On the conditioning of two-equation road traffic models

International Automotive Conference 2018

Maciejewski, M.^1

Wydzial Maszyn Roboczych i Transportu, Politechnika Poznaska, ul. Piotrowo 3, Poznan

60-965, Poland^1

关键词: Continuity equations;    Continuous levels;    Discretizations;    Effective solution;    Macroscopic traffic models;    Spectral condition number;    Traffic dynamics;    Two-equation model;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/421/2/022021/pdf
DOI  :  10.1088/1757-899X/421/2/022021

来源: IOP

【 摘 要 】

This article deals with two-equation macroscopic traffic models, which in addition to the standard continuity equation (the LWR model), contain an additional differential equation expressing the traffic dynamics, specifically the process of speed adaptation to road traffic conditions. There are many two-equation models with various forms of the traffic dynamics equation with different possibilities to achieve an accurate, stable and effective solution. The most popular models have been collected here and presented in a unified matrix form. The quality of particular two-equation traffic models, and thus the quality of the results obtained, depends on the quality of the model itself, and on the discretization and approximation of the problem. In this article, the evaluation of particular models is considered only on a continuous level, i.e. at the level of theoretical description of the models. Standard conditioning measures such as the spectral radius and the spectral condition number were used for this purpose. The results of the estimations have been used to compare particular models as well as to characterize two basic classes of models, i.e. isotropic (symmetrical) and anisotropic (asymmetric) models, and to evaluate the stability and potential computational efficiency of solutions of these two-equation models.