Fundamental diagram estimation using GPS trajectories of probe vehicles

A fundamental diagram (FD), which determine relation among flow, destiny, and speed of traffic, is one of the most important principles in traffic flow theory. Conventionally, the FD has been estimated by measurements from detectors which are fixed on roads. Therefore, it has been difficult to estimate FDs over wide spatial domain, due to high installation and maintenance cost of detectors. In this study, a method of estimating FD using measurements from GPS-equipped probe vehicles (also known as connected vehicles) is developed. Specifically, the proposed method estimate values of free-flow speed and backward wave speed of so-called triangular FD based on trajectories of multiple probe vehicles which are randomly sampled. Since probe vehicles can collect data from wide spatial domain, it can be expected that the proposed method enable to estimate FD continuously in large area. The proposed method was verified by using actual traffic data in an urban expressway.