Estimation of Macroscopic Fundamental Diagram Solely From Probe Vehicle Trajectories With an Unknown Penetration Rate

The Macroscopic Fundamental Diagram (MFD) is a parsimonious modelling tool for monitoring and controlling urban traffic networks. MFD can be derived based on traffic data (empirical or simulation), or approximated analytically. Deriving the MFD based on traffic data is rather challenging due to difficulties in acquiring adequate data in large-scale urban networks. Previous studies have attempted to estimate the MFD based on probe vehicle trajectories assuming an a priori penetration rate, which is unlikely to be known in reality. This assumption was relaxed in other studies incorporating loop detector observations which provide the total number of vehicles on the links. The present study aims to estimate the MFDs using only probe vehicle trajectories where the probe penetration rate is not known a priori nor constant over time and space. Our approach relies on queue lengths at signalised intersections that can be inferred from probe vehicle positions. Considering the number of probe vehicles in a given cycle and the queue length inferred from probe vehicle positions, a penetration rate can be estimated for each approach of signalised intersections. We also define neighborhood penetration rates to account for spatial variability of the penetration rate as well as to estimate the penetration rate of links that are not connected to signalized intersections.