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Internet topology dynamics in ten minutes
Sergey Kirgizov under the supervision of Clémence Magnien
Complex Networks ⊂ LIP6 ⊂ (UPMC × CNRS)
4 March 2014
Outline
1 What do we observe?
2 Why it is so important?
3 How do we study our observations?
2
What do we observe?
Internet IP-level topology
Nodes: IP addressesLinks: connections between hosts
Impossible to obtain a full map
3
Internet IP-level topology
Nodes: IP addressesLinks: connections between hosts
Impossible to obtain a full map
3
Ego-centered views
m
d1 d2
(shortest) paths between monitor and destinations
4
Ego-centered views
m
d1 d2
a measurement by tracetree
4
Ego-centered views
m
d1 d2
another measurement by tracetreeload-balancing
4
Ego-centered views
m
d1 d2
yet another measurement by tracetreeevolution of routes
4
Ego-centered view dynamics
m
d1 d2
m
d1 d2
m
d1 d2
Time
Fast periodic measurements =⇒ study of the dynamics
5
Why we should study this?
Some possible applications
• Develop a good model of the network• Security (unstable routes means more spyware?)• Robustness of the network and protocols• Event detection• Web caching• etc
6
Can we see the dynamics?
Evolution of symmetric difference betweenmeasurements (one destination)
m1 mi
Measurement is a set of IP-linksm1 : first measurementmi : i-th measurement
d (m1,mi ) = |m1 ∩mi |
2 4 6 8 10 12 14
05
1015
20
i
d(m
1,m
i)
(delay ≈ 1 min 30 sec)7
Evolution of symmetric difference betweenmeasurements (one destination)
m1 mi
Measurement is a set of IP-linksm1 : first measurementmi : i-th measurement
d (m1,mi ) = |m1 ∩mi |
2 4 6 8 10 12 14
05
1015
20
i
d(m
1,m
i)
(delay ≈ 1 min 30 sec)7
Evolution of symmetric difference betweenmeasurements (one destination)
m1 mi
Measurement is a set of IP-linksm1 : first measurementmi : i-th measurement
d (m1,mi ) = |m1 ∩mi |
2 4 6 8 10 12 14
05
1015
20
i
d(m
1,m
i)
(delay ≈ 1 min 30 sec)
Load-balancing
7
Evolution of symmetric difference betweenmeasurements (one destination)
m1 mi
Measurement is a set of IP-linksm1 : first measurementmi : i-th measurement
d (m1,mi ) = |m1 ∩mi |
2 4 6 8 10 12 14
05
1015
20
i
d(m
1,m
i)
(delay ≈ 1 min 30 sec)
Load-balancing
7
Evolution of symmetric difference betweenmeasurements (one destination)
m1 mi
Measurement is a set of IP-linksm1 : first measurementmi : i-th measurement
d (m1,mi ) = |m1 ∩mi |
2 4 6 8 10 12 14
05
1015
20
i
d(m
1,m
i)
(delay ≈ 1 min 30 sec)
Load-balancing
7
Evolution of symmetric difference betweenmeasurements (one destination)
m1 mi
Measurement is a set of IP-linksm1 : first measurementmi : i-th measurement
d (m1,mi ) = |m1 ∩mi |
2 4 6 8 10 12 14
05
1015
20
i
d(m
1,m
i)
(delay ≈ 1 min 30 sec)
Load-balancing
7
Evolution of symmetric difference betweenmeasurements (one destination)
m1 mi
Measurement is a set of IP-linksm1 : first measurementmi : i-th measurement
d (m1,mi ) = |m1 ∩mi |
2 4 6 8 10 12 14
05
1015
20
i
d(m
1,m
i)
(delay ≈ 1 min 30 sec)
Load-balancing
7
Evolution of symmetric difference betweenmeasurements (one destination)
m1 mi
Measurement is a set of IP-linksm1 : first measurementmi : i-th measurement
d (m1,mi ) = |m1 ∩mi |
2 4 6 8 10 12 14
05
1015
20
i
d(m
1,m
i)
(delay ≈ 1 min 30 sec)
Load-balancing
7
Evolution of symmetric difference betweenmeasurements (one destination)
m1 mi
Measurement is a set of IP-linksm1 : first measurementmi : i-th measurement
d (m1,mi ) = |m1 ∩mi |
2 4 6 8 10 12 14
05
1015
20
i
d(m
1,m
i)
(delay ≈ 1 min 30 sec)
Load-balancing
7
Evolution of symmetric difference betweenmeasurements (one destination)
m1 mi
Measurement is a set of IP-linksm1 : first measurementmi : i-th measurement
d (m1,mi ) = |m1 ∩mi |
2 4 6 8 10 12 14
05
1015
20
i
d(m
1,m
i)
(delay ≈ 1 min 30 sec)
Load-balancing
7
Evolution of symmetric difference betweenmeasurements (one destination)
m1 mi
Measurement is a set of IP-linksm1 : first measurementmi : i-th measurement
d (m1,mi ) = |m1 ∩mi |
2 4 6 8 10 12 14
05
1015
20
i
d(m
1,m
i)
(delay ≈ 1 min 30 sec)
Load-balancing
7
Evolution of symmetric difference betweenmeasurements (one destination)
m1 mi
Measurement is a set of IP-linksm1 : first measurementmi : i-th measurement
d (m1,mi ) = |m1 ∩mi |
2 4 6 8 10 12 14
05
1015
20
i
d(m
1,m
i)
(delay ≈ 1 min 30 sec)
Load-balancing
7
Evolution of symmetric difference betweenmeasurements (one destination)
m1 mi
Measurement is a set of IP-linksm1 : first measurementmi : i-th measurement
d (m1,mi ) = |m1 ∩mi |
2 4 6 8 10 12 14
05
1015
20
i
d(m
1,m
i)
(delay ≈ 1 min 30 sec)
Load-balancing
7
Evolution of symmetric difference betweenmeasurements (one destination)
m1 mi
Measurement is a set of IP-linksm1 : first measurementmi : i-th measurement
d (m1,mi ) = |m1 ∩mi |
2 4 6 8 10 12 14
05
1015
20
i
d(m
1,m
i)
(delay ≈ 1 min 30 sec)
Load-balancing
7
Evolution of symmetric difference betweenmeasurements (one destination)
m1 mi
Measurement is a set of IP-linksm1 : first measurementmi : i-th measurement
d (m1,mi ) = |m1 ∩mi |
2 4 6 8 10 12 14
05
1015
20
i
d(m
1,m
i)
(delay ≈ 1 min 30 sec)
Load-balancing
7
Evolution of symmetric difference betweenmeasurements (one destination)
m1 mi
Measurement is a set of IP-linksm1 : first measurementmi : i-th measurement
d (m1,mi ) = |m1 ∩mi |
5 10 15 20
05
1015
20
i
d(m
1,m
i)
(delay ≈ 1 min 30 sec)
Load-balancing
7
Evolution of symmetric difference betweenmeasurements (one destination)
m1 mi
Measurement is a set of IP-linksm1 : first measurementmi : i-th measurement
d (m1,mi ) = |m1 ∩mi |
0 10 20 30 40 50
05
1015
20
i
d(m
1,m
i)
(delay ≈ 1 min 30 sec)
Load-balancing
7
Evolution of symmetric difference betweenmeasurements (one destination)
m1 mi
Measurement is a set of IP-linksm1 : first measurementmi : i-th measurement
d (m1,mi ) = |m1 ∩mi |
0 20 40 60 80 100
05
1015
20
i
d(m
1,m
i)
(delay ≈ 1 min 30 sec)
Load-balancing
7
Evolution of symmetric difference betweenmeasurements (one destination)
m1 mi
Measurement is a set of IP-linksm1 : first measurementmi : i-th measurement
d (m1,mi ) = |m1 ∩mi |
0 200 400 600 800 1000
05
1015
20
i
d(m
1,m
i)
(delay ≈ 1 min 30 sec)
Load-balancing
7
Evolution of symmetric difference betweenmeasurements (one destination)
m1 mi
Measurement is a set of IP-linksm1 : first measurementmi : i-th measurement
d (m1,mi ) = |m1 ∩mi |
0 200 400 600 800 1000
05
1015
20
i
d(m
1,m
i)
(delay ≈ 1 min 30 sec)
Load-balancing
7
Evolution of symmetric difference betweenmeasurements (one destination)
m1 mi
Measurement is a set of IP-linksm1 : first measurementmi : i-th measurement
d (m1,mi ) = |m1 ∩mi |
0 50000 150000 250000
05
1015
20
i
d(m
1,m
i)
(delay ≈ 1 min 30 sec)
Evolution
7
Delay: 1 min 30 sec 3 min
1500
Destinations
0 1000 2000 3000
02
46
8
0 1000 2000 3000
040
080
0
0 1000 2000 3000 0 1000 2000 3000
Delay: 1 min 30 sec 3 min
1500
Destinations
0 1000 2000 3000
02
46
8
0 1000 2000 3000
040
080
0
0 1000 2000 3000 0 1000 2000 3000
Overview of problems and methods
observedevolution
number ofdestinations
frequencyof observations
?
Methods:• Real-world measurements• Simulated measurements using random graphs• Theoretical study of dynamic random graphs• Stochastic process estimation from partial observations
9