From Random Walker to Vehicular Traffic: Motion on a Circle

  • Hans Weber
  • Reinhard Mahnke
  • Jevgenijs Kaupužs
Conference paper


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.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Hans Weber
    • 1
  • Reinhard Mahnke
    • 2
  • Jevgenijs Kaupužs
    • 3
    • 4
  1. 1.Department of PhysicsLuleå University of TechnologyLuleåSweden
  2. 2.Institute of PhysicsRostock UniversityRostockGermany
  3. 3.Institute of Mathematical Sciences and Information TechnologiesUniversity of LiepajaLiepajaLatvia
  4. 4.Institute of Mathematics and Computer ScienceUniversity of LatviaRigaLatvia

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