Characterizing spatial distributions of urban systems using Voronoi diagrams and Lévy flights
A Voronoi diagram was constructed using the centroids of 2D buildings obtained from OpenStreetMap. From there, a novel and intuitive power law relation between the Voronoi polygon area and population enabled a high-resolution population dataset to be quickly estimated. The obtained population is then redistributed for a finite number of chosen locations in space. The chosen locations include schools, hospitals, fire stations, police stations, places of worship, and town halls. These simulate evacuation centers during an emergency scenario. Furthermore, we propose a model that potentially describes the generative mechanism for the heavy-tailed spatial distribution of buildings in urban areas. We used the theory of Lévy flights to model building agglomeration and we qualitatively compared the probability distributions of the synthetic data from the model with the actual building data.
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