2017/10/13 by Michaël Herty, Salissou Moutari, Herty, Michael +3 · 1 citation
Engineering · Social Sciences · #35L65 #35Q91 #90B20 #91B74 #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA) #Physics and Society (physics.soc-ph) #Traffic Prediction and Management Techniques #Traffic control and management #Transportation Planning and Optimization
paper · pdf · doi:10.48550/arxiv.1710.07209
openalex publication_date 2017/10/13 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
Lane changing is one of the most common maneuvers on motorways. Although,\nmacroscopic traffic models are well known for their suitability to describe\nfast moving crowded traffic, most of these models are generally developed in\none dimensional framework, henceforth lane changing behavior is somehow\nneglected. In this paper, we propose a macroscopic model, which accounts for\nlane-changing behavior on motorway, based on a two-dimensional extension of the\nAw and Rascle [Aw and Rascle, SIAM J.Appl.Math., 2000] and Zhang [Zhang,\nTransport.Res.B-Meth., 2002] macroscopic model for traffic flow. Under\nconditions, when lane changing maneuvers are no longer possible, the model\n"relaxes" to the one-dimensional Aw-Rascle-Zhang model. Following the same\napproach as in [Aw, Klar, Materne and Rascle, SIAM J.Appl.Math., 2002], we\nderive the two-dimensional macroscopic model through scaling of time\ndiscretization of a microscopic follow-the-leader model with driving direction.\nWe provide a detailed analysis of the space-time discretization of the proposed\nmacroscopic as well as an approximation of the solution to the associated\nRiemann problem. Furthermore, we illustrate some features of the proposed model\nthrough some numerical experiments.\n