Vattay Ne X tworking’03 June 23-25,2003, Chania, Crete, Greece The First COST-IST(EU)-NSF(USA)...

NeXtworking’03 June 23-25,2003, Chania, Crete, GreeceThe First COST-IST(EU)-NSF(USA) Workshop on EXCHANGES & TRENDS IN NETWORKING

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Interacting Network Elements: Chaos and Congestion Propagation

Gábor Vattay

Department of Physics of Complex Systems[1]

Eötvös University, Budapest, Hungary

Ericsson Telecommunication Hungary

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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

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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

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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…

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Congestion propagation

Fukuda &Takayasu 1999

Router-to-router congestion propagation

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A congestion propagation model

Vattay, Steger, Vaderna 2003

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Simulation results: 10 queues, 10 TCP

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50 queues, 1 TCP/queuedeffect propagation

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10 queues, 5 TCP/queue, web traffic

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1TCP/que with initial delay t_dt_d [ms] timespan 0-4000 sec

0 0.01 0.1 0.2 0.3 0.4 0.5 0.6

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Measuring the speed of propagation: center of mass velocity

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td[ms] Site/sec

0 -0.154421

.1 -0.140778

.2 -0.141784

.3 -0.120683

.4 -0.059653

.5 -0.103517

.6 -0.032555

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What causes congestion propagation?

1 TCP/queue (ns2) Our fluid model using Baccelli-Hong (2002)

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Only one assumption is needed: packet loss is more likely for a joining TCP

flow at the router

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Simplest network model

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Periodicity

Veres & Boda INFOCOM 2000

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Ljapunov properties

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3 TCPs with different round trip times

Vattay, Marodi, Steger 2002

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Congestion window evolution

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Poincarè surface of section

Symbols: 1,2,3

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Fractal dimension of the attractor

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Symbol sequence probability

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Topological entropy

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Basin of attraction

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2 TCPs surface of section

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Topological entropy

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Interaction of flows

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Interacting traffic flows

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

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Kenesi, Molnár, Veres, Vattay SIGCOMM 2000

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Mode locking structure of adaptation

Buchta & Vattay 2003

Background (UDP)

Bandwidth C

Vattay Ne X tworking’03 June 23-25,2003, Chania, Crete, Greece The First COST-IST(EU)-NSF(USA)...

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