Exact solutions to traffic density estimation problems involving the Lighthill-Whitham-Richards traffic flow model using mixed integer programming

Edward S. Canepa, Christian G. Claudel

Research output: Chapter in Book/Report/Conference proceedingConference contribution

22 Scopus citations

Abstract

This article presents a new mixed integer programming formulation of the traffic density estimation problem in highways modeled by the Lighthill Whitham Richards equation. We first present an equivalent formulation of the problem using an Hamilton-Jacobi equation. Then, using a semi-analytic formula, we show that the model constraints resulting from the Hamilton-Jacobi equation result in linear constraints, albeit with unknown integers. We then pose the problem of estimating the density at the initial time given incomplete and inaccurate traffic data as a Mixed Integer Program. We then present a numerical implementation of the method using experimental flow and probe data obtained during Mobile Century experiment. © 2012 IEEE.
Original languageEnglish (US)
Title of host publication2012 15th International IEEE Conference on Intelligent Transportation Systems
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Pages832-839
Number of pages8
ISBN (Print)9781467330640
DOIs
StatePublished - Sep 2012

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