Jamming transition of high-dimensional traffic dynamics

Phase transition and critical phenomenon are investigated in high-dimensional traffic flow numerically and analytically. The two-dimensional lattice traffic model is extended to the three- and d-dimensional traffic flows. 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 in the two-, three-, and four-dimensional traffic simulations. The phase separation line and the critical point of the d-dimensional traffic are consistent with those of the one-dimensional traffic. The time-dependent Ginzburg–Landau (TDGL) equation for the d-dimensional traffic is derived by the use of the nonlinear analysis. The phase separation line, the spinodal line, and the critical point are calculated from the TDGL equation. It is found that the phase transition and critical phenomenon are independent of the space dimension.