{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/computational-investigations-of-a-two-class","title":"Computational investigations of a multi-class traffic flow model: mean-field and microscopic dynamics","arxiv_id":"2306.13543","date":"2023-06-23","proceeding":null,"authors":["Amal Machtalay","Abderrahmane Habbal","Ahmed Ratnani","Imad Kissami"],"abstract":"We address a multi-class traffic model, for which we computationally assess the ability of mean-field games (MFGs) to yield approximate Nash equilibria for traffic flow games of intractable large finite-players. We introduce ad hoc numerical methodologies, with recourse to techniques such as High-Performance Computing (HPC) and regularization of Loose Generalized Minimal Residual (LGMRES) solvers. The developed apparatus allows us to perform simulations at significantly larger space and time discretization scales. For three generic scenarios of cars and trucks, and three cost functionals, we provide numerous numerical results related to the autonomous vehicles (AVs) traffic dynamics, which corroborate for the multi-class case the effectiveness of the approach emphasized in [22]. We additionally provide several original comparisons of macroscopic Nash mean-field speeds with their microscopic versions, allowing us to computationally validate the so-called $\\epsilon-$Nash approximation, with a rate slightly better than theoretically expected.","url_abs":"https://arxiv.org/abs/2306.13543v2","url_pdf":"https://arxiv.org/pdf/2306.13543v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"computational-investigations-of-a-two-class","repo_url":"https://github.com/amalmach/MFG_Traffic","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}