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arXiv · 2501.09440

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

Ilaria Ciaramaglia·Paola Goatin·Gabriella Puppo
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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.

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Ilaria Ciaramaglia, Paola Goatin, Gabriella Puppo. 2025-01-16. A multi-class non-local macroscopic model with time delay for mixed autonomous / human-driven traffic. https://arxiv.org/abs/2501.09440

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