Scaling in the recovery of urban transportation systems from massive events

Abstract

Public transportation is a fundamental infrastructure for the daily mobility in cities. Although its capacity is prepared for the usual demand, congestion may rise when huge crowds concentrate in special events such as massive demonstrations, concerts or sport events. In this work, we study the resilience and recovery of public transportation networks from massive gatherings by means of a stylized model mimicking the mobility of individuals through the multilayer transportation network. We focus on the delays produced by the congestion in the trips of both event participants and of other citizens doing their usual traveling in the background. Our model can be solved analytically for regular lattices showing that the average delay scales with the number of event participants with an exponent equal to the inverse of the lattice dimension. We then switch to real transportation networks of eight worldwide cities, and observe that there is a whole range of exponents depending on where the event is located. These exponents are distributed around 1/2, which indicates that most of the local structure of the network is two dimensional. Yet, some of the exponents are below (above) that value, implying a local dimension higher (lower) than 2 as a consequence of the multimodality and multifractality of transportation networks. In fact, these exponents can be also obtained from the scaling of the capacity with the distance from the event. Overall, 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.

Empirical dynamics of railway delay propagation identified during the large-scale Rastatt disruption

“…Exponential scaling models or epidemic spreading models could be further extended to include the observed performance-depending vulnerability effects. Simulation 51 , 52 or optimization models 53 need to bridge the large gap between detail and complexity of microscopic and macroscopic studies, which we only scratched in this study 54 .…”

First-Passage Times to Quantify and Compare Structural Correlations and Heterogeneity in Complex Systems

“…Although being a relatively simple and intuitive tool, random walks have been extensively and successfully used to model and characterise transportation [48,49], biological [50,51], and financial systems [52]. They have proven useful to detect meaningful structural properties in complex networks [53,54], including communities [55][56][57], node roles [58], navigability [59], and temporal variability [60].…”

First-passage times to quantify and compare structural correlations and heterogeneity in complex systems

“…Although being a relatively simple and intuitive tool, random walks have been extensively and successfully used to model and characterise transportation [50,51], biological [52,53], and financial systems [54]. They have proven useful to detect meaningful structural properties in complex networks [14,55], including communities [56][57][58], node roles [59], navigability [60], and temporal variability [61].…”