Theoretical approach to two-dimensional traffic flow models
Abstract
In this paper we present a theoretical analysis of a recently proposed two-dimensional Cellular Automata model for traffic flow in cities with the novel ingredient of turning capability. Numerical simulations of this model show that there is a transition between a freely moving phase with high velocity to a jammed state with low velocity. We study the dynamics of such a model starting with the microscopic evolution equation, which will serve as a basis for further analysis. It is shown that a kinetic approach, based on the Boltzmann assumption, is able to provide a reasonably good description of the jamming transition. We further introduce a space-time continuous phenomenological model leading to a couple of partial differential equations whose preliminary results agree rather well with the numerical simulations.
Cite
@article{arxiv.comp-gas/9406001,
title = {Theoretical approach to two-dimensional traffic flow models},
author = {J. M. Molera and F. C. Martinez and J. A. Cuesta and R. Brito},
journal= {arXiv preprint arXiv:comp-gas/9406001},
year = {2009}
}
Comments
15 pages, REVTeX 3.0, 7 uuencoded figures upon request to cuesta@ing.uc3m.es