The role of passing in a two-dimensional network

The phenomenon of passing on a two-dimensional network has been studied through lattice hydrodynamic approach. Near the critical point, the effect of passing is investigated theoretically and numerically. The modified Korteweg–de Vries equation near the critical point is derived using the reduction perturbation method through nonlinear analysis. Analytically, it is shown that for all possible configurations of vehicle, the stable region significantly reduces with an increase in the passing rate. It is shown that the jamming transition occurs among no jam to chaotic jam for any configuration of vehicles for larger rate of passing constant, while for smaller rate of passing, the jamming transitions occur from no jam to chaotic jam through kink jam for any configuration of vehicles. The results show that the modified model is able to explain the complex phenomena of traffic flow at a better level of accuracy than the most of the existing models. Simulation results are found consistent with the theoretical findings, which confirm that the passing plays a significant role in a two-dimensional traffic system.