Analytical approaches to CA for traffic flow: Approximations and exact solutions
arXiv:cond-mat/9711296
Abstract
Cellular automata have turned out to be important tools for the simulation of traffic flow. They are designed for an efficient impletmentation on the computer, but hard to treat analytically. Here we discuss several approaches for an analytical description of the Nagel-Schreckenberg (NaSch) model and its variants. These methods yield the exact solution for the special case $\vm=1$ of the NaSch model and are good approximations for higher values of the velocity ($\vm > 1$). We discuss the validity of these approximations and the conclusions for the underlying physics that can be drawn from the success or failure of the approximation.
15 pages, 10 postscript figures, to be published in the Proceedings of the conference "Traffic and Granular Flow '97", Duisburg, Germany, October 5-8, 1997
References in corpus (9)
- Discrete stochastic models for traffic flow
- Cellular automaton models and traffic flow
- Traffic flow models with 'slow-to-start' rules
- Jamming transition in a cellular automaton model for traffic flow
- Car-oriented mean-field theory for traffic flow models
- Particle-hopping Models of Vehicular Traffic: Distributions of Distance Headways and Distance Between Jams
- Metastable States in CA models for Traffic Flow
- Disorder Effects in CA-Models for Traffic Flow
- Distributions of Time Headways in Particle-hopping Models of Vehicular Traffic