Velocity Statistics of the Nagel-Schreckenberg Model

Nicolas Bain 1 Thorsten Emig 1, 2 Franz-Joseph Ulm 3 Michael Schreckenberg 4

Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2016, 93, pp.022305

The statistics of velocities in the cellular automaton model of Nagel and Schreckenberg for traffic are studied. From numerical simulations, we obtain the probability distribution function (PDF) for vehicle velocities and the velocity-velocity (vv) correlation function. We identify the probability to find a standing vehicle as a potential order parameter that signals nicely the transition between free congested flow for sufficiently large number of velocity states. Our results for the vv correlation function resemble features of a second order phase transition. We develop a 3-body approximation that allows us to relate the PDFs for velocities and headways. Using this relation, an approximation to the velocity PDF is obtained from the headway PDF observed in simulations. We find a remarkable agreement between this approximation and the velocity PDF obtained from simulations.

  • 1. Massachussetts Institute of Technology
  • 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
  • 3. Department of Civil and Environmental Engineering
  • 4. Universität Duisburg-Essen [Essen]