Lattice models of the optimal traffic current

Abstract

Based on the lattice model of traffic flow, the lattice models which consider the next-nearest-neighbour flow on traffic and pay attention to the following vehicle as well as the preceding vehicle are presented, respectively. The stability criterion is derived by the linear stability analysis. The evolution of density wave has been investigated analytically with the perturbation method. The results show that the occurrence of traffic jamming transitions is described by the kink solution of the modified KdV equation. The theoretical results are in good agreement with the simulation. Moreover, the simulation indicates that the lattice models considering the next-nearest-neighbour interaction can stabilize the traffic flow, but the other model is just in opposition to the former model.

A traffic flow lattice model considering relative current influence and its numerical simulation

“…In comparison with Xue's model, [21] our extended model has a stable area that is enlarged obviously in the range…”

“…After that, Xue [21] improved the lattice version of traffic model by considering the next-nearestneighbour headway and described it as…”

Analysis of a Novel Two-Lane Hydrodynamic Lattice Model Accounting for Driver’s Aggressive Effect and Flow Difference Integral

“…Based on the lattice hydrodynamic model of Nagatani [13], many extended models are proposed to study the nonlinear phenomena in traffic flow under intelligent transportation environment. Xue [14] established a one-dimensional traffic flow lattice hydrodynamic model considering the interaction between the nearest neighbor and the next-nearest neighbor lattices. Using the linear stability theory, they deduced the neutral stability conditions of traffic flow and the mKdV equation describing the phase transition of traffic congestion by using the nonlinear analysis method.…”

The Korteweg-de Vires equation for the bidirectional pedestrian flow model considering the next-nearest-neighbor effect

“…Then, the author extended it to two-dimensional model such as BML model [13] in two-lane traffic flow, [14] to describe two-lane traffic flow. Considering the nearest-neighbor sites effect, Xue Yu proposed a new one-dimensional lattice model [15] in traffic flow. Based on it, Tian got a bidirectional model [16] and Xue got a pathchanging bidirectional model [17] in pedestrian flow.…”