Jamming transition in a two-dimensional traffic flow model

Phase transition and critical phenomenon are investigated in the two-dimensional traffic flow numerically and analytically. The one-dimensional lattice hydrodynamic model of traffic is extended to the two-dimensional traffic flow in which there are two types of cars (northbound and eastbound cars). It is shown that the phase transition among the freely moving phase, the coexisting phase, and the uniformly congested phase occurs below the critical point. Above the critical point, no phase transition occurs. The value $a_c$ of the critical point decreases as increasing fraction c of the eastbound cars for $c<~\mathrm{0.5.}$ The linear stability theory is applied. The neutral stability lines are found. The time-dependent Ginzburg-Landau (TDGL) equation is derived by the use of nonlinear analysis. The phase separation lines, the spinodal lines, and the critical point are calculated from the TDGL equation.