To Investigate the Hidden Gap between Traffic Flow Fundamental Diagrams and the Derived Microscopic Car Following Models: A Theoretical Analysis

Traffic flow fundamental diagram, or simply speed–density relationship and/or flow–density relationship, is the basis of traffic flow theories and road performance studies since it depicts the mathematical relationship among three traffic flow fundamental parameters—density, speed, and traffic flow. In this paper, through mathematical analyses and simulations, we find that for all existing fundamental diagram models, their derived microscopic car following models do not perform well and cannot reproduce the status of the stable flow described by the corresponding fundamental diagrams. The results indicate that there seems to exist a hidden gap between existing traffic flow fundamental diagrams and the corresponding microscopic car following models. We further discuss about the fundamental causes behind such gap and propose a simple yet incomplete solution at the end of this paper