Determining the macroscopic fundamental diagram from mixed and partial traffic data

The macroscopic fundamental diagram (MFD) is a graphical method used to characterize the traffic state in a road network and to monitor and evaluate the effect of traffic management. For the determination of an MFD, both traffic volumes and traffic densities are needed. This study introduces a methodology to determine an MFD using combined data from probe vehicles and loop detector counts. The probe vehicles in this study were taxis with GPS. The ratio of taxis in the total traffic was determined and used to convert taxi density to the density of all vehicles. This ratio changes over the day and between different links. We found evidence that the MFD was rather similar for days in the same year based on real data collected in Changsha, China. The difference between MFDs made of data from 2013 and 2015 reveals that the modification of traffic control can influence the MFD significantly. A macroscopic fundamental diagram could also be drawn for an area with incomplete data gained from a sample of loop detectors. An MFD based on incomplete data can also be used to monitor the emergence and disappearance of congestion, just as an MFD based on complete traffic data.