Discrete stochastic models for traffic flow

1994/12/09 by M. Schreckenberg, Michael Schreckenberg, A. Schadschneider +5 · 8 citations
Computer Science · Mathematics · Physics and Astronomy · #Cellular Automata and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat

paper · pdf · doi:10.1103/physreve.51.2939

Revtex, 30 pages, full postscript version (including figures) available by anonymous ftp from "fileserv1.mi.uni-koeln.de" in the directory "pub/incoming/" paper accepted for publication in Phys.Rev.E

arxiv created 1994/12/09 · openalex publication_date 1995/04/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate a probabilistic cellular automaton model which has been introduced recently. This model describes single-lane traffic flow on a ring and generalizes the asymmetric exclusion process models. We study the equilibrium properties and calculate the so-called fundamental diagrams (flow versus density) for parallel dynamics. This is done numerically by computer simulations of the model and by means of an improved mean-field approximation which takes into account short-range correlations. For cars with a maximum velocity of 1, the simplest nontrivial approximation gives the exact result. For higher velocities, the analytical results, obtained by iterated application of the approximation scheme, are in excellent agreement with the numerical simulations.

Citations

• Fast Low Fidelity Microsimulation of Vehicle Traffic on Supercomputers
• An exact solution of a one-dimensional asymmetric exclusion model with open boundaries

Cited by

• Nondeterministic Nagel-Schreckenberg traffic model with open boundary conditions
• Critical behavior of a traffic flow model
• A Vehicular Traffic Flow Model Based on a Stochastic Acceleration Process
• Simulation of pedestrian dynamics using a two-dimensional cellular automaton
• Flow properties of driven-diffusive lattice gases: Theory and computer simulation
• The effect of mixture lengths of vehicles on the traffic flow behaviour in one-dimensional cellular automaton
• Queuing transitions in the asymmetric simple exclusion process
• Fractal behind coin-reducing payment