1. Introduction
Air transport demand has been increasing continuously before the coronavirus pandemic. The number of flights performed in mainland China by passenger airlines reached 4.611 million in 2019, which is 6.1% higher than the previous year. The on-time performance has been improved as well. The punctuality in 2019 is 81.65%, while the average flight delay is 14 min per flight [
1]. Although the coronavirus pandemic has brought a huge impact on the air transport industry, it is foreseen that air traffic would recover quickly when the pandemic ends. Nevertheless, air transport demand at most busy airports will exceed airport capacity due to slow improvement in airport capacity. Thus, demand and capacity management is still one of the most important issues in the air transportation field.
Slot allocation is an effective means of airport demand-capacity management [
2,
3]. A slot is defined as the right given to an air carrier to use all the infrastructure and services within the airport at a specific date and time. The slot coordinator or slot coordination department will allocate slots to the airlines under the guidance of certain rules given airlines’ slot requests and the declared capacity of the airport. The Worldwide Airport Slot Guidelines (WASG) issued by the International Air Transport Association (IATA) is a fundamental regulatory reference for most countries. The slot allocation process takes place twice a year, namely the summer season and the winter season [
4]. The summer season starts on the last Saturday in March of the calendar year, and it ends on the Saturday before the last Sunday in October of the following year, while the winter season is from the Saturday before the last Sunday of October of the calendar year to the last Sunday of March of the following year. Airlines generate flight schedules based on the allocated slots to provide air transport services to customers. The flight schedule, which is up to several months prior to the day of the flight operation, is mainly based on the allocated airport slots. This flight schedule submitted by the airline after the slot allocation is also known as the strategic flight schedule. The strategic flight schedule is generally in the form of a series of scheduled arrival and departure operations. For example, flight CA1365 is scheduled to operate at 4 p.m. every day from Monday to Sunday, taking off from Beijing Capital International Airport (IATA code: PEK) and landing at Guangzhou Baiyun International Airport (IATA code: CAN), using the Airbus A330 aircraft.
Much research effort has been devoted to the optimization of slot allocation, which generally aims to minimize displacements to airline’s slot requests [
5]. In [
2], the authors present an extensive review of the current slot allocation models and practices. They classified the models into two categories: single airport slot allocation optimization model and network-wide slot allocation optimization model. A single airport slot allocation optimization model, with the goal of minimizing the displacements between the airlines’ slot requests, is developed in [
3]. The testing results at several airports in Europe show that fewer interventions could achieve the optimal allocation of slots with such an optimization model. In practice, airlines have to obtain at least one departure slot at the origin airport and one landing slot at the destination airport to operate a flight. Sometimes, an airline may have to negotiate with other airlines or slot coordinators to swap/adjust the allocated slot to match the origin airport slot. An integer linear programming model is developed in [
6] to study slot allocation at all airports in Europe, considering all the constraints in a single slot allocation model as well as flying time constraints. Both single airport slot allocation and network-wide slot allocation ensure that the number of scheduled flights per unit of time does not exceed the airport declared capacity. There would be no delay if the flights departed or arrived at their scheduled slots. However, flights often experience arrival/departure delays during the day of the operation due to uncertainties such as weather, aircraft maintenance, and passengers. The currently published strategic flight schedules do not provide information on the potential flight delays that may occur.
Over the past years, there are extensive studies on flight delays from various perspectives, including modeling and measuring delay propagation [
7,
8,
9,
10] and predicting flight delays [
11,
12,
13,
14]. Of particular interest is predicting flight delays using machine learning techniques. A recent study [
15] presents a review of flight delay prediction works. The commonly investigated methods include decision tree, Bayesian learning, neural networks, support vector machines, and random forest [
16,
17,
18]. One group of studies aims to predict the values of flight delay. For instance, a reinforcement learning algorithm is developed to predict the average airport delay time. The algorithm is tested with data from the New York John F. Kennedy Airport (JFK). The results show that if the accuracy is set within the ±5 min range, the prediction accuracy can achieve 60% approximately [
19]. To account for the importance of weather in affecting flight delays, a prediction model that estimates airport delays using data from weather forecast products is developed in [
20]. In [
21], the authors propose a random forest algorithm to predict flight departure delay in the air traffic network. The most delayed network connections (i.e., origin–destination airport pair) are selected for testing. The results show that the average regression test error achieves 19% for a 2 h prediction horizon with a 60 min delay threshold. The second group of studies aims to predict the levels of flight delays. This group of studies is also known as delay classification prediction. For example, the authors uses recurrent neural networks to classify delays at several airports [
16]. The performance of the model at the network level would be enhanced if one uses a deeper network architecture. The work in [
17] combines the multi-label random forest classification algorithm and the approximate delay propagation model to improve the prediction performance.
Although machine learning methods are extensively used in flight delay prediction, most of the works focus on short-range flight delay prediction, from a few hours to a few days (see
Figure 1). The common purpose of predicting tactical/pre-tactical flight delays is to support the preparation and implementation of traffic flow management initiatives, such as Ground Delay Programs, Mile-In-Trail restrictions, etc. Little work has been conducted to predict flight delay at the strategic stage. Of course, the needs for predicting flight delays at the strategic level are different from the former two. One possible application of strategic flight delay prediction is to assess the quality of flight schedule. Airlines and airports may need that information to develop strategic plans for preparing their resources in reaction to severe flight delays. For example, additional staff would be scheduled in a particular time because those frequent long-time flight delays were predicted. An urgent need for strategic flight delay prediction is the setting of airport declared capacity. As discussed above, great efforts have been devoted to optimizing slot allocation under the assumption that the airport declared capacity is determined (i.e., how flights can be scheduled in one time unit). In fact, setting airport declared capacity is challenging due to unresolved issues [
22]. Setting a higher declared capacity can schedule more flights, but it may result in frequent flight delays because of low operation capacity. Setting lower declared capacity can provide high on-time performance, but it may waste scarce airport capacity. The prediction of flight delays at the strategic level can provide support to decision makers to choose airport declared capacity.
We note that the work in [
23] develops a machine learning approach to predict flight delays and cancellations in the strategic phase (6 months prior to the day of the operation) using features from the strategic flight schedule. The machine learning algorithms, LightGBM, multilayer perceptron (MLP), and random forest (RF), were tested with the data from London Heathrow Airport. Among many input features of the model, the arrival Air Traffic Flow Management (ATFM) delay deserves further debate. ATFM delay is defined as “the duration between the last Estimated Take-Off Time (ETOT) and the Calculated Take-Off Time (CTOT) allocated by the Network Manager” [
24]. Thus, predicting flight delay requires calculating the CTOT, which is estimated from software (Network Manager). As expected, the overall prediction accuracy varies between 0.75 and 0.79 depending on the machine learning algorithms. The recall is around 0.5. Predicting the status of a flight several months in advance is indeed challenging.
Almost all the above-mentioned work aims to predict the deterministic status of flight delay, which is either given by the value of flight delay or by the status of delay (on-time, delayed, cancelled). In contrast, Zoutendijk and Mitici [
25] develops a machine learning method, using mixture density networks and random forest regression to predict probabilistic individual flight delays. The estimated distribution of flight delays was integrated into a flight-to-gate assignment model. The results show that integrating probabilistic delay prediction into the flight-to-gate assignment problem can significantly improve the robustness of the solution.
In [
23], the authors develop classification algorithms for flight delay prediction. However, simply predicting whether a strategic flight has an arrival/departure delay is only a rough reflection of the strategic flight’s performance. So, we convert the strategic flight delays prediction problem into a forecasting problem. Forecasting strategic flight delays is a huge challenge in the strategic phase because it occurs long before the day of the execution. To improve the robustness of the forecasting algorithms, we focus on the prediction of the distribution for flight delay. To the best of our knowledge, in this paper, we address for the first time the prediction distributions of strategic flight delays. Taken together, we propose a machine learning-based approach to predict distributions of strategic flight delays. Specifically, we propose supervised machine learning algorithms to predict distributions of flight delays scheduled in the strategic phase (several months prior to the day of operation). Three evaluation metrics are proposed to measure the prediction results. We demonstrate the performance of our approach using flight schedule data from Guangzhou Baiyun International Airport in the period 2017–2019.
The structure of this paper is organized as follows.
Section 2 describes the data used in this paper.
Section 3 introduces the features engineering and machine learning algorithms. Three metrics are proposed to evaluate the prediction results.
Section 4 compares the performance of algorithms.
Section 5 summarizes the contributions of this paper and provides outlines for future research.
2. Data
The scheduled flights data of Guangzhou Baiyun International Airport (ICAO code: ZGGG) were used in this study. The data contain six strategic flight schedules covering all the flights operated from 26 March 2017 to 28 March 2020. An example of scheduled flights from the data is shown in
Table 1. Every scheduled flight has the following information: flightID, aircraft type, origin airport, destination airport, Estimated Time of Departure (ETD), Estimated Time of Arrival (ETA), and days of the week. Days of the week shows which days of the week the strategic flight will be executed. For example, “123....” means that the strategic flight will be executed on Monday, Tuesday, and Wednesday each week. The Actual Time of Departure (ATD) and Actual Time Arrival (ATA) of a scheduled flight are recorded if the flight was operated. A flight is said to be delayed if it departs (arrives) more than 15 min after the scheduled time of departure (arrival). A departure (arrival) flight is considered to be cancelled if this flight is not executed in the day scheduled to depart (arrive). Due to the limitation of the data, we do not consider cancellation in this work.
According to the regulations of Federal Aviation Administration (FAA) and the Civil Aviation Administration of China (CAAC), a flight is considered to be cancelled if its delay is greater than 180 min. Thus, we removed all the flights that were delayed more than 180 min.
Figure 2 plots the average hourly departure (arrival) delay of flights operated from 6:00 a.m. to 24:00, while
Figure 3 plots the departure (arrival) delay rate of hourly flights operated from 6:00 a.m. to 24:00. The delay rate is defined as the proportion of flights with delay longer than 15 min to the total number of hourly scheduled flights. As it can be seen from
Figure 2, the average departure delay at ZGGG is significantly higher than the average arrival delay. The average arrival delay of the airport increases almost linearly before 16:00; then, it fluctuates slightly and goes up to the maximum of 20 min per flight. The average departure delay of the airport increases almost linearly before 17:00; then, it fluctuates slightly and goes up to a maximum of 35 min per flight. Similar trends can be observed in arrival delay. That is, delay increases almost linearly from 8:00 to 21:00. From
Figure 3, we can see that the average departure delay rate of the airport is significantly higher than the arrival delay rate. The average arrival delay rate at the airport is less than 0.24, while most of the hourly departure delay rates vary between 0.5 and 0.6.
Figure 4 and
Figure 5 shows the distribution of arrival (departure) delay of one flight in one schedule season. The kernel density estimation and the normal distribution fitting are used to fit the curves. It can be seen that the kernel density curve is very close to the fitted normal distribution curve. Therefore, we assume that flight delays follow normal distributions. The mean
and standard deviation
are used to describe the delay distribution. Thus, the goal of our supervised learning algorithms is to predict the
and
for every flight in the strategic flight schedules.
5. Conclusions and Discussion
In this paper, we proposed machine learning algorithms to predict the distributions of flights in a strategic schedule. We tested various distribution functions to model flight delays, including Beta distribution, Erlang distribution, and Normal distribution. The results suggest that Normal distribution is better able to capture the stochastic nature of flight delay. Three machine learning algorithms, LightGBM, MLP, and RF, have been employed to predict the distribution of flight delays. To measure prediction performance, three metrics are defined. We tested our algorithms with real flight data at Guangzhou Baiyun International Airport. The prediction accuracy of departure delay at a 0.65 confidence level and the arrival delay at the 0.50 confidence level can reach 0.80. Our work provides an alternative tool for airports and airlines managers for estimating flight delays at the strategic phase.
There are several limitations of the work. First, since there are many factors that affect flight delay, we could fit the delay distribution for every single flight with multiple normal distributions. Second, we do not predict cancellations due to the limitation of data. Given the low probability of flight cancellation, it would be much more challenging to predict correctly. Last, the prediction performance may be enhanced if a sophisticated model is constructed or if a more precise loss function is developed for each machine learning algorithm.