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- 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.