Analysis of Internet topology data Johnson Chen and Ljiljana Trajkovi - - PowerPoint PPT Presentation

Analysis of Internet topology data

Johnson Chen and Ljiljana Trajković

hchenj, ljilja@cs.sfu.ca Communication Networks Laboratory http://www.ensc.sfu.ca/cnl Simon Fraser University Vancouver, BC, Canada

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Road map

Introduction Data analysis Routing policies Conclusions References

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Autonomous System (AS)

Internet is a network of Autonomous Systems:

groups of networks sharing the same routing policy identified with Autonomous System Numbers (ASN)

Autonomous System Numbers:

http://www.iana.org/assignments/as-numbers

Internet topology on AS-level:

the arrangement of ASs and their interconnections

Border Gateway Protocol (BGP):

inter-AS protocol used to exchange network reachability information

among BGP systems

reachability information is stored in routing tables

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Internet AS-level data

Source of data are routing tables:

Route Views: http://www.routeviews.org

most participating ASs reside in North America

RIPE (Réseaux IP européens): http://www.ripe.net/ris

most participating ASs reside in Europe

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Internet AS-level data

Data used in prior research (partial list):

Yes Yes Mihail, 2003 No Yes Vukadinovic, 2001 Yes Yes Chang, 2001 No Yes Faloutsos, 1999 RIPE Route Views

Research results have been used in developing Internet

simulation tools:

power-laws are employed to model and generate

Internet topologies: BA model, BRITE, Inet2

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Data sets

Emerging concerns about the use of the two datasets:

different observations about AS degrees:

power-law distribution: Route Views [Faloutsos, 1999] Weibull distribution: Route Views + RIPE [Chang,

2001]

data completeness:

RIPE dataset contains ~ 40% more AS connections

and 2% more ASs than Route Views [Chang, 2001]

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Analysis of datasets

Goals:

discover characteristics of the two datasets identify geography-related routing policies in Internet

Approaches:

spectral analysis notion of “reverse pairs” and their use to analyze

combined data from both datasets

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Route Views and RIPE: statistics

35,225 34,878 AS pairs 15,433 15,418 Probed ASs 6,375,028 6,398,912 AS paths RIPE Route Views Number of

AS pair: a pair of connected ASs 15,369 probed ASs (99.7%) in both datasets are

identical

29,477 AS pairs in Route Views (85%) and in RIPE

(84%) are identical

Route Views and RIPE samples collected on May 30,

2003

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Core ASs

ASs with largest degrees

281 6347 258 7132 20 296 16631 263 3786 19 305 3257 263 4766 18 305 4323 277 3257 17 313 6730 289 8220 16 412 13237 291 6347 15 429 3303 294 16631 14 450 8220 315 4323 13 476 6461 468 4513 12 482 4589 498 6461 11 489 1 556 2914 10 561 2914 562 702 9 580 702 617 3549 8 612 3549 662 3356 7 673 3356 863 209 6 705 3561 999 1 5 861 209 1036 3561 4 1638 7018 1999 7018 3 1784 1239 2569 1239 2 2448 701 2595 701 1 Degree AS Degree AS RIPE Route Views

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Core ASs

ASs with largest degrees 16 of the core ASs in

Route Views and RIPE are identical

Core ASs in Route Views

have larger degrees than core ASs in RIPE

281 6347 258 7132 20 296 16631 263 3786 19 305 3257 263 4766 18 305 4323 277 3257 17 313 6730 289 8220 16 412 13237 291 6347 15 429 3303 294 16631 14 450 8220 315 4323 13 476 6461 468 4513 12 482 4589 498 6461 11 489 1 556 2914 10 561 2914 562 702 9 580 702 617 3549 8 612 3549 662 3356 7 673 3356 863 209 6 705 3561 999 1 5 861 209 1036 3561 4 1638 7018 1999 7018 3 1784 1239 2569 1239 2 2448 701 2595 701 1 Degree AS Degree AS RIPE Route Views

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Spectral analysis of graphs

Normalized Laplacian matrix N(G) [Chung, 1997]:

di and dj are degrees of node i and j, respectively

The second smallest eigenvalue [Fiedler, 1973] The largest eigenvalue [Chung, 1997] Characteristic valuation [Fiedler, 1975]

       − ≠ = =

• therwise

adjacent are j and i if d d d and j i if j i N

j i i

1 1 ) , (

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Characteristic valuation: example

The second smallest eigenvector: 0.1, 0.3, -0.2, 0 AS1(0.1), AS2(0.3), AS3(-0.2), AS4(0) Sort ASs by element value: AS3, AS4, AS1, AS2 AS3 and AS1 are connected

AS3 AS4 AS2 AS1 1

index of elements connectivity status

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Spectral analysis of topology data

• Consider only ASs with the first 30,000 assigned AS numbers
• AS degree distribution in Route Views and RIPE datasets:

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(c) RouteViews_min (d) RIPE_min (a) RouteViews_original (b) RIPE_original Before the sort After the sort

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Before the sort (a) RouteViews_original (b) RIPE_original (c) RouteViews_max (d) RIPE_max After the sort

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Data analysis results

The second smallest eigenvector:

separates connected ASs from disconnected ASs Route Views and RIPE datasets are similar on a coarser

scale

The largest eigenvector:

reveals highly connected clusters Route Views and RIPE datasets differ on a finer scale

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Observations

The two datasets are similar on coarse scales:

number of ASs, number of AS connections, core ASs

They exhibit different clustering characteristics:

Route Views data contain larger AS clusters core ASs in Route Views have larger degrees than core

ASs in RIPE

core ASs in Route Views connect a larger number of

smaller ASs

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Unidirectional routes

Most ASs are access-providers They often prefer that incoming traffic be localized in their

specific geographic areas

Routing policies on incoming traffic influence AS

connectivity:

unidirectional routes are present

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ASs in Route Views:

prefer that incoming traffic be localized to North

America and select ASs in North America as their next hop in routing tables

if ASs in North America cannot be found, ASs in Europe

are selected

special unidirectional routes from North America to

Europe are formed

Special unidirectional routes can suggest geography-

related routing policies dealing with incoming traffic

Special unidirectional routes

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Definition: Two ASs, A and B, are called a reverse pair in data sets S and T if:

• (A-B) ∈ (AS pairs in S)
• (A-B) ∉ (AS pairs in T)
• (B-A) ∈ (AS pairs in T)
• (B-A) ∉ (AS pairs in S)

A B C D E A B H M E A B H M E C D

Route Views RIPE Reverse pair (A,B)

Reverse pairs

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Reverse pairs: properties

For a reverse pair (AS1, AS2): outdegree of AS1 in Route

Views is the indegree of AS1 in RIPE

Reverse pairs indicate the existence of special

unidirectional routes

reverse pairs in dataset of Route Views have more

• riginating ASs in North America

reverse pairs in dataset of RIPE have more originating

ASs in Europe

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558 reverse pairs found:

1.60 % of AS pairs (34,878) in Route Views 1.58 % of AS pairs (35,225) in RIPE

The number of reverse pairs:

the two datasets have ~ 85% of AS pairs in common proportion of reverse pairs in the remaining 15%

distinct AS pairs is not small

Outdegrees of ASs belonging to reverse pairs indicate

• riginating ASs

an AS that is the originating AS of 2 reverse pairs has

an outdegree of 2

Reverse pairs: observations

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ASs with outdegree + indegree ≥ 10

EU 1 10 6467 EU 1 10 1759 EU 1 12 286 EU 1 13 2529 EU 14 13129 EU 3 15 6762 NA 15 297 EU 2 16 13237 EU 2 17 8220 EU 3 18 5400 NA 1 18 4200 EU 1 19 3300 EU 1 20 15412 EU 1 21 4589 EU 3 24 3320 EU 3 27 6730 EU 3 35 3303 Location Indegree Outdegree AS EU 10 5511 NA 10 6453 EU 3 10 1299 NA 8 10 702 EU 11 3333 NA 12 7911 NA 12 2914 NA 12 2497 ASIA 13 2516 NA 14 8001 NA 14 1239 ASIA 15 4637 NA 15 3549 EU 16 3246 EU 17 12956 NA 18 3561 NA 22 3356 NA 24 4513 NA 26 6461 EU 1 29 3257 Location Indegree Outdegree AS

RIPE Route Views

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RIPE:

15 out of 17 originating ASs in reverse pairs are

located in Europe

Route Views:

12 out of 20 originating ASs in reverse pairs are in

North America

Most are large ASs, with degree > 100

large ASs have regional routing policies [Huston, 2001]

Reverse pairs: observations

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We analyzed two Internet datasets: Route Views and RIPE

spectral analysis techniques revealed distinct clustering

characteristics of Route Views and RIPE

reverse pairs were introduced to explore geography-

based routing policies

geographic locations of ASs influence Internet routing

policies

Conclusions

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References

• M. Faloutsos, P. Faloutsos, and C. Faloutsos, “On power-law relationships of the

Internet topology,” Proc. of ACM SIGCOMM ’99, Cambridge, MA, Aug. 1999, pp. 251– 262.

• H. Chang, R. Govindan, S. Jamin, S. Shenker, and W. Willinger, “Towards capturing

representative AS-level Internet topologies,” Proc. of ACM SIGMETRICS 2002, New York, NY, June 2002, pp. 280–281.

• D. Vukadinovic, P. Huang, and T. Erlebach, “On the Spectrum and Structure of Internet

Topology Graphs,” in H. Unger et al., editors, Innovative Internet Computing Systems, LNCS2346, pp. 83–96. Springer, Berlin, Germany, 2002.

• M. Mihail, C. Gkantsidis, and E. Zegura, “Spectral analysis of Internet topologies,” Proc.
• f Infocom 2003, San Francisco, CA, Mar. 2003, vol. 1, pp. 364-374.
• G. Huston, “Interconnection, peering and settlements-Part II,” Internet Protocol Journal,

June 1999: http://www.cisco.com/warp/public/759/ipj_2-2/ipj_2-2_ps1.html.

• F. R. K. Chung, Spectral Graph Theory. Providence, Rhode Island: Conference Board of

the Mathematical Sciences, 1997, pp. 2–6.

• M. Fiedler, “Algebraic connectivity of graphs,” Czech. Math. J., vol. 23, no. 2, pp. 298–

305, 1973.