Universality, criticality and complexity of flight delay propagation

Passenger flight delay propagation of air transportation systems causes significant disruption to people’s daily lives, and many studies have therefore been conducted to understand the underlying mechanisms. However, whether the behaviors work near the criticality macroscopically and which specific delay propagation dynamics dominate microscopically still remain unclear. In this work, we investigate the statistical laws of bursty activity of delay propagation based on the historical records of the United States from 2004 to 2023. Our empirical results provide support for the process of delay propagation in real systems’ operating near a critical state. Furthermore, we firstly identify that the behaviors of Full Service Carriers (FSCs) and Low Cost Carriers (LCCs) may fall into the universality classes of complex and simple contagion, respectively. By analyzing the individual time series of airports microscopically together with the topological properties of delay propagation networks, we confirm that the propagation dynamics of flight delays are determined by the characteristics of network structures of airlines. The point-to-point (P2P) patterns of LCCs make sudden delays unable to be processed timely and thus easily propagate, which meets the scenario of simple contagion. While for FSCs, we find that the hub-and-spoke (HS) structures result in the simple contagion dynamics for hub airports and complex contagion for spoke airports, the complexity of which is empirically shown to originate from their ability of absorbing delays. Consequently, we identify an anti-reinforcement mechanism for the delay propagation behaviors of FSCs from empirical data. We believe that the general ideas presented here will stimulate further research on modeling flight delay propagation dynamics and contribute to solving practical problems in other fields.