Anisotropic effect on two-dimensional cellular automaton traffic flow with periodic and open boundaries

TL;DR

This study uses computer simulations to explore how anisotropic direction-changing probabilities affect phase transitions and flow dynamics in two-dimensional cellular automaton traffic models with different boundary conditions.

Contribution

It reveals the impact of anisotropy on jamming transitions, phase diagram shapes, and density profiles, extending understanding of traffic flow behavior under various directional change probabilities.

Findings

First order jamming transition disappears with anisotropy.

The phase diagram's transition line curves under open boundaries.

Density profile decays with exponent approximately 1/4 in maximal current phase.

Abstract

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 ($p_{ur}$) and from right to up ($p_{ru}$), 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 ($p_{ur}\neq 0$ and/or $p_{ru}\neq 0$). 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 ($p_{ru}=p_{ur}=1$), 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 $\gamma \approx {1/4}$.}