The Internet’s Dynamic Geography

1. The Internet’s Dynamic Geography Scott Kirkpatrick, School of Engineering, Hebrew University of Jerusalem and EVERGROW Collaborators (thanks, not blame…) Yuval Shavitt, Eran Shir, Shai Carmi, Shlomo Havlin, Avishalom Shalit Bremen, June 11-12, 2007

2. Measuring and monitoring the Internet • Has undergone a revolution • Traceroute – an old hack  basic tool in wide use • Active monitors – hardware intensive  distributed software • DIMES (“Dimes@home”) an example, not the only one now • Many enhancements under consideration, as the problems in traceroute become very evident • Ultimately, we expect every router (or what they become in the future internet) will participate in distributed active monitoring. • The payoff comes with interactive and distributed services that can achieve greater performance at greatly decreased overhead

3. History of TraceRoute active measurement • Jacobson, “traceroute” from LBL, February 1989 • Commonly uses ICMP echo or UDP • Variants exist – tcptraceroute, NANOG, “Paris traceroute” • And this is something that can be rewritten for special situations, such as cellphones • Single machine traces to many destinations – Lucent, 1990s (Burch and Cheswick) • Great pictures, but interpretation not clear, demonstrate need for more analytic visualization techniques • But excellent for magazine covers, t-shirts… • First attempt to determine the time evolution of the Internet • First experience in operating under the “network radar” • Lumeta, their spinoff, ended up as a network radar supplier.

4. IP address map of August 1998

5. IP address map of Jan 1999

6. IP address map of June 1999

7. Map interpreted: color by ISPs

8. History of Internet Measurement, ctd. • Skitter and subsequent projects at CAIDA (SDSC) • 15-50 machines (typically <25), at academic sites around world • RIPE and NLANR, 1-200 machines, commercial networks and telco backbones, information is proprietary • DIMES (>10,000 software agents) represents the next step • A complementary approach is available at the coarser level of ISPs (actually “autonomous systems” or ASes) • RouteViews (Univ. of Oregon) since 2001 has monitored BGP preferred routes broadcast from a healthy sampling of ASes’ border routers.

9. Traceroute is more than a piece of string • A flood of feigned suicide packets (with TTL values t=1 to about 30 hops), each sent more than one time. • Ideal situation, each packet dies at step t, router returns echo message, “so sorry, your packet died at ip address I, time T” • Non ideal situations must be filtered to avoid data corruption: • Errors – router inserts destination address for I • Non-response is common • Multiple interfaces for a single (complex) router • Route flaps, load balancing create false links • Route instabilities can be reduced with careful header management (requires guessing router tricks)

10. The Internet is more than a random graph • Internet is a federation of subnetworks (ASs or ISPs) • It has at least a two-level structure (AS, ip-level) because two different routing strategies and software are used to direct packets. Other coarse grain views – country, city, POP… • There are no global databases, many local databases, poor data quality available. • Models have evolved steadily • Waxman (Random graph with Poisson distribution of ngbrs) • “Transit-stub” model with two-level hierarchy • Power law pictures, such as preferential attachment, reordering • Jellyfish and Medusa

11. What is the quality of today’s measurements? • Bias issues – does a superposition of shortest-path trees converge to the actual underlying graph? • Concerns about diminishing returns? • Filters needed to screen as many false links as possible. • Once you have a flood of data, need to address two issues: • Has it converged to cover the real graph? • Betweenness and visit count help address this • How stable are the measurements over time? • And finally, how does traceroute discovery compare with online tables of AS-disclosed information (BGP tables)?

12. What do we see with DIMES? • New graphical analysis methods reveal considerable structure, apparently related to function. Yes, Virginia, there are power laws! But the initial conditions and some of the patterns of growth reflect distinct roles of subnetworks as well as growth dynamics, and economic incentives. • The Internet is a moving target, and we are observing it through a very shaky telescope. How should we characterize its evanescent behavior? How to integrate to see the fainter stars? • Discussions of bias and “diminishing returns” may be addressing the wrong hypotheses.

13. Use a new analytical tool – k-pruning • Prune by grouping sites in “shells” with a common connectivity further into the Internet: All sites with connectivity 1 are removed (recursively) and placed in the “1-shell,” leaving a “2-core” then 2-shell, 3-core and so forth. • The union of shells 1-k is called the “k-crust” • At some point, kmax, pruning runs to completion. • Identify nucleus as kmax-core • This is a natural, robust definition, and should apply to other large networks of interest in economics and biology. • Cluster analysis finds interesting structure in the k-crusts

14. Does degree of site relate to k-shell?

15. Numbers of site-distinct paths in the nucleus kmax (03-06) = 41 kmax (05-06) = 39 Conclusion: innermost k-cores are k-connected. But outer k-cores (2,3,4) show exceptions (sites with 1,2,3 paths).

16. Distances and Diameters in cores

17. Distances and Diameters

18. K-crusts show percolation threshold  These are the hanging tentacles of our (Red Sea) Jellyfish For subsequent analysis, we distinguish three components: Core, Connected, Isolated Largest cluster in each shell Data from 01.04.2005

19. Shells Core 1 2 3 Michalis Faloutsos’ Jellyfish • Highly connected nodes form the core • Each Shell: adjacent nodes of previous shell, except 1-degree nodes • Importance decreases as we move away from core • 1-degree nodes hanging • The denser the 1-degree node population the longer the stem

20. Meduza (מדוזה) model This picture has been stable from January 2005 (kmax = 30) to present day, with little change in the nucleus composition. The precise definition of the tendrils: those sites and clusters isolated from the largest cluster in all the crusts – they connect only through the core.

21. Non-communication Networks

22. Communication networks

23. Who’s “tier-1” in Medusa? 1668 496 16150 460 6395 453 3257 450 286 391 3246 389 8342 387 5511 384 4766 367 25462 365 8928 360 7473 359 3292 347 3786 343 2516 330 3209 329 12989 327 6539 317 6320 283 10026 283 6695 277 3352 263 8001 259 1257 258 22773 250 6327 247 5650 245 19151 239 13237 237 4436 98 6389 96 8210 95 4788 93 23352 89 19548 87 23342 80 10310 75 812 64 15169 50 8075 226 2497 225 15412 213 6762 208 19029 206 4589 203 5459 202 5089 197 852 180 5462 176 15290 174 577 156 2856 153 8546 153 9318 145 6079 137 13768 136 4725 133 22822 128 293 122 4134 122 3300 117 4355 113 6830 110 12322 108 • 701 2992 • 7018 2766 • 3356 2665 • 1239 2619 • 174 1967 • 209 1387 • 12956 1261 • 1299 1251 • 3549 1219 • 3561 1215 • 2914 998 • 7132 951 • 702 923 • 6730 923 • 6461 907 • 4323 772 • 1273 728 • 3491 687 • 6453 644 • 3303 612 • 3320 590 • 6939 584 • 2828 577 • 4513 570 • 4637 544 • 7911 542 • 8220 531 • 5400 522 • 1221 508 Data from months 10-12, 2005 kmax = 42, 93 nodes All fall within CAIDA’s top 200 ASes, measured by size of “customer input cone.”

24. What about the error bars, the bias, etc.? • Need to address the specifics of the “network discoveries” • How frequently observed? • How sensitive are the observations to the number of observers? • How do the measurements depend on the time of observation? • The extensive literature on the subject is mostly straw-man counterexamples, that show bias from this class of observation can be serious, in graphs of known structure, but do not address how to estimate structure from actual measurements.

25. Lecture 2 • Efforts to model the Internet • Waxman (Poisson statistics, single scale) • Zegura and co-workers (GaTech) two scales • “Transit” and “stub” • Preferential attachment • Shalit et al (2001) showed exponent in (2,3) possible, and k-shells also give simple power laws • Counterattack of the establishment • Luddites?

26. The Empire Strikes Back!

27. Willinger et al. analysis of models • Is a particular model “descriptive” or “explanatory”? • Descriptive models are • “evocative • “data-driven” • But too generic in nature • Explanatory models are • Structural • Can close the loop by validating the explanatory steps with real data • “Demystify emergent phenomena”

28. So models  excerpts of actual measurements • Power laws occur in the k-shells as well as in degree distrib: But the k-cores are not scale invariant!

29. Where is a pure “emergent phenomenon” happening? • Box cover construction shows true fractal only as the shells percolate

30. Back to the actual data • Visit count and betweenness • Best evidence for reliability of data • How much better will it get with 100,000 agents observing? • Can’t ask the question. But can ask, how much worse will it be with fewer. • Three approaches in prospect. All future work. • Study betweenness of present graph with reduced traffic model • Reanalyze our raw data with fewer agents included • Run retrospective experiments with agents selected specially

31. What sort of coverage is obtained?

32. Agents from entire two years participate

33. Weekly coverage and agent utilization

34. Time dependences – even RouteViews’ BGP speakers vary • Study 6 weeks in 2006 (June, July) • 50,245 to 51,309 edges found per week • In wk 26, 48,221 edges seen all week • 335 edges seen for 6 days • 192 edges seen only 5 days • 294 edges seen only 4 days • 354 edges seen only 3 days • 260 edges seen only 2 days • 175 edges seen only 1 day • 451 edges seen only one time. • Single observations peak on Sunday (149 edges, other days typically ~40) • Edges seen 3 or more days peak at ends of the week • Twice as many edges are created on Monday as are deleted on Sunday…

35. Random scale-free graphs produce the same basic structure, different details

36. Percolation “attacks” K-core based attack (“by reputation”) is comparable to accurate degree-based attack for random networks, but not for the real AS graph.

37. Preliminary reachability data (using whole graph) Sites reachable

38. Now restrict to the 20-crust Up then down Side step at top Three sidesteps