Exact solutions to traffic density estimation problems involving the Lighthill-Whitham-Richards traffic flow model using mixed integer programming
KAUST DepartmentElectrical Engineering Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Distributed Sensing Systems Laboratory (DSS)
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AbstractThis 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.
Conference/Event name2012 15th International IEEE Conference on Intelligent Transportation Systems, ITSC 2012