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Optimization and phase transitions in a chaotic model of data traffic M. Woolf,1,2
 

Summary: Optimization and phase transitions in a chaotic model of data traffic
M. Woolf,1,2
D. K. Arrowsmith,1
R. J. MondragoŽn-C,2
and J. M. Pitts2
1
Mathematics Research Centre, Queen Mary, University of London, London E1 4NS, United Kingdom
2
Department of Electronic Engineering, Queen Mary, University of London, London E1 4NS, United Kingdom
Received 30 January 2002; revised manuscript received 3 May 2002; published 10 October 2002
Ohira and Sawatari Phys. Rev E 58, 193 1998 introduced a simple model for a packet-switching network
which was extended by SoleŽ and Valverde Physica A 289, 595 2001 . Both models used Poisson-like traffic
sources. SoleŽ and Valverde demonstrated that long-range dependence LRD in autocorrelation behavior can be
seen in the queue length dynamics at a given node. Actual network traffic sources are known to exhibit
long-range autocorrelation. To simulate the real case more closely, we have studied the effect of introducing
LRD behavior at an earlier stage. We replaced the Poisson-like sources with LRD sources, modeled using
chaotic maps. As was seen in the previous models, a phase transition occurs as the traffic load on a network is
increased and the network changes to a congested state where the time taken for delivery of packets increases
dramatically and throughput collapses. The paper reports extensive numerical results from our simulations
using both Poisson and LRD sources. It demonstrates the natural network-induced LRD when sources are

  

Source: Arrowsmith, David - School of Mathematical Sciences, Queen Mary, University of London

 

Collections: Mathematics