Traffic flow-density models based on systems theory

This paper presents the derivation of macroscopic speed-density and flow-density relations based on the statistic average behaviors of microscopic driver-vehicle cells. The microscopic model for a single vehicle introduces a systemic approach of the human in the loop represented by a cascade control structure. When in a constrained situation, by the presence of other vehicles, the distance regulation performed by the human driver is proposed to have a proportional-derivative action, not integral, which results in a tracking error that is linearly dependent with speed. This relation is the base for the speed-density curve for each vehicle. The paper presents a methodology, based on statistic data of road usage, to build the fundamental diagram for traffic control developments.