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

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

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

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

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

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

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

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

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

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.
BOS 1.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

Where are the routers?
USA

Europe

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

People Per Interface (Skitter)
837 8,379 100,011
S. America 341 10,131 33,752 21.9
2,161
154 4,361 35,534 3.4
W. Europe 366 95,993 3,817 143.1
1,489
136 37,649 3,631 47.1
1,250
18 18,277 975 10.0
299 282,048 1,061 166.1

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

Routers and People
Upper, Mercator; Lower, Skitter
USA Europe Japan

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

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

Spatial model: 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

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

Degree-based Models
• 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

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

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

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

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

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

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

Limits to distance sensitivity
Mercator Skitter
Limit % Links
< Limit
USA 820 mi.
Limit % Links
< Limit
82.1% 818 mi. 77.2%
Europe 383 mi.
97.3% 366 mi.
95.4%
Japan 165 mi.
91.5% 116 mi.
92.8%

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)

Generating Topologies: a new recipe
1. Good models for population density exist
– CIESIN’s Gridded Population of the World
– 2.5 arc minutes (<5 mi 2 ) … very high quality
– Time trends also available
2. Router density then follows from population relationship
3. Link formation driven by hybrid process
– Distance-dependent and –independent

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

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

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

Routers and People: North America

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

Economic Heterogeneity

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”

Routers and Economics
Matrix.net: hosts Mercator: routers

Penultimate Geographic Map, Oct 1980

Last Complete Geographic Map, Aug 1982