modeling the evolution of the as-level internet: integrating aspects of traffic, geography and...
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Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Modeling the evolution of the AS-levelInternet: 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/
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Autonomous Systems
Internet is divided into differentsubnetworks—Autonomous Systems (AS)
An IP network (or collection of IP networks) with the samerouting policy.
Typically one AS corresponds to one administrative unit.
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Autonomous Systems
Internet is divided into differentsubnetworks—Autonomous Systems (AS)
An IP network (or collection of IP networks) with the samerouting policy.
Typically one AS corresponds to one administrative unit.
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Autonomous Systems
Internet is divided into differentsubnetworks—Autonomous Systems (AS)
An IP network (or collection of IP networks) with the samerouting policy.
Typically one AS corresponds to one administrative unit.
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Autonomous Systems
Internet is divided into differentsubnetworks—Autonomous Systems (AS)
An IP network (or collection of IP networks) with the samerouting policy.
Typically one AS corresponds to one administrative unit.
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
BGP routing
Border Gateway Protocol determines how packets arerouted between ASes
Each server keeps a list of paths it can route a packetsthrough.
Policy (economical agreements) determines the order ofpaths.
→ 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 wholeAS-graph.
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
BGP routing
Border Gateway Protocol determines how packets arerouted between ASes
Each server keeps a list of paths it can route a packetsthrough.
Policy (economical agreements) determines the order ofpaths.
→ 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 wholeAS-graph.
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
BGP routing
Border Gateway Protocol determines how packets arerouted between ASes
Each server keeps a list of paths it can route a packetsthrough.
Policy (economical agreements) determines the order ofpaths.
→ 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 wholeAS-graph.
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
BGP routing
Border Gateway Protocol determines how packets arerouted between ASes
Each server keeps a list of paths it can route a packetsthrough.
Policy (economical agreements) determines the order ofpaths.
→ 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 wholeAS-graph.
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
BGP routing
Border Gateway Protocol determines how packets arerouted between ASes
Each server keeps a list of paths it can route a packetsthrough.
Policy (economical agreements) determines the order ofpaths.
→ 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 wholeAS-graph.
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
BGP routing
Border Gateway Protocol determines how packets arerouted between ASes
Each server keeps a list of paths it can route a packetsthrough.
Policy (economical agreements) determines the order ofpaths.
→ 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 wholeAS-graph.
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Degree distribution
Broad degree-distribution (possibly power-law, or log-normal).
1 10 100 1000k
10−4
10−3
0.01
0.1
1P
(k)
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
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.)
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
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.)
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
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.)
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
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.)
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
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.)
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
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.)
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Barabasi–Albert model
probability of attachment: ∝ ki
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Barabasi–Albert model
probability of attachment: ∝ ki
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Barabasi–Albert model
probability of attachment: ∝ ki
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Barabasi–Albert model
probability of attachment: ∝ ki
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Barabasi–Albert model
probability of attachment: ∝ ki
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
FKP model
attach i to vertex j minimizing:|ri − r j| + αd( j, 0)
0
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
FKP model
attach i to vertex j minimizing:|ri − r j| + αd( j, 0)
|r1 − r0|0
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
FKP model
0
attach i to vertex j minimizing:|ri − r j| + αd( j, 0)
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
FKP model
0
attach i to vertex j minimizing:|ri − r j| + αd( j, 0)
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
FKP model
0
attach i to vertex j minimizing:|ri − r j| + αd( j, 0)
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
FKP model
0
attach i to vertex j minimizing:|ri − r j| + αd( j, 0)
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
FKP model
0
attach i to vertex j minimizing:|ri − r j| + αd( j, 0)
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
FKP model
0
attach i to vertex j minimizing:|ri − r j| + αd( j, 0)
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Radial structure
Plot quantities as function of the average distance to the rest ofthe AS graph.
P. Holme, J. Karlin and S. Forrest, Proc. R. Soc. A 463,1231–1246 (2007).
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Radial structure
0
0.05
0.1
0.15
0.2
2 3 4 5 6 7average distance,d
AS ’06BA modelInet model
frac
tion
ofve
rtic
es
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Radial structure
AS ’06BA modelInet model
1
10
100
1000
2 3 4 5 6 7average distance,d
aver
age
degr
ee,k
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Radial structure
AS ’06BA modelInet model
0
0.05
0.1
0.15
0.2cl
uste
ring
coeffi
cien
t,C
2 3 4 5 6 7average distance,d
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Radial structure
AS ’06BA modelInet model
0.01de
letio
nim
pact
,φ
2 3 4 5 6 7average distance,d
10−6
10−5
10−4
10−3
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Aim
Make a mechanistic model that:
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Aim
Make a mechanistic model that:
has spatially explicit ASes
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Aim
Make a mechanistic model that:
has spatially explicit ASes
flowing between themwith realistic traffic
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Aim
Make a mechanistic model that:
has spatially explicit ASes
flowing between themwith realistic traffic
that give the ASes income
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Aim
Make a mechanistic model that:
has spatially explicit ASes
flowing between themwith realistic traffic
that give the ASes income
that the AS can invest in geographical growth
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Aim
Make a mechanistic model that:
has spatially explicit ASes
flowing between themwith realistic traffic
that increase / affectthe traffic
that give the ASes income
that the AS can invest in geographical growth
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Overall structure
The model begins with one agent located at the pixel with thehighest population density. The model then iterates over thefollowing steps:
1 Network growth. The number of agents is increased. Theagents are expanded geometrically, and their capacitiesare adjusted.
2 Network traffic. Messages are created, migrated towardtheir targets, and delivered. This process is repeatedNtraffic times before the next network-growth step.
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Overall structure
The model begins with one agent located at the pixel with thehighest population density. The model then iterates over thefollowing steps:
1 Network growth. The number of agents is increased. Theagents are expanded geometrically, and their capacitiesare adjusted.
2 Network traffic. Messages are created, migrated towardtheir targets, and delivered. This process is repeatedNtraffic times before the next network-growth step.
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Overall structure
The model begins with one agent located at the pixel with thehighest population density. The model then iterates over thefollowing steps:
1 Network growth. The number of agents is increased. Theagents are expanded geometrically, and their capacitiesare adjusted.
2 Network traffic. Messages are created, migrated towardtheir targets, and delivered. This process is repeatedNtraffic times before the next network-growth step.
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Network Growth
geography represented as sq. grid
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Network Growth
geography represented as sq. grideach pixel has a pop. density
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Network Growth
geography represented as sq. grideach pixel has a pop. densitythe ASes are modeled as:
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Network Growth
geography represented as sq. grideach pixel has a pop. densitythe ASes are modeled as:
a set of locations (coordinates)
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Network Growth
geography represented as sq. grideach pixel has a pop. densitythe ASes are modeled as:
a set of locations (coordinates)set of links (to AS at same pixel)
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Network Growth
geography represented as sq. grideach pixel has a pop. densitythe ASes are modeled as:
a set of locations (coordinates)
budgetset of links (to AS at same pixel)
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Network Growth
geography represented as sq. grideach pixel has a pop. densitythe ASes are modeled as:
a set of locations (coordinates)
budgetset of links (to AS at same pixel)
queue
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Network Growth
geography represented as sq. grideach pixel has a pop. densitythe ASes are modeled as:
a set of locations (coordinates)
budget
capacity
set of links (to AS at same pixel)
queue
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Network Growth
geography represented as sq. grideach pixel has a pop. densitythe ASes are modeled as:
a set of locations (coordinates)
budget
capacity
set of links (to AS at same pixel)
queue
costs for: increasing capacityconnecting to other, adding loc.
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Network Growth
geography represented as sq. grideach pixel has a pop. densitythe ASes are modeled as:
a set of locations (coordinates)
budget
capacity
set of links (to AS at same pixel)
queue
costs for: increasing capacityconnecting to other, adding loc.income prop. to traffic
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Network Growth
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Network Growth
1. (while nwk too dense,) add ASes
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Network Growth
1. (while nwk too dense,) add ASes2. increase capacity as much as needed
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Network Growth
1. (while nwk too dense,) add ASes2. increase capacity as much as needed
3. link addition
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Network Growth
1. (while nwk too dense,) add ASes2. increase capacity as much as needed
3. link addition
connect unconnected pairs at random
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Network Growth
1. (while nwk too dense,) add ASes2. increase capacity as much as needed
3. link addition
connect unconnected pairs at random
(if both ASes can afford a connection)
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Network Growth
1. (while nwk too dense,) add ASes2. increase capacity as much as needed
3. link addition
connect unconnected pairs at random
(if both ASes can afford a connection)
4. spatial extension
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Network Growth
1. (while nwk too dense,) add ASes2. 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
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Network Growth
1. (while nwk too dense,) add ASes2. 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
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Traffic dynamics
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Traffic dynamics
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Traffic dynamics
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Traffic dynamics
s
t
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Traffic dynamics
s
t s
t
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Traffic dynamics
t = 1
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Traffic dynamics
t = 2
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Traffic dynamics
t = 3
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Time evolution
a
b
c
〈τ p〉,〈
d〉100
104
1
103
number of agents, nnumber of links, m
n,m
frac
tion
ofto
tal
0.25
0.5
0.75
0
covered populationcovered area
120 140 160 200180
120 140 160 200
time, τ
2
3
4
5
6
7〈d〉〈τp〉
100180 100001000time, τ number of ASs, n
8
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Degree distribution
1 10 100 1000 1 10 100 1000 1 100 100010k k k
10−4
10−3
0.01
0.1
1P
(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
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Degree distribution
10−5 10−6 10−4 10−31
10
104
104 105 106103
traffic load
degr
ee,k 100
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Radial statistics
0
0.1
0.2
our model
AS06 FKPBAfr
actio
nof
vert
ices
5 6 5 65 6 3 4 3 43 4average distance,d average distance,d average distance,d
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Radial statistics
3 4 3 43 4average distance,d average distance,d average distance,d
5 6 5 65 6
aver
age
degr
ee
1
10
102
103
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Traffic vs centrality
10−6 10−310−410−5 10−110−2
10−4
10−3
10−5
1 5 10 50
traffi
cde
nsity
,ρ
betweenness, CB ×104
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Geography
100 200 300population density (people per square mile)
0
t = 14λ = 6
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Geography
100 200 300population density (people per square mile)
0
λ = 15t = 23
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Geography
100 200 300population density (people per square mile)
0
t = 28λ = 69
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Geography
100 200 300population density (people per square mile)
0
λ = 272t = 28
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Geography
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Geography
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
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 oftraffic, geography and economy in the Internet. ComputerCommunication Review 32, 7–15 (2008).
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
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 oftraffic, geography and economy in the Internet. ComputerCommunication Review 32, 7–15 (2008).
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
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 oftraffic, geography and economy in the Internet. ComputerCommunication Review 32, 7–15 (2008).
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
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 oftraffic, geography and economy in the Internet. ComputerCommunication Review 32, 7–15 (2008).
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
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 oftraffic, geography and economy in the Internet. ComputerCommunication Review 32, 7–15 (2008).
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
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 oftraffic, geography and economy in the Internet. ComputerCommunication Review 32, 7–15 (2008).
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
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 oftraffic, geography and economy in the Internet. ComputerCommunication Review 32, 7–15 (2008).
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Other integrative mechanistic models
S. Shakkottai et al.. Evolution of the Internet Ecosystem.
S. Bar, M. Gonen & A. Wool. A geographic directedpreferential Internet topology model. Computer Networks51, 4174–4188 (2007).
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Other integrative mechanistic models
S. Shakkottai et al.. Evolution of the Internet Ecosystem.
S. Bar, M. Gonen & A. Wool. A geographic directedpreferential Internet topology model. Computer Networks51, 4174–4188 (2007).
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Other integrative mechanistic models
S. Shakkottai et al.. Evolution of the Internet Ecosystem.
S. Bar, M. Gonen & A. Wool. A geographic directedpreferential Internet topology model. Computer Networks51, 4174–4188 (2007).
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Future
Including economy.
Simple models.
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Future
Including economy.
Simple models.
Modeling theevolution ofthe AS-level
Internet:Integratingaspects of
traffic,geography
and economy
PETTERHOLME
Introduction
Our model
Numericalresults
Future
Including economy.
Simple models.