TY - GEN

T1 - Exact solutions to traffic density estimation problems involving the Lighthill-Whitham-Richards traffic flow model using mixed integer programming

AU - Canepa, Edward S.

AU - Claudel, Christian G.

N1 - KAUST Repository Item: Exported on 2020-10-01

PY - 2012/9

Y1 - 2012/9

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/564593

UR - http://ieeexplore.ieee.org/document/6338639/

UR - http://www.scopus.com/inward/record.url?scp=84871255228&partnerID=8YFLogxK

U2 - 10.1109/ITSC.2012.6338639

DO - 10.1109/ITSC.2012.6338639

M3 - Conference contribution

SN - 9781467330640

SP - 832

EP - 839

BT - 2012 15th International IEEE Conference on Intelligent Transportation Systems

PB - Institute of Electrical and Electronics Engineers (IEEE)

ER -