CHAPTER 4 EMPIRICAL STUDY
4.2 Delay Modeling
This research employs the Cox PH model to develop departure and arrival delay models to explore the problem of flight delay propagation in an airline network. The actual turnaround and block operation times (instead of scheduled times) of Airline A are then used to estimate the models. Because Airline A operates short-haul routes with many of its aircraft flying up to 10 consecutive segments in a day, delays in one segment could easily propagate to following flights. Figure 4.6 shows that the distribution of delay time is
“right-skewed,” indicating that the airline has more short delays and fewer long delays. Meanwhile, the relationship between departure and arrival delays is analyzed as presented in Figures 4.7 and 4.8. Figure 4.7 reveals that departure and arrival delays are closely related as the lines for them are close to each other. That is, longer departure delays normally cause longer arrival delays, while shorter departure delays usually result in shorter arrival delays. This relationship is also proved in Figure 4.8 with a Pearson’s correlation coefficient of 0.978. Thus, this research considers the factors influencing turnaround and block operations, including arrival delay, ground handling time, turnaround buffer time, departure delay, taxi-out time, airborne time, taxi-in time, and block buffer time, as the covariates for developing the flight delay models.
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aDelay times are measured in minutes.
bDotted lines represent the fitted density curves.
Figure 4.6 Histograms of departure delays and arrival delays.
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aVertical axis and horizontal axis denote delay time (measured in minute) and the associated delayed flights (excluding cancelled flights) according to the sequence of flights in schdeule, respectively.
bBlack line and red line represent departure delays and arrival delays, respectively.
Figure 4.7 Departure and arrival delays of various routes.
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aVertical axis and horizontal axis denote delay time (measured in minute) and the associated delayed flights (excluding cancelled flights) according to the sequence of flights in schdeule, respectively.
bBlack line and red line represent departure delays and arrival delays, respectively.
Figure 4.7 Departure and arrival delays of various routes (Continued).
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aVertical and horizontal axes are measured in minutes.
bPearson’s correlation coefficient equals 0.978 (p-value=0.000).
Figure 4.8 Correlation of departure delays and arrival delays.
Although airline companies normally schedule buffer times within turnaround operations at airports in addition to the ground handling time required, the information related to actual turnaround buffer time was unavailable in the dataset of Airline A. To obtain this information, the actual turnaround times of flights in each route were ordered from the smallest to the largest. The 25th percentile (1st quartile) of the ordered actual turnaround times was selected as the required ground handling time, the minimum time required to complete all turnaround activities. Therefore, for every outbound aircraft,
actual turnaround buffer time =scheduled time of departure - actual time of arrival - required ground handling time. (4.1)
This means that after an inbound aircraft arrives at the gate, the difference between the actual time of arrival and the scheduled time of departure for the next flight is the time available for the turnaround of the aircraft. The actual turnaround buffer time can be derived by subtracting the required ground
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handling time from the available turnaround time. Thus, the actual turnaround buffer time is positive if the available turnaround time exceeds the required ground handling time, and negative (generally resulting from a late flight arrival) if the available turnaround time is shorter than the required ground handling time.
Conversely, the block time includes block buffer time and required block operation time, which is the minimum time required to complete the activities of taxi-out, airborne operation, and taxi-in. However, the obtained dataset did not contain the information related to actual block buffer time. To derive this information, the actual block times of flights in each route were ordered from the smallest to the largest. The 25th percentile of the ordered actual block times was then selected as the required block operation time. Therefore, for every inbound aircraft,
actual block buffer time = scheduled time of arrival - actual time of departure - required block operation time. (4.2)
In other words, after an outbound aircraft departs from the airport gate, the difference between the actual time of departure and the scheduled time of arrival represents the time available for the block operation of the aircraft. The actual block buffer time can be derived by deducting the required block operation time from the available block time. Thus, the actual block buffer time is positive if the available block time exceeds the required block operation time, and negative (generally resulting from a late flight departure) if the available block time is shorter than the required block operation time.
Because airlines often assign different types of aircraft to various routes in aircraft daily operations, the distributions of flight delays may be influenced by aircraft type, route, peak/off-peak hour, and season, in addition to delay cause (Wu and Wong, 2007; Vranas et al., 1994; Tu et al., 2008; Eurocontrol, 2003;
Allan et al., 2001; Santos and Robin, 2010; Fricke and Schultz, 2009), which
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are also discussed in Section 4.1. Therefore, the survival curves of flight delays using the Kaplan-Meier estimator are used to examine the possible impact of factors on delays in departure and arrival.
●Aircraft Type
In aircraft’s daily operations, turnaround times vary for different aircraft designs and depend on the amount of resources allocated to a turnaround at a specific airport. Bigger aircraft typically need more ground handling time to complete the activities required at airports. In addition, Cavcar and Cavcar (2004) compared different aircraft types and concluded that the rate of climb and cruising speeds of different aircraft types have different effects on air traffic delays. Table 4.6 shows the routes, represented by the origin airport codes and the destination airport codes, and assigned aircraft types of Airline A.
The delays of the two types of aircraft are analyzed and illustrated in Figure 4.9.
Although Fokker 100 aircraft is larger than Fokker 50 aircraft, the survival curves reveal that Fokker 50 aircraft tend to have longer survival times of delays than Fokker 100 aircraft. This may be due to better performance of Fokker 100 aircraft. Besides, according to the delay causes recorded by Airline A, most of the airports at which Fokker 100 aircraft operate exhibit better management of turnaround activities. On the contrary, Fokker 50 aircraft have more technical problems and a higher frequency of not being able to be released because of maintenance reasons. Also, some of the airports at which Fokker 50 aircraft operate often have runway closures because the weather is below safe operating limits.
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Table 4.6 Routes and assigned aircraft types
Route Aircraft Type Route Aircraft Type
HUN→KHH Fokker50 RMQ→KNH Fokker50
HUN→RMQ Fokker50 RMQ→MZG Fokker50
KHH→HUN Fokker50 RMQ→TSA Fokker50
KHH→TSA Fokker100 RMQ→TTT Fokker50
KNH→RMQ Fokker50 TSA→KHH Fokker100
KNH→TSA Fokker100 TSA→KNH Fokker100
MZG→RMQ Fokker50 TSA→RMQ Fokker50
RMQ→HUN Fokker50 TTT→RMQ Fokker50
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Figure 4.9 Survival curves of various types of aircraft.
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●Route
The survival curves for the 16 routes indicate that delays are different from individual to individual for both departure and arrival (Figure 4.10). Since all aircraft operate short-distance flights with various block times from 40 to 70 minutes, it is usually difficult to make up the flight delays in the air. The recorded delay causes show that the facilities and management efficiency vary from one airport to another. For instance, TSA and KHH have better airport facilities and management. By contrast, at KNH flight delays are sometimes caused by insufficient airport facilities. RMQ and KNH, on the other hand, often have foggy weather, leading to runway closures. The problem gets worse since RMQ is the home base of Airline A with the company’s maintenance hangar located here. Because of many flights operating between RMQ and other airports, runway closures at RMQ prevent flights from operating to other segments and even propagate delays to several segments. Similarly, MZG often has flight delays resulting from windy weather.
Table 4.6 shows that Fokker 100 aircraft operate only four routes:
KHH→TSA, KNH→TSA, TSA→KHH, and TSA→KNH. Particularly, TSA and KHH are with better airport facilities and management as mentioned above.
On the contrary, Fokker 50 aircraft operate 12 of the total 16 routes, to which flight delays tend to happen. Especially, the flight delays for routes between RMQ and other airports have serious effects on schedule reliability. Therefore, flight delays are closely related to the types of the aircraft used and the routes to which the aircraft are assigned.
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Figure 4.10 Survival curves of various routes.
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●Delay Cause
Because flight delays may have a wide range of causes and the associated disturbances may result in various durations of flight delays, it is worthwhile investigating the relationship between delays and their causes. Figure 4.11 shows that ‘weather’ and ‘technical and aircraft equipment’ tend to result in longer departure delays. ‘Reactionary,’ which corresponds to the delays due to late arrival of aircraft from previous segments, is also a major cause for departure delays. On the other hand, the survival curves for arrival delays show that ‘weather’ has much serious impact on flight operations than ‘air traffic control restrictions’. The analysis reveals that different categories of delay causes have different effects on flight delays.
●Peak/Off-peak
In most cases, the flights operating in peak hours are more likely to be delayed. This may be, for example, because passengers are held up at check-in, security controls, and customs, or aircraft wait a long time in queue to obtain clearances to take off. The survival curves of peak hour show only slightly different from those of off-peak hours for both departure and arrival delays (Figure 4.12). This indicates that flights operating in off-peak hours may be disturbed by some important factors, which are worth investigating.
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Figure 4.11 Survival curves of various categories of delay causes.
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Figure 4.12 Survival curves of peak/off-peak hours.
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●Season
The recorded delay causes reveal that the foggy weather in spring often results in runway closures, especially at RMQ and KNH. The initial delays even propagate to several flight segments in the network. On the other hand, it features in rainy weather in summer and fall, which also frequently causes runway closures, especially at TSA, RMQ, KNH, MZG, and HUN. In winter, the operations of most flight routes are influenced by monsoons. Though weather conditions in different seasons often cause flight delays, Figure 4.13 shows that the survival curves of different seasons are quite close to one another for both departure and arrival delays.
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Figure 4.13 Survival curves of seasons.
Using the log-rank tests, the results in Table 4.7 indicate significant differences in the survival distributions of flight delays for the selected
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variables. Therefore, in addition to the variables influencing turnaround and block operations, aircraft type, route, delay cause, peak/off-peak hour, and season are also considered as the covariates for developing the flight delay models.
Table 4.7 Difference test of survival curves
Factor Departure/Arrival Delay Chi-square
Aircraft type Departure delay 158.2***
Arrival delay 107.4***
Route Departure delay 305.3***
Arrival delay 271.1***
Delay cause Departure delay 373.8***
Arrival delay 10.1***
Peak/off-peak hour Departure delay 11.8**
Arrival delay 12.3**
Season Departure delay 7.6***
Arrival delay 10.7***
Significance levels: 0%***, 0.1% **, 1%*.
To formulate a departure delay model, the relationship between variables must be further clarified. First of all, there will be a longer buffer time in turnaround operations if ground handling activities are completed rapidly;
conversely, there will be a shorter turnaround buffer time if more time is required to complete ground handling activities. In addition, the late arrival of flights also results in a reduction in turnaround buffer time. Therefore, to avoid any bias resulting from the highly correlated relationship with ‘turnaround buffer time’, ‘arrival delay’ and ‘ground handling time’ should be deleted from the model. Similarly, the routes of Airline A are operated using different types of aircraft, and flight delays are subject to the routes to which the aircraft are assigned. Accordingly, ‘route’ should also be removed from the model because the delays associated with a ‘route’ are already reflected in the delays of the
‘aircraft type’, and a bias would be generated if both ‘route’ and ‘aircraft type’
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are used as covariates. Furthermore, a delay caused by ‘late arrival of an aircraft’, recorded as ‘reactionary’ by airlines, is already counted as an ‘arrival delay’ and reflected in ‘turnaround buffer time’ in the model. Consequently,
‘reactionary’ should also be deleted from the delay causes considered. Thus, the departure delay model is formulated as Equation (4.3).
(4.3) off-peak hours, the delay information associated with these factors can also be obtained from ‘peak/off-peak hour’ in the model. Therefore, ‘departure delay’,
‘taxi-out time’, ‘airborne time’, and ‘taxi-in time’ should be removed from the model to avoid an interdependent relationship between these covariates and the
‘block buffer time’. Similarly, ‘route’ should also be deleted to avoid simultaneously including both ‘route’ and ‘aircraft type’, as discussed in the establishment of the departure delay model. The arrival delay model is therefore formulated as Equation (4.4).
(4.4)
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Therefore, the variables used in the departure and arrival delay models for capturing the chain effects of flight delay propagation are listed in Table 4.8.
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Table 4.8 Variables used in departure and arrival delay models Variable Departure Delay
Model
Arrival Delay Model
Dummy Code
Description
Turnaround buffer time － －
Block buffer time － －
Aircraft type 0 Fokker 100
1 Fokker 50
Category of delay cause
0 Airport facilities or governmental authorities
1 Flight operations and crewing, cargo and mail handling, technical and aircraft equipment, passenger and baggage handling, weather, air traffic control restrictions, miscellaneous
0 Air traffic control restrictions
1 Weather#
Peak/off-peak hour 0 Peak hour
1 Off-peak hour
Season 0 Spring
1 Summer, fall, winter
a*: Including ground handling impaired by adverse weather conditions, weather at departure airport, weather en-route, and weather at destination or alternative airport.
b#: Including “only” weather en-route and weather at destination or alternative airport.
cDummy code 0: Base type.
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Due to the strong causal relationship between departure and arrival delays via aircraft routing, flight delay propagation can be investigated by recursively combining the departure and arrival delay models. Here, ‘recursively’ means that the output of the departure delay model serves as the input of the arrival delay model, and the output of the arrival delay model serves as the input of the departure delay model.