Data-driven fundamental models for pedestrian movements

The focus of the thesis is the utilization of the data collected using state-of-the-art tracking technologies for the characterization and modeling of pedestrian movements. In this context, the main objectives are the development of (i) data-driven definitions of fundamental variables and (ii) data-inspired mathematical formulations of fundamental relationships characterizing pedestrian traffic. The motivation of this research comes from the analysis of a real dataset collected in the train station in Lausanne, Switzerland. To collect the raw data, a large-scale network of smart sensors has been deployed in the station. We consider this case study to illustrate and validate our methodology. The definitions of fundamental traffic variables (speed, density and flow), existing in the literature are extended through a data-driven discretization framework. The framework is based on spatio-temporal Voronoi diagrams, designed using pedestrian trajectory data. The new definitions are (i) independent from an arbitrarily chosen discretization, (ii) appropriate for the multi-directional composition of pedestrian traffic, (iii) able to reflect the heterogeneity of pedestrian population and (iv) applicable to pedestrian trajectories described either analytically or as a sample of points. The performance of the approach and its advantages are illustrated empirically. Our approach outperforms the existing methodologies from the literature, in terms of the smoothness of the results, and in terms of the robustness with respect to the simulation noise and sampling frequency. To represent fundamental relationships of pedestrian traffic, we introduce probabilistic speed-density models. The approach is motivated by the high scatter in the data that we have analyzed. To characterize the observed pattern we relax the homogeneity assumption of the equilibrium relationships, and propose two models. The first model is based on distributional assumptions. The second model is more advanced, and it includes structures that are designed to capture specific aspects of the walking behavior. Various empirical tests validate the specification of both models. Contrasted with existing approaches, they yield a more realistic representation of the empirically observed phenomena. This thesis contributes with respect to the utilization of data potential in modeling of fundamental aspects related to pedestrian traffic. This becomes essential in the context of the growing data revolution and interconnected technologies that can help improve the safety and convenience of pedestrians. The methodological framework is fairly general, and it can be adapted to various pedestrian facilities.

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