Point-Process Modeling and Divergence Measures Applied to the Characterization of Passenger Flow Patterns of a Metro System

The problem of characterizing the passengers’ movement in a public transport system has
been considered in the literature for analysis, simulation and optimization purposes. In particular, origindestination matrices are commonly used to describe the total number of passengers that travel between two
points during a given time interval. In this paper, we propose to model the instantaneous rate of arrival
of passengers for the origin-destination pairs of a metro system using point processes. More specifically,
we apply the Expectation-Maximization algorithm to estimate the parameters of a Gaussian mixture intensity
function for the daily flow of passengers using data from multiple days provided by EFE Valparaíso. The
uncertainty in the parameter estimates is quantified computing standard errors and confidence intervals.
Secondly, we quantitatively analyze the similarity of the obtained intensity functions among the different
origin-destination pairs. In particular, we propose a dissimilarity index based on the Kullback-Leibler
divergence and we apply this index in hierarchical agglomerative and partitioning methods to cluster origindestination pairs with similar daily flow of passengers. The obtained numerical results confirm expert
knowledge about the passengers’ behavior in EFE Valparaíso metro system and, more interestingly, provide
additional insights on the passengers’ behaviour for specific origin-destination pairs.