Scaling in the recovery of urban transportation systems from special events

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.