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

Using computer simulations we investigate, in a version of the Biham-Middleton-Levine model with random sequential update on a square lattice, the anisotropy effect of the probabilities of the change of the motion directions of cars, from up to right (p(ur)) and from right to up (p(ru)), on the dynamical jamming transition and velocities under periodic boundaries on one hand and the phase diagram under open boundaries on the other hand. However, in the former case, the sharp jamming transition appears only for p(ur)=0=p(ru)=0 (i.e., when the cars alter their motion directions). 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 expands as well as the contraction of the jamming and maximal current phases takes place. Moreover, in the anisotropic case, the transition between the jamming phase (or moving phase) and the maximal current phase is of second order while in the isotropic case, and when each car changes its direction of motion at every time step (p(ru)=p(ur)=1), the transition is of first order. Furthermore, in the maximal current phase, the density profile decays with an exponent gamma approximately 1/4.