Effect of malicious cyber-attack on jamming transition in a multi-phase mixed flow model under regular vehicles and connected vehicles environment

With the promotion of policies and technological progress, accelerate the advancement of Internet of Vehicles (IOVs) and refine it considerably, and then the real-time communication of vehicle-vehicle, vehicle-infrastructure and vehicle cloud will be realized, which will provide more abundant data for connected vehicles (CVs); however, the large-scale popularization of the vehicle was a drawn-out procedure, and regular vehicles (RVs) and connected vehicles will share road infrastructure within this duration. Aiming at the significant distinctions in exogenous information acquisition mode between the two types of vehicles, and considering that the latter is vulnerable to cyber-attacks from hackers when it plays the advantage of information sharing in an open workshop communication environment. Motivation by this, we extended the optimal velocity car-following model and provided an original mixed-flow model accounting for the malicious cyber-attack effect, moreover, introducing a multi-phase optimal velocity function to describe the discontinuous acceleration phenomenon in real traffic. In the linear stability analysis part, we employ the reductive perturbation approaches to figure out the stability requirement for the new model, which reveals that the permeability of CVs and the intensity of cyber-attacks have a substantial influence on the traffic dynamics, and the number of phases of transition stages highly dependent on the count of the turning points in the optimal velocity function; subsequently, in the nonlinear analysis part, the modified Korteweg-de Vries (mKdV) equation is developed to illustrate the emerge and spatiotemporal progression of traffic jams when stability criteria is not achieved. At last, the above theoretical arguments are supported by the numerical simulation results.