4 research outputs found
Phase Transitions in Two-Dimensional Traffic Flow Models
We introduce two simple two-dimensional lattice models to study traffic flow
in cities. We have found that a few basic elements give rise to the
characteristic phase diagram of a first-order phase transition from a freely
moving phase to a jammed state, with a critical point. The jammed phase
presents new transitions corresponding to structural transformations of the
jam. We discuss their relevance in the infinite size limit.Comment: RevTeX 3.0 file. Figures available upon request to e-address
[email protected] (or 'dopico' or 'molera' or 'anxo', same node
Theoretical approach to two-dimensional traffic flow models
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.Comment: 15 pages, REVTeX 3.0, 7 uuencoded figures upon request to
[email protected]
Anisotropic effect on two-dimensional cellular automaton traffic flow with periodic and open boundaries
By the use of computer simulations we investigate, in the cellular automaton
of two-dimensional traffic flow, the anisotropic effect of the probabilities of
the change of the move directions of cars, from up to right () and from
right to up (), on the dynamical jamming transition and velocities
under the periodic boundary conditions in one hand and the phase diagram under
the open boundary conditions in the other hand. However, in the former case,
the first order jamming transition disappears when the cars alter their
directions of move ( and/or ). In the open boundary
conditions, it is found that the first order line transition between jamming
and moving phases is curved. Hence, by increasing the anisotropy, the moving
phase region expand as well as the contraction of the jamming phase one.
Moreover, in the isotropic case, and when each car changes its direction of
move every time steps (), the transition from the jamming
phase (or moving phase) to the maximal current one is of first order.
Furthermore, the density profile decays, in the maximal current phase, with an
exponent .}Comment: 13 pages, 22 figure