Kinetic derivation of Aw-Rascle-Zhang-type traffic models with driver-assist vehicles

TL;DR

This paper derives advanced traffic flow models from kinetic equations considering driver-assist vehicles, providing a physical basis for macroscopic models and demonstrating how these vehicles can improve traffic stability and flow.

Contribution

It introduces a kinetic derivation of Aw-Rascle-Zhang-type models incorporating driver-assist controls, linking microscopic strategies to macroscopic traffic dynamics.

Findings

Driver-assist vehicles lead to homogenized traffic flow.

Models justify the structure of hydrodynamic equations with control strategies.

Simulation shows potential for traffic stabilization and flow optimization.

Abstract

In this paper, we derive second order hydrodynamic traffic models from kinetic-controlled equations for driver-assist vehicles. At the vehicle level we take into account two main control strategies synthesising the action of adaptive cruise controls and cooperative adaptive cruise controls. The resulting macroscopic dynamics fulfil the anisotropy condition introduced in the celebrated Aw-Rascle-Zhang model. Unlike other models based on heuristic arguments, our approach unveils the main physical aspects behind frequently used hydrodynamic traffic models and justifies the structure of the resulting macroscopic equations incorporating driver-assist vehicles. Numerical insights show that the presence of driver-assist vehicles produces an aggregate homogenisation of the mean flow speed, which may also be steered towards a suitable desired speed in such a way that optimal flows and traffic stabilisation are reached.