*4.1. Analysis of LECMPAU Air Traffic and ATFCM Regulations*

Before starting to test the model and analyse its explainability, it is important to understand the operation in the Pamplona Upper (LECMPAU) sector, as well as the behaviour of the regulations in the sector. To study traffic behaviour, the methodology developed by CRIDA has been used to organise traffic into flows. The flows obtained from the methodology are presented in this paper as part of the input variables of the machine learning model will be whether there are aircraft in each flow or not. The flows are presented in Figure 4.

The air traffic flows identified have been divided into four main groups. The flows that cross the sector from north to south are of great importance in the operation of the sector, as they contain flights that normally depart from or go to the Madrid-Barajas airport. Other flows of great interest are those crossing the sector from east to west, as these will normally be associated with flights departing from or going to Barcelona-El Prat. With this, it can also be said that LECMPAU is a sector whose operation is very complex, as it includes operations around the two largest airports in Spain, making it a sector of great interest.

Additionally, there is another group of flows that cross the sector diagonally from the west of the sector to the north or vice versa. Flights belonging to these flows are more variable and difficult to classify into a single flight type.

With these air traffic flows, an attempt to characterise the traffic in the sector simply is made, taking into account the different trajectories that can be flown. In addition, it is important to characterise the regulations in the LECMPAU sector, as it will be possible to see certain patterns in the appearance of these regulations that can be used to validate the results of the machine learning model.

Overall, there were 150 regulations in LECMPAU in 2019. These regulations had a mean regulation time of 121.9 min, and a standard deviation of 71.16. To be more specific, the boxplot of the regulation time is presented in Figure 5.

**Figure 4.** LECMPAU Air Traffic Flows.

**Figure 5.** Boxplot of Regulation time in LECMPAU.

In the boxplot, it can be seen that most of the regulations have a regulation time between 50 and 200 min. There are cases of outliers due to both deficit and excess. With this data, only 18,285 min in the whole year will be regulated. This is 3.5% of the total time analysed. As the model will tell whether the sector is regulated or not, there is likely an imbalance in the sample to be analysed, as LECMPAU is much longer unregulated than regulated.

Rather than the duration of these regulations, it is of interest to know how they are distributed over time. This information is presented in Figure 6, which shows histograms of the regulations according to their month (a), day of the week (b), and start time (c).

**Figure 6.** Temporal analysis of regulations in LECMPAU, of hour of regulation (**a**), month of regulation (**b**) and Day of the week of the regulation (**c**).

The temporal analysis indicates that most of the regulations will occur in summer. This is normal, as Barcelona and Mallorca are common holiday destinations, and flights from the US to these airports will pass through LECMPAU via flows crossing the sector from east to west. This increase in traffic will lead to more capacity regulations. As for the day of the week, most of the regulations will occur on weekends, mainly on Saturdays. This is also natural, as weekend traffic will be higher than Monday to Friday. Finally, the hourly analysis indicates that regulation will be centred at 05:00, with three secondary peaks of regulation at 06:00, 15:00, and 18:00. These are the most common times for business and holiday flights.

With this information, it is possible to find patterns in the behaviour of regulations in 2019, so it is possible that the machine learning algorithm, which is mainly based on temporal variables, will find these patterns and manage to act satisfactorily. The results of the model are presented below.
