Congested traffic patterns of lattice hydrodynamic model in a connected mixed traffic environment with overtaking effect

Abstract In the presence of Vehicle-to-everything (V2X) communication technologies, connected automated vehicles (CAVs) can extend the drivers’ perception ranges and obtain more abundant road vehicle information to regulate the vehicle status in real time. Nevertheless, promoting CAVs is a long process, and there will be both artificially human-driven vehicles (HDVs) and CAVs on the road during this transition era. Besides, as one of the basic microscopic driving behaviors, overtaking is relatively rare in the traffic flow model, especially in mixed-traffic environments. To fill this gap, we propose a novel heterogeneous traffic flow accounting for the HDVs and CAVs with passing effects from a macroscopic perspective. Subsequently, we conduct the linear stability analysis to determine the stability norm corresponding to the new model. When the above stability criterion is not established, we investigate the nonlinear phenomenon of the proposed model, and the modified Korteweg-de Vries (mKdV) equation and its existing conditions are obtained separately. When the overtaking ratio is adequately low such that the existence condition is met, the entire phase space consists of two parts, no jam and kink jam; when the passing ratio surpasses the threshold and the existence condition is not satisfied, the original unstable region can be further subdivided into kink jam sub-region and chaotic sub-region, and the density wave gradually evolved from kink-Bando traffic wave into the chaotic phase with the increasing of penetration rate. The results of the numerical examples verify the theoretical derivation.