Data fusion for estimating Macroscopic Fundamental Diagram in large-scale urban networks

Since the concept of the Macroscopic Fundamental Diagram (MFD) has been introduced, many studies have investigated the existence and characteristics of the MFD using empirical and simulation data. MFD is a powerful and efficient model for monitoring and managing largescale urban networks. However, estimating the MFD for large-scale networks faces important challenges; monitoring resources are often limited in such networks. Furthermore, common sensors that are used to collect traffic data (i.e., loop detectors and probe vehicles), have limitations of their own. For instance, loop detectors are fixed sensors and cannot provide accurate density measurements. On the other hand, to estimate the MFD using probe vehicle data, the probe penetration rate must be known a priori. Given that the individual sensors cannot provide complete and accurate traffic measurements, combining the traffic data from multiple sources may improve the estimation of the MFD. The aim of this study is to combine two traffic data sources to estimate the MFD for a large-scale urban network, where the distribution of probe vehicles across the network is not necessarily homogeneous. The two traffic data sets used in this study are probe vehicle data with an unknown penetration rate, and fullscale approximate traffic data which is produced based on loop detector data. We compare the results of the fusion method with the results of a baseline method, which only uses loop detector measurements. The average flow and density estimations resulting from the Bayesian fusion method outperform the baseline method. We observe a particularly significant improvement in average density estimations, which reaffirms that loop detectors cannot accurately measure the average density.