Conference Paper

Exact solutions to traffic density estimation problems involving the Lighthill-Whitham-Richards traffic flow model using Mixed Integer Programming

DOI: 10.1109/ITSC.2012.6338639 Conference: 15th International IEEE Conference on Intelligent Transportation Systems

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.

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    • "For general convex or concave flux functions, the model constraints are mixed integer convex, and boil down to mixed integer linear inequalities for specific flux functions such as the triangular flux function [13] [14]. Since the constraints of the model are encoded in a tractable form, the resulting framework is very useful for solving a variety of transportation engineering problems: estimation [7], boundary control, model parameter estimation, which all result in optimization problems with mixed integer convex constraints. The same framework can be extended to study security and user privacy problems, which is the contribution of this article. "
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