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Linking Cellular Automata and Optimal-Velocity Models Through Wave Selections at Bottlenecks

In: Traffic and Granular Flow’05

Author

Listed:
  • Peter Berg

    (University of Ontario Institute of Technology, Faculty of Science)

  • Justin Findlay

    (University of Ontario Institute of Technology, Faculty of Science)

Abstract

Summary A bottleneck simulation of road traffic on a loop, using the cellular automata Nagel-Schreckenberg model (with p = 0), reveals three types of stationary wave solutions. They consist of i) two shock waves at the bottleneck boundaries, ii) one shock wave at the boundary and one on the “open” road and iii) the trivial solution, i.e. homogeneous, uniform flow. These solutions are selected dynamically from a range of stationary wave solutions, similar in fashion to the wave selection in a bottleneck simulation of the optimal-velocity model. This is yet another indication that CA and OV models share certain underlying dynamics, although the former are discrete in space and time while the latter are continuous.

Suggested Citation

  • Peter Berg & Justin Findlay, 2007. "Linking Cellular Automata and Optimal-Velocity Models Through Wave Selections at Bottlenecks," Springer Books, in: Andreas Schadschneider & Thorsten Pöschel & Reinhart Kühne & Michael Schreckenberg & Dietrich E. Wol (ed.), Traffic and Granular Flow’05, pages 515-520, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-47641-2_48
    DOI: 10.1007/978-3-540-47641-2_48
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