Fast L2 Calibration for Inexact Highway Traffic Flow Systems

Transportation systems need more accurate predictions to further optimize traffic network design with the development and application of autonomous driving technology. In this article, we focus on highway traffic flow systems that are often simulated by the modified Greenshields model. However, this model can not perfectly match the true traffic flow due to its underlying simplifications and assumptions, implying that it is inexact. Specifically, some parameters affect the simulation accuracy of the modified Greenshields model, while tuning these parameters to improve the model's accuracy is called model calibration. The parameters obtained using the L-2 calibration have the advantages of high accuracy and small variance for an inexact model. However, the method is calculation intensive, requiring optimization of the integral loss function. Since traffic flow data are often massive, this paper proposes a fast L-2 calibration framework to calibrate the modified Greenshields model. Specifically, the suggested method selects a sub-design containing more information on the calibration parameters, and then the empirical loss function obtained from the optimal sub-design is utilized to approximate the integral loss function. A case study highlights that the proposed method preserves the advantages of L-2 calibration and significantly reduces the running time.