The Fragile Nature of Road Transportation Systems
For traffic engineers and urban planners, this work provides a rigorous theoretical foundation for fragility in road networks and a practical metric, but it is incremental as it extends existing traffic flow theory.
This paper mathematically proves that road transportation systems are fragile, meaning performance loss grows exponentially with disruption magnitude, and proposes a skewness-based indicator to compare fragility across networks using macroscopic fundamental diagram parameters. Numerical simulations with real data confirm the theoretical findings.
Major cities worldwide experience problems with the performance of their road transportation systems, 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 increasing magnitude of disruptions. Meanwhile, the risk engineering community is embracing the novel concept of antifragility, enabling systems to learn from historical disruptions and exhibit improved performance under black swan events. In this study, based on established traffic models, namely fundamental diagrams and macroscopic fundamental diagrams, we first conducted a rigorous mathematical analysis to prove the fragile nature of the systems theoretically. 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. At last, by taking real-world stochasticity into account, we implemented a numerical simulation with realistic network data to bridge the gap between the theoretical proof and the real-world operations, to reflect the potential impact of uncertainty on the fragility of the systems. This work aims to demonstrate the fragile nature of road transportation systems and help researchers better comprehend the necessity to consider explicitly antifragile design for future traffic control strategies.