Multiscale control of generic second order traffic models by driver-assist vehicles

TL;DR

This paper derives a multiscale framework for controlling traffic flow using driver-assist vehicles, linking microscopic vehicle interactions to macroscopic traffic models and optimizing traffic trends through hierarchical control strategies.

Contribution

It introduces a novel multiscale approach to incorporate driver-assist vehicle controls into macroscopic traffic models via kinetic limits and demonstrates how to optimize traffic flow using this framework.

Findings

Control can optimize vehicle flux and reduce congestion.

Hierarchical control from microscopic to macroscopic improves traffic management.

Numerical simulations validate the effectiveness of the control strategy.

Abstract

We study the derivation of generic high order macroscopic traffic models from a follow-the-leader particle description via a kinetic approach. First, we recover a third order traffic model as the hydrodynamic limit of an Enskog-type kinetic equation. Next, we introduce in the vehicle interactions a binary control modelling the automatic feedback provided by driver-assist vehicles and we upscale such a new particle description by means of another Enskog-based hydrodynamic limit. The resulting macroscopic model is now a Generic Second Order Model (GSOM), which contains in turn a control term inherited from the microscopic interactions. We show that such a control may be chosen so as to optimise global traffic trends, such as the vehicle flux or the road congestion, constrained by the GSOM dynamics. By means of numerical simulations, we investigate the effect of this control hierarchy in some specific case studies, which exemplify the multiscale path from the vehicle-wise implementation of a driver-assist control to its optimal hydrodynamic design.