Kinetic-controlled hydrodynamics for traffic models with driver-assist vehicles

TL;DR

This paper introduces a hierarchical framework combining microscopic control strategies and kinetic equations to improve traffic flow safety with driver-assist vehicles, validated through numerical simulations.

Contribution

It develops a novel multiscale modeling approach integrating microscopic vehicle controls into macroscopic traffic models using kinetic theory.

Findings

Microscopic control strategies effectively reduce road risk factors.

Hydrodynamic models incorporating controls match kinetic model predictions.

Numerical examples demonstrate improved traffic safety and flow efficiency.

Abstract

We develop a hierarchical description of traffic flow control by means of driver-assist vehicles aimed at the mitigation of speed-dependent road risk factors. Microscopic feedback control strategies are designed at the level of vehicle-to-vehicle interactions and then upscaled to the global flow via a kinetic approach based on a Boltzmann-type equation. Then first and second order hydrodynamic traffic models, which naturally embed the microscopic control strategies, are consistently derived from the kinetic-controlled framework via suitable closure methods. Several numerical examples illustrate the effectiveness of such a hierarchical approach at the various scales.