Calibration of fundamental diagram using trajectories of probe vehicles: Basic formulation and heuristic algorithm

:A fundamental diagram (FD), also known as flow-density relation, is one of the most important principles in traffic flow theory. It would be valuable if an FD could be calibrated by using GPS-equipped probe vehicles; since they can continuously collect data from wide spatiotemporal area, compared to traditional fixed sensors. This paper proposes methods for calibrating an FD from trajectories of sampled vehicles. We formulate a method that identifies values of a free-flow speed and a critical density of a tri-angular FD, while it relies on exogenous assumptions on FD's functional form and a value of its jam density. Then, a heuristic algorithm for FD calibration in actual traffic environment is developed based on the proposed method. It was validated using traffic data generated by microscopic traffic simulator. The results suggested that the proposed methods can calibrate an FD precisely and robustly. It implies that FDs in road sections on which congestion happens frequently can be calibrated using probe vehicles, if probe vehicle data were collected for a long period. Therefore, the proposed methods would contribute to significant improvement of applicability of probe vehicle-based traffic management methods.