On the Fundamental Diagram for Freeway Traffic: Exploring the Lower Bound of the Fitting Error and Correcting the Generalized Linear Regression Models
Journal article, 2023

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.

90-10

linear regression

speed and density relationship

quadratic programming

Author

Yidan Shangguan

Hong Kong Polytechnic University

Xuecheng Tian

Hong Kong Polytechnic University

Sheng Jin

Zhejiang University

Kun Gao

Chalmers, Architecture and Civil Engineering, Geology and Geotechnics

Xiaosong Hu

Chongqing University

Wen Yi

Hong Kong Polytechnic University

Yu Guo

Hong Kong Polytechnic University

Shuaian Wang

Hong Kong Polytechnic University

MATHEMATICS

2227-7390 (eISSN)

Vol. 11 16 3460

Electric Multimodal Transport Systems for Enhancing Urban Accessibility and Connectivity (eMATS)

European Commission (EC), 2023-01-01 -- 2025-12-31.

Swedish Energy Agency (2023-00029), 2023-05-05 -- 2026-04-30.

Subject Categories

Transport Systems and Logistics

DOI

10.3390/math11163460

More information

Latest update

9/15/2023