTomo--gravity in practicegravity in practice

1. Get topology & routing 2. Measure SNMP link loads 3. Derive gravity solution

Uses edge loads 4. Compute tomo-gravity solution

Use internal link dataMatches observed link loadsCan incorporate more detailed measurements to boost accuracy

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Real exampleReal example

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Example use: reliability analysisExample use: reliability analysis

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ConclusionConclusion

Tomo-gravity implementedAT&T’s IP backbone (AS 7018)Hourly traffic matrices for > 1 year (in secs)

For a number of applicationsReliability analysis (killer app…)Traffic engineeringCapacity planninghttp://www.research.att.com/

~roughan/tomogravity.html

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Key ReferencesKey References“Fast, accurate computation of large-scale IP traffic matrices from link measurements”, Y.Zhang, M.Roughan, N.Duffield and A.Greenberg, ACM SIGMETRICS 2003.“An information theoretic approach to traffic matrix estimation”, Y.Zhang, M.Roughan, C.Lund and D.Donoho, ACM SIGCOMM 2003.Both available at http://www.research.att.com/~roughan/papers.html

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Additional Slides

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Mathematical FormalismMathematical Formalism

1

3

2router

route 2

route 1

route 3

311 xxy +=

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EquationsEquations

y = AxRouting matrix

Many more unknowns than measurements

Traffic matrix

Link measurements

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Robustness (input errors)Robustness (input errors)

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Dependence on TopologyDependence on Topology

0

5

10

15

20

25

30

0 1 2 3 4 5 6 7 8 9 10 11unknowns per measurement

relative

err

ors

(%)

randomgeographicLinear (geographic)

clique

star (20 nodes)

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Additional information Additional information –– NetflowNetflow

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Local traffic matrix (George Varghese)Local traffic matrix (George Varghese)

for referenceprevious case

0%1%5%10%

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Robustness (missing data)Robustness (missing data)

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PointPoint--toto--multipointmultipoint

We don’t see whole Internet – What if an edge link fails?Point-to-point traffic matrix isn’t invariant

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PointPoint--toto--multipointmultipointIncluded in this approachImplicit in results aboveExplicit results worse

Ambiguity in demands in increasedMore demands use exactly the same sets of routes

use in applications is better

Point-to-point Point-to-multipoint

Link failure analysis