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

Abstract

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, origin-destination 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 origin-destination 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.

Keywords

• Expectation-maximization
• cluster analysis
• Kullback-Leibler divergence
• public transport