A multi-class non-local macroscopic model with time delay for mixed autonomous / human-driven traffic

TL;DR

This paper develops a non-local macroscopic traffic model with time delay to analyze interactions between autonomous and human-driven vehicles, demonstrating improved traffic flow and stability through simulations.

Contribution

It introduces a new non-local conservation law model with time delay for mixed traffic, providing existence, uniqueness, and numerical validation.

Findings

Autonomous vehicles enhance overall traffic stability.

The model captures different reaction times and interaction ranges.

Numerical simulations confirm improved flow with autonomous vehicles.

Abstract

In this paper, we present a class of systems of non-local conservation laws in one space-dimension incorporating time delay, which can be used to investigate the interaction between autonomous and human-driven vehicles, each characterized by a different reaction time and interaction range. We construct approximate solutions using a Hilliges-Weidlich scheme and we provide uniform L $\infty$ and BV estimates which ensure the convergence of the scheme, thus obtaining existence of entropy weak solutions of bounded variation. Uniqueness follows from an L 1 stability result derived from the entropy condition. Additionally, we provide numerical simulations to illustrate applications to mixed autonomous / human-driven traffic flow modeling. In particular, we show that the presence of autonomous vehicles improves overall traffic flow and stability.