Statistical Characterization of Airplane Delays

Before the COVID-19 pandemic, a major source of annoyance for international travelers was flight delays, caused by anything from engineering failures to simple traffic flow issues through the complex network of international airports. As a statistical phenomenon, such delays have been the focus of considerable prior research looking at both the expected delays and the distribution of extreme outliers, although many such studies have proceeded by assuming simple underlying forms for the probability distribution of delays.
In a recent paper, LML External Fellow Rosemary Harris and colleagues go beyond previous research to examine the entire probability density function from an empirical point of view, including both delayed flights and also flights with negative delays, i.e. flights arriving significantly earlier than scheduled. The researchers base their analysis on new data collected from 2018 to 2020 at several UK airports, making a particular focus on Heathrow, this being the most important international hub in the UK. This new data contains tens of thousands of flights, aggregated over multiple months, and therefore reflects a significant improvement on earlier studies which only investigated a couple thousand flights, thereby greatly underestimating the contribution of the tails to the probability distribution.
Harris and her colleagues’ analysis indicates that all investigated airports – as well as individual airlines at each airport – follow a qualitatively similar distribution, with an approximately exponential decay on the left flank of negative delays and a slowly decaying power law on the right flank of positive delays. The researchers found that the power law of large positive delays can be linked to a superposition of exponential delays with a varying decay parameter. In contrast, negative delays or early arrivals do not exhibit any power laws but simply behave in an exponential way, with extremely early arrivals being exponentially unlikely. The research also revealed that the global COVID-19 pandemic had an interesting effect on the delay statistics, lowering the mean delay. Given the lesser burden of fewer flights, it appears, the existing infrastructure performs much better in some respects.
The paper is available at

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