{"id":643,"date":"2023-05-07T08:55:40","date_gmt":"2023-05-07T15:55:40","guid":{"rendered":"\/wp\/hades\/?p=643"},"modified":"2023-05-07T08:55:40","modified_gmt":"2023-05-07T15:55:40","slug":"nonlinear-coupled-systems-of-pdes-for-modeling-of-multi-lane-traffic-flow-problems","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2023\/05\/07\/nonlinear-coupled-systems-of-pdes-for-modeling-of-multi-lane-traffic-flow-problems\/","title":{"rendered":"Nonlinear Coupled Systems of PDEs for Modeling of Multi-Lane Traffic Flow Problems"},"content":{"rendered":"\n\t\t\t\t\n<p>The HADES seminar on Tuesday, <strong>May 9th<\/strong>\u00a0will be at\u00a0<strong>3:30 pm<\/strong>\u00a0in\u00a0<strong>Room 740<\/strong>.     <\/p>\n\n\n\n<p><strong>Speaker:<\/strong> Nadim Saad<\/p>\n\n\n\n<p><strong>Abstract:<\/strong> In this talk, first, we start with the traditional Lighthill-Whitham-Richards (LWR) model for unidirectional traffic on a single road and present a novel traffic model which incorporates realistic driver behaviors through a non-linear velocity function. We develop a particle-based traffic model to inform the choice of velocity functions for the PDE model. We incorporate various driver behaviors in the particle-based model to generate realistic velocity functions. We explore various impacts of numerous driving behaviors on different traffic situations using both the PDE model and the particle-based model, and compare the traffic distributions and throughput of cars on the road obtained by both models. Second, we extend the one-lane model to a multi-lane traffic model and incorporate source functions representing lanes exchanges. We derive desirable mathematical conditions for source functions to ensure $L^1$ contractivity for the system of PDEs. We build a multi-lane particle-based model to inform the choice of source functions for the PDE model. We study various driver behaviors in the particle-based model to develop realistic source functions. We explore various impacts of different driving scenarios using both models. <\/p>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday, May 9th\u00a0will be at\u00a03:30 pm\u00a0in\u00a0Room 740. Speaker: Nadim Saad Abstract: In this talk, first, we start with the traditional Lighthill-Whitham-Richards (LWR) model for unidirectional traffic on a single road and present a novel traffic model which incorporates realistic driver behaviors through a non-linear velocity function. We develop a particle-based traffic [&hellip;]<\/p>\n","protected":false},"author":88,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-643","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/643","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/users\/88"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=643"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/643\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=643"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=643"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=643"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}