On the Geographic Location of Internet Resources

1. On the Geographic Location of Internet Resources or Where on Earth is the Internet? Mark Crovella Boston University Computer Science with Anukool Lakhina, John Byers, and Ibrahim Matta

2. Some observations about the Internet • Rapid, decentralized growth: • 90% of Internet systems were added in the last four years • Connecting to the network can be a purely local operation • This rapid, decentralized growth has opened significant questions about the physical structure of the network; e.g., • The number of hosts connected to the network • The properties of network links (delay, bandwidth) • The interconnection pattern of hosts and routers • The interconnection relationships of ISPs • The geographic locations of hosts, routers and links

3. Internet Science • Engineering or Science? Engineering: study of things made Science: study of things found • Although the Internet is a engineered artifact, it now presents us with questions that are better approached from a scientific posture

4. For example: where is the Internet? ? ? ? ? ? What is the relationship between geography and the network?

5. Why does this matter? • Our motivation is in developing better generators for “representative network topologies” • Many simulation based results in networking depend critically on network topology • Topology generation is still fairly ad hoc • However, there is a scientific goal as well! • We need to understand what drives Internet growth • Basic investigations will pay off in unexpected ways

6. Assumptions and Definitions • We will treat the Internet as an undirected graph embedded on the Earth’s surface • Nodes correspond to routers or interfaces • Edges correspond to physical router-router links • Not concerned with hosts (end systems) • We will ignore many higher and lower level questions • Autonomous systems • Link layers

7. Some Basic Questions • What is the relationship between population and network geometry? • What effect does distance have on network topology? Our Basic Approach • Obtain IP-level router maps • Mercator and Skitter • Find geographic locations of those routers • Ixia’s IxMapping service

8. Mercator:Govindan et al., USC/ISI, ICSI • Based on active probing from a single site • Resolves aliases • Uses loose source routing to explore alternate paths Skitter:Moore et al., CAIDA • Traceroutes from 19 monitors to large set of destinations • Does not resolve aliases • Destinations attempt to cover IP address space

9. Datasets • Mercator • Collected August 1999 • 228,263 routers • 320,149 links • Skitter • Collected January 2002 • 704,107 interfaces • 1,075,454 links

10. IxMapping:Moore et al., CAIDA • Given an IP address, infers geographic location based on a variety of heuristics • Hostnames, DNS LOC, whois e.g., 190.ATM8-0-0.GW3.BOS1.ALTER.NET is in Boston • Able to map • 99% of Mercator routers • 98.5% of Skitter interfaces • Similar to GeoTrack [Padmanabhan] which exhibits reasonable accuracy • Median error of 64 mi • 90% queries within 250 mi • for well connected nodes

11. Where are the routers? USA

12. Europe

13. Routers and People: World (Grid size: ~150 mi x 150 mi) Ugh!

14. People Per Interface (Skitter)

15. Interfaces and People: USA, Skitter Grid size: ~90 mi x 90 mi

16. Routers and PeopleUpper, Mercator; Lower, Skitter USA Europe Japan

17. Router Location: Summary • Router location is strongly driven by both population density and economic development • Superlinear relationship between router and population density: R  k Pa k varies with economic development (users online) a is greater than one • More routers per person in more densely populated areas

18. Models for Network Topology 1988 Spatial Models Structural Models 1996 Degree-based Models 1999

19. Spatialmodel: Waxman, 1988 • Nodes are distributed randomly (uniformly) in the plane. • Probability that two nodes separated by distance d are connected: P[C|d] =  exp(-d/L) 0  ,   1; L = diameter of region : degree of distance sensitivity : edge density • A spatially imbedded random graph

20. Structural Models • Real networks have structure • Always connected! • Formed by interconnection of component networks • Distinction between transit and stub networks imposes a hierarchy on resulting graph • Tiers: Doar, 1996 • GT-ITM: Calvert, Doar, Zegura, 1997

21. Degree-basedModels • Faloutsos, Faloutsos, & Faloutsos, 1999: • Empirically measured networks show a power law in degree distribution: P[node has degree d] = k d-a • Barabasi & Albert, 1999: • This property will be present in a graph where: • Nodes and links are added incrementally • Probability of connecting to a node is proportional to its degree (preferential connectivity) • BRITE: Medina, Matta, Byers, 2001

22. Empirical Evidence • Interested in influence of distance on link formation: f(d) = P[C|d] i.e., Probability two nodes separated by distance d are connected • Estimated as: number links of length d f(d) = ------------------------------------------- number of router pairs separated by d

23. Distance Sensitive Distance Insensitive f(d) for USA (Skitter)

24. Link Distance Preference for USA Skitter, d < 250, semi-log plot L  140 mi.

25. Link distance preference: all regionsUpper, Mercator; Lower, Skitter; small d USA L  140 mi Europe L  80 mi Japan L  140 mi

26. d F(d) = f(u) u=1 Large d: distance insensitivity USA data, Skitter

27. Distance insensitivity, all regions Upper, Mercator; Lower, Skitter; large d USA Europe Japan

28. Limits to distance sensitivity

29. Link Formation: Summary • Link formation seems to be a mixture of distance-dependent and –independent processes • Waxman (exponential) model remarkably good for large fraction of all links! • But, crucial difference is that we are using a very irregular spatial distribution of nodes • Small fraction of non-local links are very important (structural)

30. Generating Topologies: a new recipe • Good models for population density exist • CIESIN’s Gridded Population of the World • 2.5 arc minutes (<5 mi2) … very high quality • Time trends also available • Router density then follows from population relationship • Link formation driven by hybrid process • Distance-dependent and –independent

31. Related Work • Matrix.net: • Uses DNS hostname allocations • proprietary location methods • Akamai • Extensive peering and measurement infrastructure • Padmanabhan and Subramanian, 2000: • assessed accuracy of geographic mapping techniques • Yook, Jeong, and Barabasi, 2001: • Similar goals • Find linear (not exponential) distance dependence

32. Final Thoughts • The Internet has fully interpenetrated human society • Scientific understanding of the net is essential • Applications: • Simulation • Security • Reliability • Planning

33. Thanks! • CAIDA: • David Moore • k claffy • Andre Broido • Notre Dame: • Lazslo Barabasi • USC: • Ramesh Govindan • Hongsuda Tangmunarunkit

34. Routers and People: North America

35. Subdividing the Data N. US S. US C. A.

36. Economic Heterogeneity

37. What Influences the Formation of Links? • Waxman, 1988:spatial model • Zegura et al., 1997:structural model • Explicitly captures hierarchical structure • Barabasi et al., 1999:degree-based preferential connectivity • Matches observed power-law node degree • Inspired by Faloutsos et al., 1999 • Strogatz & Watts, 1998:small-world properties • Captures “six degrees of separation”

38. Routers and Economics Matrix.net: hosts Mercator: routers

39. Penultimate Geographic Map, Oct 1980

40. Last Complete Geographic Map, Aug 1982