Reproducible generation of experimental data sample for calibrating traffic flow fundamental diagram

Speed - density relationship, which is usually referred to as the traffic flow fundamental diagram, has been considered as the foundation of the traffic flow theory and transportation engineering. Speed - density relationship is the foundation of the traffic flow theory and transportation engineering, as it represents the mathematical relationship among the three fundamental parameters of traffic flow. It was long believed that single regime models could not well represent all traffic states ranging from free flow conditions to jam conditions until Qu et al. (2015) pointed out that the inaccuracy was not caused solely by their functional forms, but also by sample selection bias. They then applied a new calibration method (named as Qu-Wang-Zhang model hereafter) to address the sample selection bias. With this Qu-Wang-Zhang model, the result calibrated from observational data sample can consistently well represent all traffic states ranging from free flow conditions to traffic jam conditions. In the current paper, we use a fundamentally different approach that is able to yield very similar and consistent results with the Qu-Wang-Zhang model. The proposed approach firstly applies reproducible sample generation to convert the observational data to experimental data. The traditional least square method (LSM) can subsequently be applied to calibrate accurate traffic flow fundamental diagrams. Two reproducible sample generation approaches are proposed in this research. Based on our analyses, the first approach is somewhat affected by outliers and the second approach is more robust in dealing with potential outliers.