Refined macroscopic traffic modelling via systems of conservation laws

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dc.contributor.authorRichardson, Ashlin D.
dc.contributor.supervisorIllner, Reinhard
dc.date.accessioned2012-10-24T22:19:45Z
dc.date.available2012-10-24T22:19:45Z
dc.date.copyright2012en_US
dc.date.issued2012-10-24
dc.degree.departmentDepartment of Mathematics and Statistics
dc.degree.levelMaster of Science M.Sc.en_US
dc.description.abstractWe elaborate upon the Herty-Illner macroscopic traffic models which include special non-local forces. The first chapter presents these in relation to the traffic models of Aw-Rascle and Zhang, arguing that non-local forces are necessary for a realistic description of traffic. The second chapter considers travelling wave solutions for the Herty-Illner macroscopic models. The travelling wave ansatz for the braking scenario reveals a curiously implicit nonlinear functional differential equation, the jam equation, whose unknown is, at least to conventional tools, inextricably self-argumentative! Observing that analytic solution methods fail for the jam equation yet succeed for equations with similar coefficients raises a challenging problem of pure and applied mathematical interest. An unjam equation analogous to the jam equation explored by Illner and McGregor is derived. The third chapter outlines refinements for the Herty-Illner models. Numerics allow exploration of the refined model dynamics in a variety of realistic traffic situations, leading to a discussion of the broadened applicability conferred by the refinements: ultimately the prediction of stop-and-go waves. The conclusion asserts that all of the above contribute knowledge pertinent to traffic control for reduced congestion and ameliorated vehicular flow.en_US
dc.description.scholarlevelGraduateen_US
dc.identifier.urihttp://hdl.handle.net/1828/4304
dc.languageEnglisheng
dc.language.isoenen_US
dc.rights.tempAvailable to the World Wide Weben_US
dc.subjectPartial Differential Equationsen_US
dc.subjectTraffic Controlen_US
dc.subjectStop-And-Go Wavesen_US
dc.subjectFunctional-Differential Equationsen_US
dc.subjectTravelling Wavesen_US
dc.subjectSimulationen_US
dc.subjectSecond-Order Traffic Modelsen_US
dc.subjectNumerical Methodsen_US
dc.titleRefined macroscopic traffic modelling via systems of conservation lawsen_US
dc.typeThesisen_US

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