Analysis and modeling of flight delays in air traffic systems

The increase of flight delays in recent years which resulted from the rapid development of the civil aviation industry have become a worldwide challenge in recent years. Thus, it is of great importance to understand the origin and mechanism of flight delays in the complex socio-technical air traffic systems, a problem that attracted much attention recently [1,2,3]. Here, we apply a comprehensive analysis of the delay distributions and propose a mathematical model that could help to improve the understanding of delay cascades and the accuracy of flight delay predictions.
Our analysis is based on the collection of flight information of departure and arrival delay in both China and USA from [4,5]. We analyzed the probability density distribution of times of flight delays. While earlier studies conducted a decade ago suggested a Normal distribution for the flight delays [2], our study suggests that a lognormal distribution is best fitted as seen in Figure 1(a) and (b).
We also find a strong memory effect between successive departure delays, using a lagged conditional PDF method as shown in Figure 1(c). This memory effect indicates that the lognormal distribution is a result of a multiplicative process of delays causing further delay. Thus, we develop a multiplicative process model with a multiplication factor from one step delay to the next delay in aircraft itinerary. The model simulations fit the data well as shown in Figure 1(d) and could explain the empirical lognormal distribution found here for flight delays.