A multi-class non-local macroscopic model with time delay for mixed autonomous / human-driven traffic
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909457789747200 |
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| author | Ciaramaglia, Ilaria Goatin, Paola Puppo, Gabriella |
| author_facet | Ciaramaglia, Ilaria Goatin, Paola Puppo, Gabriella |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_09440 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A multi-class non-local macroscopic model with time delay for mixed autonomous / human-driven traffic Ciaramaglia, Ilaria Goatin, Paola Puppo, Gabriella Analysis of PDEs Numerical Analysis 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. |
| title | A multi-class non-local macroscopic model with time delay for mixed autonomous / human-driven traffic |
| topic | Analysis of PDEs Numerical Analysis |
| url | https://arxiv.org/abs/2501.09440 |