Topological informed optimization of car-sharing resources allocation

The goal of this thesis is analysing the mobility of the car-sharing vehicles over the city of Turin using Topological Data Analysis techniques in order to give useful information for the integration of an electric Free-Floating Car Sharing system. Specifically, since the main problem this infrastructure needs to face is the optimal placement of charging spots, the desired information consists of zones of the city in which the bookings concentrate the most. The first exploratory phase consists of analysing the data in order to extract mobility patterns between different days of the week or hours of the day. To begin, five different time slots have been individuated by considering the hours of the day that have a homogeneous number of bookings. This has been used to group the bookings per (weekday, time slot). Each group individuates a discrete probability distribution, and hence to obtain a notion of closeness between them the Wasserstein distance can be used. Then a hierarchical clustering algorithm has been applied and it revealed similarities between weekdays in the same time slot. It has also shown that Saturdays and Sundays are the days that differ the most with respect to the others. Then, before proceeding with the identification of the zones of interest, it has been an important understanding if a topological approach identified the same similarities. For this purpose, the hierarchical clustering algorithm has been repeated after having built on each of the aforesaid groupings of the data two filtrations of simplicial complexes, basic representations of a topological space: the Vietoris-Rips and the Alpha complexes. The result confirmed the first insight: the data shows a relevant pattern within the same time slot. Finally, the last step of the thesis consists of individuating the relevant zones of the city. From a topological point of view, the zones of interest are represented by cycles on the plane. The choice of those cycles is not trivial, but this problem has been solved through the concept of tight cycles that are the ones that individuate the "holes'' in a planar simplicial complex in the most accurate way. The results show that, as expected, the centre of the city is the most relevant zone. Analysing in more detail the results obtained for each pair (weekday, time slot) similarities within the same time slot are evident: between midnight and 5 a.m. the trips are spread across the whole city, in contrast in the hours 6 a.m.-10 a.m the bookings are more concentrated in the centre. Another relevant aspect to notice was that the airport in some hours of the day was a particularly relevant zone, indicating flights arriving or leaving from Turin. Finally, Saturdays and Sundays show different behaviours compared to working days. Topological informed optimization of car-sharing resources allocation