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From Random Walker to Vehicular Traffic: Motion on a Circle

In: Traffic and Granular Flow '13

Author

Listed:
  • Hans Weber

    (Luleå University of Technology, Department of Physics)

  • Reinhard Mahnke

    (Rostock University, Institute of Physics)

  • Jevgenijs Kaupužs

    (University of Liepaja, Institute of Mathematical Sciences and Information Technologies
    University of Latvia, Institute of Mathematics and Computer Science)

Abstract

Driving of cars on a highway is a complex process which can be described by deterministic and stochastic forces. It leads to equations of motion with asymmetric interaction and dissipation as well as to new energy flow law already presented at previous TRAFFIC AND GRANULAR FLOW meetings. Here we consider a model, where motion of an asymmetric random walker on a ring with periodic boundary conditions takes place. It is related to driven systems with active particles, energy input and depot. This simple model can be further developed towards more complicated ones, describing vehicular or pedestrian traffic. Three particular cases are considered, starting with discrete coordinate and time, then making time continuous and, finally, considering a drift–diffusion equation in a continuum limit.

Suggested Citation

  • Hans Weber & Reinhard Mahnke & Jevgenijs Kaupužs, 2015. "From Random Walker to Vehicular Traffic: Motion on a Circle," Springer Books, in: Mohcine Chraibi & Maik Boltes & Andreas Schadschneider & Armin Seyfried (ed.), Traffic and Granular Flow '13, edition 127, pages 347-359, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-10629-8_40
    DOI: 10.1007/978-3-319-10629-8_40
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