Probabilistic speed-density relationship for pedestrians based on data driven space and time representation

This paper proposes a mathematical framework that provides the detailed characterization of the pedestrian flow. It is specifically designed to address the heterogeneity of pedestrian population which is to be reflected through the pedestrian flow indicators. The key components of the presented work are: (i) data driven space discretization framework based on the Voronoi tessellations that allow pedestrian-oriented definition of density indicator; (ii) statistical and data driven approach to time aggregation, allowing for the pedestrian oriented definition of speed indicator; (iii) probabilistic model for speed-density relationship, so as to capture the empirically observed heterogeneity among pedestrians. The estimation and validation of the proposed model are performed on the basis of a pedestrian tracking input. Data is collected in a Lausanne railway station where a large-scale network of cameras has been installed to automatically locate and track thousands of pedestrians. Additionally, the performance provided by this methodology is compared with the well-accepted models published in the literature against empirical data with the aim at improving research on the pedestrian flow characterization.