Heterogeneous lattice hydrodynamic model and jamming transition mixed with connected vehicles and human-driven vehicles

As communication and perception technologies develop, connected vehicles (CVs) advance rapidly. In the process of popularization of CVs, it is bound to lead to the coexistence of CVs and human-driven vehicles (HDVs) on the road network for some time to come, and the previous study assumes that road vehicle is homogeneous, which could not quantify the difference between mixed vehicular flow, based on this, we consider the differences between CAVs and CVs in the way of information acquisition, a heterogeneous lattice hydrodynamics model mixing the HDVs and CVs are presented. Subsequently, by using the small perturbation method, we analyze the linear stability of the proposed model and derive the corresponding stability criteria; when the above stability norm does not hold, in order to investigate the nonlinear phenomenon, nonlinear stability analysis is performed and a modified Korteweg-de Vries equation (mKdV) corresponding to the proposed model is derived. By solving the mKdV equation, we obtain the kink-antikink solitary wave solution which can be used to explain how traffic jams form and propagate. At last, several numerical simulations were conducted to test the impact of the penetration rate of CVs and the bi-directional visual field for both forward-looking and backward-looking on the heterogeneous traffic flow stability, i.e., the first two are positive, while the last is negligible, this conclusion is consistent with the conclusion of theoretical derivation.& COPY; 2023 Elsevier B.V. All rights reserved.