Modelling Time-varying Mobility Flows Using Function-on-Function Regression: Analysis of a Bike Sharing System in the City of Milan

Abstract

In today's world, bike sharing systems are becoming increasingly common in all main cities around the world. To understand the spatiotemporal patterns of how people move by bike through the city of Milan, we apply functional data analysis to study the flows of a bike sharing mobility network. We introduce a complete pipeline to properly analyse and model functional data through a concurrent functional‐on‐functional model taking into account the effects of weather conditions and calendar on the bike flows. In the end, we develop an interactive interface to explore the results of the analyses.

Conformal Prediction Bands for Multivariate Functional Data

“…In order to illustrate the application potential of the method presented in this article, in this section we focus on a case study concerning urban mobility, and specifically the usage of a bike-sharing system in the Italian city of Milan. Moving from the raw data and the context presented in Torti et al (2021), the aim is to study the behavior of subscribers of Bikemi, a bike sharing system active in the city in which bikes are picked up and dropped off in specific docking stations located through the city. Starting from raw data providing various information about picked up bikes (simply pickups hereafter) and dropped off bikes (simply dropoffs hereafter) for each day considered, and focusing our attention -as an example -on the Duomo district only (i.e.…”

“…In so doing, y i1 (t) (y i2 (t)) represents the dropoff (pickup) rate at time t, with t ranging from 7 a.m. day i to 1 a.m. the next day (consequently, we assume that day i ends at 1 a.m. the next day). The period considered starts on 25 January 2016 and ends on 6 March 2016: due to an error in the data collection, 25 February is removed from the dataset in accordance with Torti et al (2021), and so the sample size is n = 41. Data are shown in the two top panels of Figure 3.…”

“…Data are shown in the two top panels of Figure 3. Like in Torti et al (2021), the regression estimates are obtained by fitting a concurrent functional-on-functional linear model (Ramsay and Silverman 2005). The model hereby used includes as covariates a functional intercept, the temperature function (after subtracting the average daily temperature function of the period considered) in degrees Celsius, and a dummy variable indicating whether day i is a weekday or not.…”

Bridge closure in the road network of Lombardy: a spatio-temporal analysis of the socio-economic impacts

“…In this way, we are able to explicitly model the functional nature of the data (Bouveyron et al 2015) that would be lost with a simpler approach. Previous works on mobility data have already used FDA to model, for instance, the number of vehicles passing through a specific location (Chiou 2012; Guardiola et al 2014;Crawford et al 2017), or the bike sharing demand at different bike stations (Bouveyron et al 2015;Gervini and Khanal 2019); Torti et al 2021). Differently from other works, however, we mix motifs from FDA and network theory and we represent the road network of Lombardy as a graph evolving over time.…”