3.1. Hypotheses
Departure (arrival) delay is the difference between the actual departure (arrival) time and the scheduled departure (arrival) time. Based on the
Figure 1, the departure and arrival delay can be established as Equations (1) and (2):
Equations (1) and (2) are calculated from the definition of the departure and arrival delay. However, the departure and arrival delay can also be obtained from the cause of formation. Based on this, the departure and arrival delay can be obtained from Equations (3) and (4).
Propagated arrival delay and propagated departure delay, mentioned in Equations (3) and (4), can be further extended in Equations (5) and (6), as propagated arrival (departure) delay is impacted by Delay_PreArr (Delay_PreDep) and turnaround (block) buffer time.
By conjecturing Equations (3) and (5), as well as (4) and (6), we obtain:
The difference between root departure delay and turnaround buffer time reflects the difference between departure delay and previous arrival delay. Airborne flights have more priorities than flights on the ground when using the runways, considering the fuel limitation and safety operation. This fact indicates that the root arrival delays are more likely to be smaller than root departure delays. In addition, turnaround (block) buffer time is likely to be small, as reducing buffer time leads to more flight legs per day of an aircraft to earn more profit. Therefore, the ratio of Delay_PreDep over arrival delay may correlate more highly than the ratio of Delay_PreArr over departure delay. Therefore, the first hypothesis to be tested in the paper is formalized as follows:
Hypothesis 1 (H1). Departure (arrival) delay is relatively highly correlated with Delay_PreArr (Delay_PreDep). Everything else being equal, departure (arrival) delay should increase with Delay_PreArr (Delay_PreDep). The ratio of Delay_PreDep over arrival delay should be, on average, more than that of Delay_PreArr over departure delay.
The second hypothesis also relates to delay propagation but from a different perspective. Previous delay of a flight not only increases the operating cost of the flight but can propagate to downstream flights of the same aircraft. To mitigate delay propagation, airlines tend to set a buffer time in flight scheduled turnaround or airborne operation to absorb the previous arrival (departure) delay. If the buffer time becomes longer, then the turnaround (block) time has greater capacity to absorb and prevent delay from being propagated to the next departure or arrival. This leads to the second hypothesis of the paper.
Hypothesis 2 (H2). The ratio of departure (arrival) delay over turnaround (block) buffer time should be, on average, negative. If Hypothesis 1 can be confirmed, where the Delay_PreDep impact on arrival delay is more than Delay_PreArr impact on departure delay, the absolute value of the ratio of block buffer time over arrival delay should be, on average, more than that of turnaround buffer time over departure delay.
The third hypothesis relates to the weather condition—especially for convective weather. Convective weather inducing a large clearance or landing separation leads to a widespread airport traffic congestion. Take offs and landings are even prohibited for safety reasons in case of severe convective weather, which may cause severe flight delays. Specifically, stakeholders prefer flights to holding on the ground than holding on the airborne. Based on this policy, we propose our third hypothesis:
Hypothesis 3 (H3). Flights facing convective weather will have more restrictions to take off or land at an airport, increasing departure or arrival delay. Moreover, the departure delay is affected by convective weather more greatly than arrival delay.
Finally, our study considers that the delay propagation effect will be affected by the aircraft utilization, which includes that the order of a flight operated by an aircraft per day (OrdFltOfAC) and the number flights operated by an aircraft per day (NumFltOfAC). Considering the cumulative effect of flight delays in multi-order propagation, the latter order of a flight is, the more probability the flight on-time performance is affected by the previous flight. In addition, the more flights an aircraft flies per day, the greater the impact on downstream flights of an aircraft when delay propagation occurs. To this end, airlines tend to use a better buffer setting strategy to absorb flight delays and keep on-time performance efficiently.
Hypothesis 4 (H4). The aircraft utilization will impact the delay propagation effect on flight delays. Specifically, previous delay effect grows with OrdFltOfAC increasing; buffer effect grows with NumFltOfAC increasing.
3.2. Model Specifications
Building on the hypotheses above, this subsection specifies econometric models for departure and arrival delay to be estimated in the paper. The general form of the departure and arrival delay models are presented in Equations (9) and (10) in which explanatory variables affecting departure and arrival delay are classified into three categories: operation related, time related, and weather related. The specific variables considered in the model specifications are listed in
Table 1.
To understand the impact of various factors on both departure and arrival delays, two separate specifications are considered: one for departure delay, termed the DelayDep model, as shown in Equation (9); the other for arrival delay, termed the DelayArr model, as shown in Equation (10).
Operation-related factors include the previous delay, buffer time, airport congestion, aircraft type, and hubs. For different explanatory variables of DelayDep and DelayArr model, some variables, including the previous delay, buffer time, and airport congestion, have different definitions in two models. Considering the different operational behaviors at departure and arrival, three factors, including the previous delay, buffer time, and airport congestion, have different definitions in the DelayDep and DelayArr models. For departure delay, the three factors are defined as previous arrival delay, turnaround buffer time, and cumulated departure delays in an airport. However, to analyze the arrival delay, the three factors are defined as previous departure delay, airborne buffer time, and cumulated arrival delays in an airport.
For operation-related variables, one variable is previous delay, which is intended to capture the delay propagation effect from the previous departure or arrival. In addition, propagated delay is one of the most important parts of the flight delays [
17] (Tan et al., 2021). The longer the previous delay is, the more likely the on-time performance of the flight under study will be affected by the previous delay. In the DelayDep model, the previous delay refers to Delay_PreArr. In the DelayArr model, the previous delay refers to Delay_PreDep. This variable is used to test Hypothesis 1.
The variables TT_dif and BT_dif are constructed to test Hypothesis 2 for DelayDep and DelayArr model, respectively. TT_dif (BT_dif) is defined as the difference between the scheduled turnaround (block) time and MCT (MBT). To calculate MCT, CAAC documents MCT values but does not provide details on how the values are obtained [
32]. Another method applies the statistical method to regard the 5th percentile observed turnaround time follows the idea of existing work, which makes the calculation more robust to measurement error and reduces the influence of unusually favorable conditions [
15,
33,
34]. In this paper, we prefer to use the latter method by regarding the 5th percentile observed turnaround time as MCT. Similarly, the MBT calculation also follows this statistical method. The expectation is that the less buffer time there is, the more difficult it is to maintain the scheduled departure or arrival times of flights with large previous delays.
In this paper, we use the CumDepDelay for DelayDep model and CumArrDelay for DelayArr model to present the departure and arrival congestion, respectively [
11]. CumDepDelay and CumArrDelay respectively measure the departure and arrival delays generated in the airports during the past hour. All the flight records departing from (arriving at) the airports are used to calculate the CumDepDelay (CumArrDelay), if the exact the time information (scheduled departure time, scheduled arrival time, actual departure time, and actual arrival time) can be obtained. The expectation is that serious airport delays may increase the flight delays. We use HubDep and HubArr to indicate whether a flight takes off from or lands at the airline’s hub. We speculate that a flight from or to a hub airport is likely to receive better ATC services in the terminal airspace. In addition, an airline usually has more flying experience and a stronger relationship with ATC service providers at its hub airports, which may improve flight operations.
The DelayDep and DelayArr models share a number of common time and weather-related variables. Several time variables are considered in this paper. The first one is DT, a dummy variable indicating whether a flight operates in the day or night. DT is set to be 1 if the scheduled departure (arrival) time is between 6:00 and 20:00. We postulate that there are more flights in the daytime than in the night, which will lead to traffic congestion. Second, flight delays may vary depending on whether it is a weekday or the weekend, again considering the difference in air traffic, particularly for business travel. A Wkd variable is included, which takes the value of 1 if the scheduled departure day is a weekday and 0 otherwise. Third, seasonal changes also affect the traffic demand and thus impact airline operation strategies, which may further affect flight delays. To this end, three seasonable variables, including Sprg, Sumr, and Fall, are introduced as explanatory variables.
To capture the impacts of weather on flight delays, we consider convective weather, temperature, wind speed, and visibility at the departure and arrival airports of a flight. The convective weather (ConvecWthrDep and ConvecWthrArr) is the key variable among the weather-related factors, measuring whether there is a thunderstorm at the departure or arrival end. A thunderstorm can affect an aircraft’s operation safety, further leading to severe delays. For temperature, we assume that both hot and cold temperatures present adverse weather and impact the flight delays. Hot temperature negatively affects aircraft engine performance [
35], whereas cold temperature is often associated with foggy and snowy days, which may cause poor performance on the airport surface and thereby also negatively affect flight delays. The absolute difference between the temperature at the scheduled departure (arrival) time of a flight and the average temperature associated with all departure (arrival) flights of the whole year at the same airport are considered (TempDepDif and TempArrDif). The wind-speed variables (WdspDep and WdspArr) provide the speed of the wind at the departure (arrival) airport during the hour of the scheduled departure (arrival) time of the flight. The visibility variables (VisDep and VisArr) are similarly defined but taking logarithmic values to capture the plausible nonlinear relationship between visibility and flight delay. For example, visibility decreasing from 1 km to 0.5 km impacts flight operations more than decreasing from 8 km to 7.5 km. As some records have visibility of zero miles, we add one to the exponent: VisDep = ln(Departure Visibility + 1) and VisArr = ln(Arrival Visibility + 1). Eight weather variables, including ConvecWthrDep, ConvecWthrArr, TempDepDif, TempArrDif, WdspDep, WdspArr, VisDep, and VisArr, are all considered in departure and arrival delays. This is because the departure flights will be delayed if the weather condition at the arrival airport is not appropriate for landing. The weather condition at the departure airport may extend the taxiing time or even keep waiting until aircraft enters the runway to further impact arrival delays.
Following the discussions, below are the complete DelayDep and DelayArr model specifications. In the specifications, α’s and β’s are the coefficients to be estimated, and ε and υ are the error terms.