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

Questions?

http://kirgizov.complexnetworks.fr/