Calibrating Fundamental Diagram based on Two Types of Speed-Density Data

Abstract

Speed – density relationship, which is usually referred to as the fundamental diagram, has been considered as the foundation of the traffic flow theory and transportation engineering. It has been long believed that single regime models could not well represent all traffic states ranging from free flow conditions to jam conditions. Qu et al. (2015; Transportation Research Part B, 73, 91-102) point out that the inaccuracy is not caused solely by their functional forms, but also by sample selection bias, and then apply a novel calibration approach to address the sample selection bias problem. In this technical note, we theoretically investigate how the functional forms of different models cope with the sample selection bias. A novel sampling approach is used to select uniform observational data (which would have the same characteristics with experimental data). With the selected uniform data, we can analyse the impact of functional forms themselves by eliminating the sample selection bias. As most speed – density models are derived from their corresponding car following models, we can use the aggregated macroscopic speed density data to evaluate the performance of microscopic car following models. In this way, we can establish the connection between macroscopic and microscopic traffic flow models.