Macroscopic traffic flow modeling with adaptive cruise control: Development and numerical solution

• A novel macroscopic modeling approach for Adaptive Cruise Control (ACC) in traffic flow dynamics.
• The proposed model is incorporated to a gas-kinetic (GKT) traffic flow model.
• A comparison with an alternative approach from the literature is performed.
• A high-resolution relaxation finite volume discretization (in space and time) is implemented.

The incorporation of two macroscopic approaches reflecting Adaptive Cruise Control (ACC) and Cooperative Adaptive Cruise Control (CACC) traffic dynamics in a gas-kinetic (GKT) traffic flow model is presented. The first approach was recently analyzed in the literature aiming to describe the effects induced by the ACC and CACC systems due to changes of the speed of the leading car(s) by the introduction of an acceleration/deceleration term. The second approach is a novel one and is based on the introduction of a relaxation term that satisfies the time/space-gap principle of ACC or CACC systems. In both approaches, the relaxation time is assigned on multiple leading vehicles in the CACC case; whereas in the ACC case this relaxation time is only assigned to the direct leading vehicle. We numerically approximate the resulting models by an accurate and robust high-resolution finite volume relaxation scheme, where the nonlinear system of partial differential equations is first recast to a diagonalizable semi-linear system and is then discretized by a higher-order WENO scheme. Numerical simulations investigate the effect of the different ACC and CACC approaches to traffic flow macroscopic stability with respect to perturbations introduced in a ring road and to flow characteristics in open freeways with merging flows at an on-ramp. Following from the numerical results, it can be concluded that CACC vehicles increase the stabilization of traffic flow, with respect to both small and large perturbations, compared to ACC ones. Further, the proposed CACC approach can better improve the dynamic equilibrium capacity and traffic dynamics, especially at the on-ramp bottleneck.