  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 $\gamma \approx {1/4}$.}
