Caminhos mínimos em cidades: padrões e características

Abstract

Understanding the dynamics of displacement of people in a city it is of fundamental importance for adequate and efficient planning in order to bring improvements to the population. It is a fact that the dynamics of commuters is driven by the way in which the population is spread in the city and also by the structural form of the city that is drawn over the years during its development. In this work, we perform a systematic study about the displacements carried out by users in different cities in different continents of our planet. Using a database, extracted from the Google-Maps application, we analyse the patterns of displacements considering several points of origin and destination randomly distributed in regions of cities such as Boston, Lisbon, Porto, São Francisco, Rio de Janeiro and São Paulo. In those cities, we investigate the patterns of displacements between origins and destinations base on two basic rules: minimal path and shorter time. We studied the distributions of transit time considering different distances between origin and destination, r = 1km, 2km and 3km. From this study, we found that those distributions follow a Log-normal distribution, independent of the city considered. We also found, that those distributions present a change when the distance between origins and destinations considered increases. In addition, we performed a study about which routes are most used, that is, we have calculated the betweenness centrality for the different cities based on the routes defined between the chosen points. We calculate the distribution of betweenness centrality for each city, according to the two criteria of minimum distance and minimum time and we verify that those distributions are power law followed by an exponential decay. This behaviour was invariant in terms of the established criteria and the city, although changes were observed in the power law exponents. We conclude the study, by presenting an analysis about the cities efficiency and the orientation of their streets network, in an attempt to explain the patterns in the behaviour observed for the displacements in those cities.