on the geographic location of internet resources mark crovella boston university computer science...
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On the Geographic Location of Internet Resources
Mark CrovellaBoston University Computer Science
with
Anukool Lakhina, John Byers, and Ibrahim Matta
or
Where on Earth is the Internet?
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 madeScience: 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 routersIxia’s IxMapping service
Mercator: Govindan et al., USC/ISI, ICSI
Skitter: Moore et al., CAIDA
• Based on active probing from a single site• Resolves aliases• Uses loose source routing to explore alternate
paths
• 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, whoise.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
Where are the routers? USA
Europe
Routers and People: World(Grid size: ~150 mi x 150 mi)
Ugh!
People Per Interface (Skitter)
Pop (M)
Intfs(K)
People / Intfc
Online(M)
Online/ Intfc
Africa 837 8,379 100,011
4.1 495
S. America
341 10,131 33,752
21.9 2,161
Mexico 154 4,361 35,534
3.4 784
W. Europe
366 95,993 3,817 143.1 1,489
Japan 136 37,649 3,631 47.1 1,250
Australia 18 18,277 975 10.0 552
USA 299 282,048
1,061 166.1 588
World 5,653
563,521
10,032
513.2 910
Pop (M)
Intfs(K)
People / Intfc
Online(M)
Online/ Intfc
Africa 837 8,379 100,011
4.1 495
S. America
341 10,131 33,752
21.9 2,161
Mexico 154 4,361 35,534
3.4 784
W. Europe
366 95,993 3,817 143.1 1,489
Japan 136 37,649 3,631 47.1 1,250
Australia 18 18,277 975 10.0 552
USA 299 282,048
1,061 166.1 588
World 5,653
563,521
10,032
513.2 910
Interfaces and People: USA, Skitter
Grid size: ~90 mi x 90 mi
Routers and PeopleUpper, 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 Pa
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
1999
1996
Spatial Models
Structural Models
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 regionsUpper, Mercator; Lower, Skitter; small d
USA L 140 mi
Europe L 80 mi
Japan L 140 mi
Large d: distance insensitivity
F(d) = f(u)d
u=1
USA data, Skitter
Distance insensitivity, all regions Upper, Mercator; Lower, Skitter; large d
USA Europe Japan
Limits to distance sensitivity
Mercator Skitter
Limit % Links < Limit
Limit % Links < Limit
USA 820 mi.
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 mi2) … 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
C. A.
S. US
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