Braess's Paradox of Traffic Networks and Spatial Complication of Urban Systems

  • 1. Department of Geography, Peking University, Beijing, 100871;
    2. College of Urban and Environmental Science, Northeast Normal University, Changchun, Jilin 130024

Received date: 2005-08-01

  Revised date: 2006-06-13

  Online published: 2006-11-20


One of the important projects of spatial complexity science is spatial complication, which needs concrete and substaintial researches by means of effective methods. The paradox of traffic assignment problems is taken as an example to show how a system of cities and towns become complicate with the passage of time. Planning theory, graph theory, and differential dynamics, and so on, are employed to analyze the Braess’s paradox of traffic network, and new mathematical models are built in the process of geographical analyses based on the Braess’s network that is symmetric in macro-level. After new expressway is added in the network, two changes appear: one is macro-symmetry breaking of Braess’s network, and the other is spatial interaction between vehicle flows of different communication lines. Spatial interaction is associated with time lag and feedback what always give rise to non-linearity, while symmetry breaking implies spatial order breaking and reconstruction. A conclusion is drawn that spatial interaction and macro symmetry breaking are two dynamic factors activating spatial complication of self-organizing network of cities and towns.

Cite this article

CHEN Yan-Guang, LIU Ji-Sheng . Braess's Paradox of Traffic Networks and Spatial Complication of Urban Systems[J]. SCIENTIA GEOGRAPHICA SINICA, 2006 , 26(6) : 658 -663 . DOI: 10.13249/j.cnki.sgs.2006.06.658


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