Scaling invariance in domestic passenger flight delays in the United States

Flight delays in passenger air transportation systems may cause numerous troubles to people's daily life. Empirical works show that at the microscopic level there exist differ-ent kinds of inter-correlations, while at the macroscopic level the complex system obeys a simple law similar with that for gases. The constructed theoretical models are not consistent with each other, leading to some debates. How the macroscopic law emerges from the detailed cross-correlations is an open question. And an empirical benchmark to end the debates is also required. In the present work, the cosine correlations between airports for three kinds of flight delays are calculated, the relationships of which versus delay time can be re-scaled by the average number of flights H per month to a universal scaling relation, (Cos theta lambda⟩Hp = f lambda ((T lambda⟩Hq), where p and q are exponents. Hence, the system can work in two kinds of critical phases, namely, the stable phases in the durations from 1995 to 2000 and from 2005 to 2019, and the transition phases in the durations from 2001 to 2004 and within the year 2020. The results provide an empirical benchmark for building models.(c) 2023 Elsevier B.V. All rights reserved.

Automated summary

Flight delays in passenger air transportation systems can cause various troubles to people's daily life. Empirical studies show different inter-correlations at the microscopic level, and a simple law similar to that for gases at the macroscopic level. Inconsistent theoretical models have led to debates, and the emergence of macroscopic law from detailed cross-correlations is an open question. An empirical benchmark is needed to settle the debates.