A multi-class kinetic traffic flow model: discrete-velocity formulation and diffusively-corrected macroscopic limits

[2608.27159] A multi-class kinetic traffic flow model: discrete-velocity formulation and diffusively-corrected macroscopic limits Skip to main content Search Submit Donate Log in Mathematics > Numerical Analysis arXiv:2608.27159 (math) [Submitted on 27 Aug 2026 ( v1 ), last revised 28 Aug 2026 (this version, v2)] Title: A multi-class kinetic traffic flow model: discrete-velocity formulation and diffusively-corrected macroscopic limits Authors: Carmen Mezquita-Nieto , Paola Goatin , Axel Klar View PDF HTML (experimental) Abstract: This paper introduces a multi-class extension of a discrete-velocity kinetic traffic flow model based on a non-local Prigogine-Herman framework. We derive a hyperbolically scaled system of equations from a continuous kinetic formulation describing interactions between different vehicle classes through braking and relaxation terms. The model is then discretized with respect to the velocity variable for an arbitrary number of vehicle classes, and the structural properties of the resulting formulation are analyzed. In particular, we prove hyperbolicity and total linear degeneracy. Due to the non-conservative structure of the model, we employ a path-conservative finite volume scheme for the numerical approximation of the system. Finally, we derive the corresponding diffusively-corrected macroscopic multi-class model, investigate its stability and present numerical simulations on a single-lane road to illustrate the theoretical findings. Comments: 28 pages, 9 figures Subjects: Numerical Analysis (math.NA) ; Analysis of PDEs (math.AP) Cite as: arXiv:2608.27159 [math.NA] (or arXiv:2608.27159v2 [math.NA] for this version) https://doi.org/10.48550/arXiv.2608.27159 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Carmen Mezquita-Nieto [ view email ] [v1] Thu, 27 Aug 2026 14:11:08 UTC (2,021 KB) [v2] Fri, 28 Aug 2026 09:36:01 UTC (2,021 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.NA < prev | next > new | recent | 2026-08 Change to browse by: cs cs.NA math math.AP References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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