Scaling in the recovery of urban transportation systems from special events

Aleix Bassolas1,4, Riccardo Gallotti2, Fabio Lamanna1, Maxime Lenormand3 and José J. Ramasco1

1Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Palma de Mallorca, Spain.
2Fondazione Bruno Kessler, Via Sommarive 18, 38123 Povo (TN), Italy.
3Irstea, UMR TETIS, 500 rue JF Breton, 34093 Montpellier, France.
4School of Mathematical Sciences, Queen Mary University, Mile End Road, E1 4NS, London, United Kingdom.

(February 2020)

Public transportation is a fundamental infrastructure for life in cities. Although its capacity is prepared for daily demand, congestion may rise when huge crowds gather in demonstrations, concerts or sport events. In this work, we study the robustness of public transportation networks by means of a stylized model mimicking individual mobility through the system. We find scaling relations in the delay suffered by both event participants and other citizens doing their usual traveling in the background. The delay is a function of the number of participants and the event location. The model is solved analytically in lattices proving the existence of scaling relations and the connection of their exponents to the local dimension. Thereafter, extensive and systematic simulations in eight worldwide cities reveal that a newly proposed measure of local dimension explains the exponents found in the network recovery. Our methodology allows to dynamically probe the local dimensionality of a transportation network and identify the most vulnerable spots in cities for the celebration of massive events