Jamming transition in traffic flow on triangular lattice

Phase transitions and critical phenomena are investigated in the two-dimensional traffic flow on the triangular lattice numerically and analytically. The two-dimensional traffic model on the square lattice is extended to the traffic flow on the triangular lattice where the three roads cross on a site. It is shown that the jamming transition between the freely moving and jammed phases depends on the configuration of car moving directions. It is found that the three distinct jamming transitions occur: the conventional jamming transition to the kink jams, the jamming transition to the chaotic jams, and the jamming transition to the oscillating jams. The conventional jamming transition to the kink jams is analyzed by the use of the linear stability theory and the nonlinear method. The coexisting curve between the freely moving and jammed phases is calculated from the solution of the modified Korteweg–de Vries (KdV) equation.