Comparison of the one-equation LWR models for density and for speed

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: Additional equations;    Aggregated traffics;    Continuity equations;    Continuous levels;    Macroscopic model;    One-equation model;    Road traffic flows;    Traffic parameters;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/421/2/022020/pdf
DOI  :  10.1088/1757-899X/421/2/022020

来源: IOP

【 摘 要 】

The macroscopic models describe road traffic flow without consideration of individual vehicles, but through aggregated traffic parameters, i.e. the flow rate, density and speed. The one-equation models are various LWR models that the most important component is the continuity equation. This equation must be supplemented by an additional equation that defines a specific relationship between two variables (traffic parameters), usually between speed and density. However, it is possible to eliminate one of those variables from the system, as a result of which the problem is limited only to one equation and one variable. In this article, two formulations of the one-equation LWR model will be considered, i.e. the density-dependent equation, and the speed-dependent equation. The question therefore arises, which of two formulations is more advantageous for a road traffic solution? Comparison of those two formulations of the LWR model is carried out only on a continuous level. Due to similar, quasi-linear form of both equations, the comparison has been carried out using their eigenvalues (characteristic speeds) for various static relationships between speed and density. Final evaluation of both one-equation formulations used spectral radiuses expressed as functions of the variables used in particular models.