Simulation Analysis and Model Modification of the LWR Traffic Flow Theory

The surge in urbanization and ensuing traffic congestion underscores the imperative for contemporary traffic flow control models. This paper explores the Lighthill-Whitham-Richards (LWR) theory in the macroscopic domain of traffic flow control. It evaluates the accuracy and mathematical logic of simulation performance of related models, namely Greenshields, Newell-Daganzo, Greenberg, Underwood, and California. This paper employs thorough simulations that utilize a holistic three-dimensional(3D) analysis based on time, location, and density. It provides a comprehensive comparison and discusses specific features of each model. Additionally, a modification to the macroscopic model is proposed. The modified model overcomes the shortcomings of performing well only in some specific short ranges and achieves a full range of application effects. The study offers valuable guidance for real-life scenario selections and applications in the traffic domain.