Analysis of Traffic Jerk Effect in a New Lattice Model with Density-Dependent Passing

In real traffic dynamics, non-motor vehicles often undergo sudden acceleration changes while passing, leading to traffic congestion on roads. Thus, a lattice model is modified to examine the impact of traffic jerk, taking into account the density-dependent passing behavior. The linear stability analysis is performed. It is found that the stability region reduces considerably with an increasing traffic jerk coefficient. By the reduction perturbation method, the kink-antikink soliton wave solution of the mKdV equation is attained, which describes the propagation of the density wave near the critical point. The theoretical results are validated by numerical simulation.