Heuristic Approach Based on a K-Means Algorithm to Reduce the Cost of Macroscopic Fundamental Diagram Estimation

The macroscopic fundamental diagram (MFD) is a simple aggregate model useful for characterizing a network's operation. Constructing the MFD requires straightforward yet costly data collection, as it involves data not readily available in many places. This work proposes and validates a methodology for identifying a group of links in a network whose subsequent monitoring is sufficient to reasonably estimate its MFD. The proposed methodology uses traffic data available to any user with internet access and the K-means algorithm to identify clusters of links in the network and select the most representative for each cluster. Once these representative links are equipped with technology able to measure flows and densities, providing the reduced MFD for these links, the methodology proposes a heuristic to expand these values to construct the MFD for the entire network. The methodology is validated with simulated data. The MFD estimation errors obtained are comparable to those obtained with other similar methodologies reported in the literature. However, this methodology has the advantage of not requiring fixed sensors or a dedicated fleet of probe vehicles to identify a representative link, which is a crucial aspect in several cities. The proposed methodology is finally partially applied using real data from a zone of Santiago, Chile, yielding promising results in the clusters and representative links identified.