The fragile nature of road transportation networks

Major cities worldwide experience problems with the performance of their road transportation networks, and the continuous increase in traffic demand presents a substantial challenge to the optimal operation of urban road networks and the efficiency of traffic control strategies. The operation of transportation systems is widely considered to display fragile property, i.e., the loss in
performance increases exponentially with the linearly growing magnitude of disruptions. Meanwhile, the risk engineering community is embracing the novel concept of antifragility, enabling systems to learn from past events and exhibit improved performance under disruptions of previously unseen magnitudes. In this study, based on established traffic flow theory knowledge, namely the Macroscopic Fundamental Diagram (MFD), we first conduct a rigorous mathematical analysis to theoretically prove the fragile nature of road transportation networks. Subsequently, we propose a skewness-based indicator that can be readily applied to cross-compare the degree of fragility for different networks solely dependent on the MFD-related parameters. Finally, we implement a numerical simulation calibrated with real-world network data to bridge the gap between the theoretical proof and the practical operations, with results showing the reinforcing effect of higher-order statistics and stochasticity on the fragility of the networks. This work aims to demonstrate the fragile nature of road transportation networks and guide researchers towards adopting the methods of antifragile design for future networks and traffic control strategies.