Presentation of this paper: http://dl.acm.org/citation.cfm?id=1384611

1. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Modeling the evolution of the AS-level
Internet: Integrating aspects of traffic,
geography and economy
Petter Holme, Josh Karlin, Stephanie Forrest
Royal Institute of Technology, School of Computer Science and Technology
October 8, 2008
http://www.csc.kth.se/∼pholme/

2. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Autonomous Systems
Internet is divided into different
subnetworks—Autonomous Systems (AS)
An IP network (or collection of IP networks) with the same
routing policy.
Typically one AS corresponds to one administrative unit.

3. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Autonomous Systems
Internet is divided into different
subnetworks—Autonomous Systems (AS)
An IP network (or collection of IP networks) with the same
routing policy.
Typically one AS corresponds to one administrative unit.

4. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Autonomous Systems
Internet is divided into different
subnetworks—Autonomous Systems (AS)
An IP network (or collection of IP networks) with the same
routing policy.
Typically one AS corresponds to one administrative unit.

5. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Autonomous Systems
Internet is divided into different
subnetworks—Autonomous Systems (AS)
An IP network (or collection of IP networks) with the same
routing policy.
Typically one AS corresponds to one administrative unit.

6. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
BGP routing
Border Gateway Protocol determines how packets are
routed between ASes
Each server keeps a list of paths it can route a packets
through.
Policy (economical agreements) determines the order of
paths.
→ a hierarchy where packets are routed up (to provider),
sideways (to peer), and downwards (to customer).
A BGP server has a quite incomplete picture of the whole
AS-graph.

7. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
BGP routing
Border Gateway Protocol determines how packets are
routed between ASes
Each server keeps a list of paths it can route a packets
through.
Policy (economical agreements) determines the order of
paths.
→ a hierarchy where packets are routed up (to provider),
sideways (to peer), and downwards (to customer).
A BGP server has a quite incomplete picture of the whole
AS-graph.

8. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
BGP routing
Border Gateway Protocol determines how packets are
routed between ASes
Each server keeps a list of paths it can route a packets
through.
Policy (economical agreements) determines the order of
paths.
→ a hierarchy where packets are routed up (to provider),
sideways (to peer), and downwards (to customer).
A BGP server has a quite incomplete picture of the whole
AS-graph.

9. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
BGP routing
Border Gateway Protocol determines how packets are
routed between ASes
Each server keeps a list of paths it can route a packets
through.
Policy (economical agreements) determines the order of
paths.
→ a hierarchy where packets are routed up (to provider),
sideways (to peer), and downwards (to customer).
A BGP server has a quite incomplete picture of the whole
AS-graph.

10. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
BGP routing
Border Gateway Protocol determines how packets are
routed between ASes
Each server keeps a list of paths it can route a packets
through.
Policy (economical agreements) determines the order of
paths.
→ a hierarchy where packets are routed up (to provider),
sideways (to peer), and downwards (to customer).
A BGP server has a quite incomplete picture of the whole
AS-graph.

11. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
BGP routing
Border Gateway Protocol determines how packets are
routed between ASes
Each server keeps a list of paths it can route a packets
through.
Policy (economical agreements) determines the order of
paths.
→ a hierarchy where packets are routed up (to provider),
sideways (to peer), and downwards (to customer).
A BGP server has a quite incomplete picture of the whole
AS-graph.

12. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Degree distribution
Broad degree-distribution (possibly power-law, or log-normal).
1 10 100 1000
k
10−4
10−3
0.01
0.1
1
P(k)

13. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Mechanistic models of AS graph
Typically focus on network topology.
. . . possibly with a geometry.
. . . or traffic.
No geographically explicit ASes.
No explicit economic modeling (pricing, etc.)

14. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Mechanistic models of AS graph
Typically focus on network topology.
. . . possibly with a geometry.
. . . or traffic.
No geographically explicit ASes.
No explicit economic modeling (pricing, etc.)

15. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Mechanistic models of AS graph
Typically focus on network topology.
. . . possibly with a geometry.
. . . or traffic.
No geographically explicit ASes.
No explicit economic modeling (pricing, etc.)

16. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Mechanistic models of AS graph
Typically focus on network topology.
. . . possibly with a geometry.
. . . or traffic.
No geographically explicit ASes.
No explicit economic modeling (pricing, etc.)

17. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Mechanistic models of AS graph
Typically focus on network topology.
. . . possibly with a geometry.
. . . or traffic.
No geographically explicit ASes.
No explicit economic modeling (pricing, etc.)

18. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Mechanistic models of AS graph
Typically focus on network topology.
. . . possibly with a geometry.
. . . or traffic.
No geographically explicit ASes.
No explicit economic modeling (pricing, etc.)

19. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Barab´asi–Albert model
probability of attachment: ∝ ki

20. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Barab´asi–Albert model
probability of attachment: ∝ ki

21. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Barab´asi–Albert model
probability of attachment: ∝ ki

22. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Barab´asi–Albert model
probability of attachment: ∝ ki

23. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Barab´asi–Albert model
probability of attachment: ∝ ki

24. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
FKP model
attach i to vertex j minimizing:
|ri − rj| + αd( j, 0)
0

25. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
FKP model
attach i to vertex j minimizing:
|ri − rj| + αd( j, 0)
|r1 − r0|
0

26. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
FKP model
0
attach i to vertex j minimizing:
|ri − rj| + αd( j, 0)

27. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
FKP model
0
attach i to vertex j minimizing:
|ri − rj| + αd( j, 0)

28. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
FKP model
0
attach i to vertex j minimizing:
|ri − rj| + αd( j, 0)

29. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
FKP model
0
attach i to vertex j minimizing:
|ri − rj| + αd( j, 0)

30. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
FKP model
0
attach i to vertex j minimizing:
|ri − rj| + αd( j, 0)

31. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
FKP model
0
attach i to vertex j minimizing:
|ri − rj| + αd( j, 0)

32. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Radial structure
Plot quantities as function of the average distance to the rest of
the AS graph.
P. Holme, J. Karlin and S. Forrest, Proc. R. Soc. A 463,
1231–1246 (2007).

33. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Radial structure
0
0.05
0.1
0.15
0.2
2 3 4 5 6 7
average distance, ¯d
AS ’06
BA model
Inet model
fractionofvertices

34. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Radial structure
AS ’06
BA model
Inet model
1
10
100
1000
2 3 4 5 6 7
average distance, ¯d
averagedegree,k

35. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Radial structure
AS ’06
BA model
Inet model
0
0.05
0.1
0.15
0.2
clusteringcoefficient,C
2 3 4 5 6 7
average distance, ¯d

36. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Radial structure
AS ’06
BA model
Inet model
0.01deletionimpact,φ
2 3 4 5 6 7
average distance, ¯d
10−6
10−5
10−4
10−3

37. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Aim
Make a mechanistic model that:

38. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Aim
Make a mechanistic model that:
has spatially explicit ASes

39. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Aim
Make a mechanistic model that:
has spatially explicit ASes
flowing between them
with realistic traffic

40. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Aim
Make a mechanistic model that:
has spatially explicit ASes
flowing between them
with realistic traffic
that give the ASes income

41. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Aim
Make a mechanistic model that:
has spatially explicit ASes
flowing between them
with realistic traffic
that give the ASes income
that the AS can invest in geographical growth

42. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Aim
Make a mechanistic model that:
has spatially explicit ASes
flowing between them
with realistic traffic
that increase / affect
the traffic
that give the ASes income
that the AS can invest in geographical growth

43. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Overall structure
The model begins with one agent located at the pixel with the
highest population density. The model then iterates over the
following steps:
1 Network growth. The number of agents is increased. The
agents are expanded geometrically, and their capacities
are adjusted.
2 Network traffic. Messages are created, migrated toward
their targets, and delivered. This process is repeated
Ntraffic times before the next network-growth step.

44. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Overall structure
The model begins with one agent located at the pixel with the
highest population density. The model then iterates over the
following steps:
1 Network growth. The number of agents is increased. The
agents are expanded geometrically, and their capacities
are adjusted.
2 Network traffic. Messages are created, migrated toward
their targets, and delivered. This process is repeated
Ntraffic times before the next network-growth step.

45. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Overall structure
The model begins with one agent located at the pixel with the
highest population density. The model then iterates over the
following steps:
1 Network growth. The number of agents is increased. The
agents are expanded geometrically, and their capacities
are adjusted.
2 Network traffic. Messages are created, migrated toward
their targets, and delivered. This process is repeated
Ntraffic times before the next network-growth step.

46. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Network Growth
geography represented as sq. grid

47. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Network Growth
geography represented as sq. grid
each pixel has a pop. density

48. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Network Growth
geography represented as sq. grid
each pixel has a pop. density
the ASes are modeled as:

49. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Network Growth
geography represented as sq. grid
each pixel has a pop. density
the ASes are modeled as:
a set of locations (coordinates)

50. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Network Growth
geography represented as sq. grid
each pixel has a pop. density
the ASes are modeled as:
a set of locations (coordinates)
set of links (to AS at same pixel)

51. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Network Growth
geography represented as sq. grid
each pixel has a pop. density
the ASes are modeled as:
a set of locations (coordinates)
budget
set of links (to AS at same pixel)

52. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Network Growth
geography represented as sq. grid
each pixel has a pop. density
the ASes are modeled as:
a set of locations (coordinates)
budget
set of links (to AS at same pixel)
queue

53. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Network Growth
geography represented as sq. grid
each pixel has a pop. density
the ASes are modeled as:
a set of locations (coordinates)
budget
capacity
set of links (to AS at same pixel)
queue

54. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Network Growth
geography represented as sq. grid
each pixel has a pop. density
the ASes are modeled as:
a set of locations (coordinates)
budget
capacity
set of links (to AS at same pixel)
queue
costs for: increasing capacity
connecting to other, adding loc.

55. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Network Growth
geography represented as sq. grid
each pixel has a pop. density
the ASes are modeled as:
a set of locations (coordinates)
budget
capacity
set of links (to AS at same pixel)
queue
costs for: increasing capacity
connecting to other, adding loc.
income prop. to traffic

56. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Network Growth

57. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Network Growth
1. (while nwk too dense,) add ASes

58. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Network Growth
1. (while nwk too dense,) add ASes
2. increase capacity as much as needed

59. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Network Growth
1. (while nwk too dense,) add ASes
2. increase capacity as much as needed
3. link addition

60. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Network Growth
1. (while nwk too dense,) add ASes
2. increase capacity as much as needed
3. link addition
connect unconnected pairs at random

61. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Network Growth
1. (while nwk too dense,) add ASes
2. increase capacity as much as needed
3. link addition
connect unconnected pairs at random
(if both ASes can afford a connection)

62. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Network Growth
1. (while nwk too dense,) add ASes
2. increase capacity as much as needed
3. link addition
connect unconnected pairs at random
(if both ASes can afford a connection)
4. spatial extension

63. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Network Growth
1. (while nwk too dense,) add ASes
2. increase capacity as much as needed
3. link addition
connect unconnected pairs at random
(if both ASes can afford a connection)
4. spatial extension
ASes spend their budget on new loc

64. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Network Growth
1. (while nwk too dense,) add ASes
2. increase capacity as much as needed
3. link addition
connect unconnected pairs at random
(if both ASes can afford a connection)
4. spatial extension
ASes spend their budget on new loc
choose affordable pixel w highest pop

65. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Traffic dynamics

66. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Traffic dynamics

67. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Traffic dynamics

68. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Traffic dynamics
s
t

69. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Traffic dynamics
s
t s
t

70. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Traffic dynamics
t = 1

71. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Traffic dynamics
t = 2

72. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Traffic dynamics
t = 3

73. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Time evolution
a
b
c
τp,d
100
104
1
103
number of agents, n
number of links, m
n,mfractionoftotal
0.25
0.5
0.75
0
covered population
covered area
120 140 160 200180
120 140 160 200
time, τ
2
3
4
5
6
7
d
τp
100180 100001000
time, τ number of ASs, n
8

74. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Degree distribution
1 10 100 1000 1 10 100 1000 1 100 100010
k k k
10−4
10−3
0.01
0.1
1
P(k)
real
model 10−4
10−3
0.01
0.1
1
BA model
P(k)
10−3
0.01
0.1
1
P(k)
FKP model
10−4

75. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Degree distribution
10−5
10−6
10−4
10−3
1
10
104
104
105
106
103
traffic load
degree,k
100

76. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Radial statistics
0
0.1
0.2
our model
AS06 FKPBA
fractionofvertices
5 6 5 65 6 3 4 3 43 4
average distance, ¯d average distance, ¯d average distance, ¯d

77. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Radial statistics
3 4 3 43 4
average distance, ¯d average distance, ¯d average distance, ¯d
5 6 5 65 6
averagedegree
1
10
102
103

78. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Traffic vs centrality
10−6
10−3
10−4
10−5
10−1
10−2
10−4
10−3
10−5
1 5 10 50
trafficdensity,ρ
betweenness, CB ×104

79. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Geography
100 200 300
population density (people per square mile)
0
t = 14
λ = 6

80. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Geography
100 200 300
population density (people per square mile)
0
λ = 15
t = 23

81. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Geography
100 200 300
population density (people per square mile)
0
t = 28
λ = 69

82. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Geography
100 200 300
population density (people per square mile)
0
λ = 272
t = 28

83. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Geography

84. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Geography

85. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Summary
Mechanistic growth model of AS-level Internet
Degree distribution matches
Periphery not as complex as reality
Traffic fluctuations affect low- and medium-sized ASes
Spatial distribution not completely crazy
P. Holme, J. Karlin and S. Forrest, An integrated model of
traffic, geography and economy in the Internet. Computer
Communication Review 32, 7–15 (2008).

86. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Summary
Mechanistic growth model of AS-level Internet
Degree distribution matches
Periphery not as complex as reality
Traffic fluctuations affect low- and medium-sized ASes
Spatial distribution not completely crazy
P. Holme, J. Karlin and S. Forrest, An integrated model of
traffic, geography and economy in the Internet. Computer
Communication Review 32, 7–15 (2008).

87. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Summary
Mechanistic growth model of AS-level Internet
Degree distribution matches
Periphery not as complex as reality
Traffic fluctuations affect low- and medium-sized ASes
Spatial distribution not completely crazy
P. Holme, J. Karlin and S. Forrest, An integrated model of
traffic, geography and economy in the Internet. Computer
Communication Review 32, 7–15 (2008).

88. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Summary
Mechanistic growth model of AS-level Internet
Degree distribution matches
Periphery not as complex as reality
Traffic fluctuations affect low- and medium-sized ASes
Spatial distribution not completely crazy
P. Holme, J. Karlin and S. Forrest, An integrated model of
traffic, geography and economy in the Internet. Computer
Communication Review 32, 7–15 (2008).

89. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Summary
Mechanistic growth model of AS-level Internet
Degree distribution matches
Periphery not as complex as reality
Traffic fluctuations affect low- and medium-sized ASes
Spatial distribution not completely crazy
P. Holme, J. Karlin and S. Forrest, An integrated model of
traffic, geography and economy in the Internet. Computer
Communication Review 32, 7–15 (2008).

90. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Summary
Mechanistic growth model of AS-level Internet
Degree distribution matches
Periphery not as complex as reality
Traffic fluctuations affect low- and medium-sized ASes
Spatial distribution not completely crazy
P. Holme, J. Karlin and S. Forrest, An integrated model of
traffic, geography and economy in the Internet. Computer
Communication Review 32, 7–15 (2008).

91. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Summary
Mechanistic growth model of AS-level Internet
Degree distribution matches
Periphery not as complex as reality
Traffic fluctuations affect low- and medium-sized ASes
Spatial distribution not completely crazy
P. Holme, J. Karlin and S. Forrest, An integrated model of
traffic, geography and economy in the Internet. Computer
Communication Review 32, 7–15 (2008).

92. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Other integrative mechanistic models
S. Shakkottai et al.. Evolution of the Internet Ecosystem.
S. Bar, M. Gonen & A. Wool. A geographic directed
preferential Internet topology model. Computer Networks
51, 4174–4188 (2007).

93. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Other integrative mechanistic models
S. Shakkottai et al.. Evolution of the Internet Ecosystem.
S. Bar, M. Gonen & A. Wool. A geographic directed
preferential Internet topology model. Computer Networks
51, 4174–4188 (2007).

94. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Other integrative mechanistic models
S. Shakkottai et al.. Evolution of the Internet Ecosystem.
S. Bar, M. Gonen & A. Wool. A geographic directed
preferential Internet topology model. Computer Networks
51, 4174–4188 (2007).

95. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Future
Including economy.
Simple models.

96. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Future
Including economy.
Simple models.

97. Modeling the
evolution of
the AS-level
Internet:
Integrating
aspects of
traffic,
geography
and economy
PETTER
HOLME
Introduction
Our model
Numerical
results
Future
Including economy.
Simple models.