Kinetic theory derivation of a second-order continuum viscous traffic model for vehicles with adaptive cruise control system

In this paper we propose a second-order continuum viscous traffic model for vehicles equipped with adaptive cruise control (ACC) system. The model is derived from the Paveri–Fontana kinetic traffic equation, incorporating a follow-the-leader formulation to capture the ACC typical behavior. The traffic pressure arising from a Maxwellian iteration procedure is proportional to the velocity gradient which results in a viscous term not present in previous work. Additionally, we have incorporated to our model a density dependent response coefficient of the ACC system which plays a crucial role to improve traffic stability. We compute the model characteristic speeds and compare them with those of manually driven vehicles. Both, the stability analysis and the numerical simulations under prescribed initial conditions have indicated that the introduction of ACC systems in real traffic should have a positive effect on stabilizing traffic flow, with the ACC relaxation time playing a crucial role.