A methodology for identifying critical links and estimating macroscopic fundamental diagram in large-scale urban networks

The Macroscopic Fundamental Diagram (MFD), which exhibits the relationship between average flow and average density of an urban network, is a promising framework for monitoring and controlling urban traffic networks. Given that monitoring resources (e.g. loop detectors, probe vehicle data, etc.) are limited in real-world networks, acquiring adequate data to estimate an MFD is of crucial importance. This study presents a novel, network-wide approach to identifying critical links and estimating average traffic flow and density. The proposed model estimates the MFD using flow and density measurements from those critical links, which constitute only a small subset of all the links in the network. To find the critical links, we rely on historical probe vehicle data, and propose a model that builds on Principal Component Analysis (PCA), a dimensionality reduction and a feature selection method. Essentially, using PCA, a large number of possibly interrelated variables in a dataset can be reduced to a set of smaller uncorrelated variables, while maintaining as much information as possible in the dataset. The resulting uncorrelated variables, or the principal components, indicate the major patterns or the dominating features of the original dataset. Additionally, PCA enables the (approximate) reconstruction of the full-scale dataset from the selected features (or principal components). In this work, we apply PCA in order to identify the main traffic features from a probe vehicle dataset; then, we find the links that are associated with these features (i.e., critical links); then, we locate loop detectors on those links to collect flow and density data; and finally, we reconstruct the full-scale data, building on the PCA mechanism. This gives us the flow and density of all links, from which we can effectively estimate the MFD.