NeXtworking

1
Interacting Network Elements Chaos and
Congestion Propagation

• Gábor Vattay
• Department of Physics of Complex Systems1
• Eötvös University, Budapest, Hungary
• and
• Ericsson Telecommunication Hungary

2
Outline

• The more complex word of ad-hoc, mobile networks
  and p2p applications
• Complex system approach
• Pattern formation in traffic, congestion
• propagation
• Chaotic and non-linear dynamics

3
The new more complex word

• P2P traffic vs. web traffic ? hosts are more
  equal, core/access distinction is not that
  important
• Mobile, ad-hoc bandwidth is fully utilized
• Strong interaction

4
Complexity and non-linear research

• Complexity research deals with large number of
  strongly interacting systems, (IST-FET-Complexity)
  
• Chaos, fractals/scaling pattern formation,
  granular and vehicular traffic

5
Congestion propagation
6
Router-to-router congestion propagation
Fukuda Takayasu 1999
7
A congestion propagation model
Vattay, Steger, Vaderna 2003
8
Simulation results 10 queues, 10 TCP




9
50 queues, 1 TCP/queuedeffect propagation




10
10 queues, 5 TCP/queue, web traffic
11
1TCP/que with initial delay t_d
12
Measuring the speed of propagation center of
mass velocity
13
(No Transcript)
14
What causes congestion propagation?
1 TCP/queue (ns2)
Our fluid model using Baccelli-Hong (2002)
15
Only one assumption is needed packet loss is
more likely for a joining TCP flow at the router
16
Chaos
17
Simplest network model
18
Periodicity
Veres Boda INFOCOM 2000
19
Chaos
Veres Boda INFOCOM 2000
20
Ljapunov properties
Veres Boda INFOCOM 2000
21
Veres Boda INFOCOM 2000
22
3 TCPs with different round trip times
Vattay, Marodi, Steger 2002
23
Congestion window evolution
24
Poincarè surface of section
Symbols 1,2,3
25
Fractal dimension of the attractor
26
Symbol sequence probability
27
Topological entropy
28
Basin of attraction
29
2 TCPs surface of section
30
Topological entropy
31
Interaction of flows
32
Interacting traffic flows

• Traffic flows crossing the same bottleneck can
  inherit scaling properties from each other

33
Kenesi, Molnár, Veres, Vattay SIGCOMM 2000
34
Mode locking structure of adaptation
TCP
Bandwidth C
Background (UDP)
Buchta Vattay 2003