On the Fundamental Diagram for Freeway Traffic: Exploring the Lower Bound of the Fitting Error and Correcting the Generalized Linear Regression Models

Yidan Shangguan, Xuecheng Tian (), Sheng Jin, Kun Gao, Xiaosong Hu, Wen Yi, Yu Guo and Shuaian Wang
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Yidan Shangguan: Department of Logistics and Maritime Studies, Faculty of Business, The Hong Kong Polytechnic University, Hung Hom, Hong Kong
Xuecheng Tian: Department of Logistics and Maritime Studies, Faculty of Business, The Hong Kong Polytechnic University, Hung Hom, Hong Kong
Sheng Jin: College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China
Kun Gao: Department of Architecture and Civil Engineering, Chalmers University of Technology, 412 96 Göteborg, Sweden
Xiaosong Hu: State Key Laboratory of Mechanical Transmission/Automotive Collaborative Innovation Center, Chongqing University, Chongqing 400044, China
Wen Yi: Department of Building and Real Estate, The Hong Kong Polytechnic University, Hung Hom, Hong Kong
Yu Guo: Department of Logistics and Maritime Studies, Faculty of Business, The Hong Kong Polytechnic University, Hung Hom, Hong Kong
Shuaian Wang: Department of Logistics and Maritime Studies, Faculty of Business, The Hong Kong Polytechnic University, Hung Hom, Hong Kong

Mathematics, 2023, vol. 11, issue 16, 1-15

Abstract: In traffic flow, the relationship between speed and density exhibits decreasing monotonicity and continuity, which is characterized by various models such as the Greenshields and Greenberg models. However, some existing models, i.e., the Underwood and Northwestern models, introduce bias by incorrectly utilizing linear regression for parameter calibration. Furthermore, the lower bound of the fitting errors for all these models remains unknown. To address above issues, this study first proves the bias associated with using linear regression in handling the Underwood and Northwestern models and corrects it, resulting in a significantly lower mean squared error (MSE). Second, a quadratic programming model is developed to obtain the lower bound of the MSE for these existing models. The relative gaps between the MSEs of existing models and the lower bound indicate that the existing models still have a lot of potential for improvement.

Keywords: speed and density relationship; linear regression; quadratic programming (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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