The jamming transition of multi-lane lattice hydrodynamic model with passing effect

Abstract

Multi-lane environments are not uncommon on the highway. In multi-lane scenarios, vehicles can not only switch freely between lanes but also overtake each other. However, as basic driving behavior, the passing effect under multi-lane environments has been neglected in traffic flow research. To fill this gap, we present a modified multi-lane lattice hydrodynamic model considering the passing effect. Based on the reduction perturbation method, the corresponding stability norm of the proposed model is obtained, which reveals that the total number of lanes is positively correlated with the stability of traffic flow. When the stability condition does not hold, to further examine the formation and transmission process of traffic jams near the neutral stability curve, we carry out a nonlinear stability analysis of the model. The modified Korteweg-de Vries (mKdV) equation and the existence of the above mKdV equation are deduced, respectively. When the passing ratio is sufficiently small, i.e., the above existence holds, we observe that the jamming transition emerges between uniform flow and kink jam; once the passing ratio exceeds the threshold, the jamming transition occurs among uniform flow and kink-Bando traffic wave through the chaotic phase. We also conduct numerical simulations to verify the theoretical derivation.