A Road Traffic 'Behavioral Analysis': Mathematical Modeling and Numerical Simulation

摘要

This paper considers the mathematical modeling and numerical simulation of macroscopic traffic flow on a road segment (with finite length) subdivided into three sections. A set of coupled equations is obtained to express the temporal evolution of the fundamental parameters of traffic (i. e., density, speed, and flow) on each of the three sections of the road segment. A numerical simulation of the set of coupled equations is carried out in order to depict the possible states of traffic flow. Three main states of traffic are depicted namely, the state undersaturation, the state at saturation, and the state oversa-turation (ending to complete jam). The aforementioned traffic states are depicted through the plots of various 2D-fundamental diagrams expressing the mutual effects of "flow versus density", "speed versus flow", and "speed versus density". In order to validate the results obtained a benchmarking is considered, which consists of comparing the fundamental diagrams obtained (in this paper) with the fundamental diagrams provided by the classical and popular Greenshields models. The comparison shows a good agreement between the results.