Analysis of patterns and trends in air traffic behaviour in different en-route atc sectors using a complexity indicator

Air traffic is currently increasing. But the ATC service, which is responsible for providing control of aircraft crossing the airspace, is unable to increase its capacity to cope with this demand. This makes airspace an increasingly complex environment. Complexity is thus becoming an area of interest. This paper aims to develop a complexity indicator based on the behaviour of the main flows of a sector. By means of Exploratory Data Analysis, it is possible to obtain a study that allows the complexity of different sectors to be compared with each other, as well as to analyse in detail the complexity of a sector or its causes. This exploratory analysis carried out for the study of complexity is very extensive, and can allow the ATC service to have a general or specific view of the complexity of the sectors, or even of the behaviour of certain air traffic flows. This is of great help, and can be a tool for optimising human and technological resources within the ATC service.


Introduction and objectives
Air Traffic complexity is a term that usually describes the air traffic situation [1].The traffic situation is becoming increasingly complex because dynamic optimisations of traffic flow and airspace configuration are employed to safely accommodate the rapid development of air transport.This leads to an increasing need for ATCO (Air Traffic Controller) resources to ensure efficiency and safety [2].For this reason, the study of air traffic complexity is becoming increasingly important within the ATM (Air Traffic Management) industry.
Complexity is commonly understood as a combination of different air traffic characteristics, including the number of flights or their interaction [3].But combining these variables to produce a single representative indicator is complex.This means that, to date, it has not been possible to arrive at a universal indicator of complexity [4].
The complexity indicators aim to analyse air traffic behaviour in order to quantify how difficult a traffic situation is for an ATCO to manage.They are therefore closely related to the workload of ATCOs [5].Despite having a common objective, a variety of different indicators have been developed, such as indicators based on airspace disturbances [6], or indicators based on mathematical models such as Lapunov exponents [7].
But in recent years, artificial intelligence has played a major role in the development of complexity indicators.The latest developed complexity indicators include artificial intelligence.Thanks to this tool, predictions of future complexity can be made, which can help dynamic sectorisation and complexity forecasting and improve the management of human and technological resources [8].But it can also help to overcome a weakness of previous complexity indicators: the subjectivity that many indicators are based on the operational knowledge of different stakeholders, such as the ATCOs themselves.These indicators are influenced by different people's opinions, which may differ from the rest and lead to less robust complexity indicators [9].
Following the recent studies of [3] and [9], the aim of this paper is to develop a complexity indicator to characterise ATC (Air Traffic Control) sectors according to their complexity.This indicator has the advantage of being influenced by machine learning models, as follows: -The indicator is mainly influenced by the data, eliminating the subjectivity present in the complexity indicators as much as possible.-The indicator is capable of being used in sectors of different nature without the need to adapt the model.In addition to the development of a complexity indicator, this paper develops its own methodology for analysing traffic patterns using this indicator.Thanks to EDA (Exploratory Data Analysis) [10], it is possible to study traffic in detail, trying to find patterns in the traffic behaviour.
The knowledge of traffic patterns can make it possible to foresee possible areas or situations of conflict, in which the ATC service has a greater complexity and workload.With this, it is possible to anticipate the management of ATC service resources to the planned operation, by knowing these areas of high complexity.
This paper is part of a collaboration between ENAIRE, C.R.I.D.A and the UPM, with the aim of creating a complexity indicator that is able to describe the airspace and characterise it according to the behaviour of its air traffic flows, and to be able to predict the complexity of the airspace by means of this indicator with the help of mahine learning models.
Section 2 explains the development of the complexity indicator and the pattern analysis methodology using EDA.In Section 3, an application case is made and in Section 4, the conclusions of the work are developed and future steps are proposed.

Methodology
This section develops the complexity indicator and the methodology for analysing air traffic patterns using this indicator with the help of the EDA.In order to have a robust complexity indicator, strengths and weaknesses of previous indicators considered important indicators within the study area have been analysed ( [6], [7], [8], [11] and [12]).From this analysis, the following complexity indicator is developed.

Complexity indicator
Following the analysis of weaknesses and strengths, a complexity indicator has been proposed that is capable of determining this complexity in terms of the main traffic flows in the sector.This will take into account the trajectories of the flights, but also their uncertainty, by bringing together different trajectories in a single flow.Another consideration obtained from the strengths and weaknesses analysis is that the proposed indicator will classify complexity in 5 levels, with 1 being the lowest level and 5 the highest level.With this, the strength of the ranking-based models is maintained.The indicator will be influenced by traffic density, but also by more variables of both the flights and the sector's own structural variables, since, according to [13], Air Traffic Complexity is based on traffic behaviour, but also on the structural aspects of the ATC sectors.
And finally, it has also been decided to develop a model influenced by Machine Learning.Complexity indicators are starting to be based on Artificial Intelligence, and it is also a strength as it eliminates the dependence on human bias.
According to these considerations, a methodology explained in Fig. 1 is proposed.Within these four initial fields, different variables, obtained after the analysis of [3] and [9], are considered and presented in Table 1.From these variables, the values of the variables and the variability coefficients (Eq.( 1)) are used.

𝐶. 𝑉. = 𝜎/𝜇
(1) These values are calculated for each of the sector's flows.The purpose of this indicator is to define complexity in terms of the main flows in the sector.For this reason, these variables, calculated for each flow, are combined.Specifically, the values of the variables are combined to give the mean impact.The variability coefficients are combined to give the impact variability.This combination is done by a weighted sum of the variables.The relative weights of this weighted sum have been obtained after performing a machine learning model following the indications of [9].
The mean impact and the impact variability are then combined in a table model [3] to give the impact of the flows.
Similarly, the calculation of complexity is done using the five variables at the bottom of Figure 1.These variables are divided into two groups, the "Flow parameter" brings together all the variables related to the nature of the flows.This parameter is the one that links the complexity analysis with the impact analysis.The "Sector parameter" is a combination of the three variables that try to expose the structural aspect of the sectors [9].Their combination by means of a table model [3] results in complexity.

Validation of complexity indicator
Although the aim of the paper is to develop an indicator that can objectively characterise airspace, a process of validation of the indicator has been carried out through the previous experience of ENAIRE's ATCOs.The aim was to create a complexity indicator based on machine learning tools.However, when it comes to evaluating the applicability of the indicator in a real scenario, and the real usefulness of this indicator, it is the ATCOs who have to determine that the indicator meets the objective for which it was created.
This validation period consisted of two parts: -Firstly, the variables that form part of the complexity indicator have been validated.The air traffic complexity has to consider many aspects of different nature [3].Therefore, after having selected the variables that were taken into account in the development of the indicator, a workshop was held with ENAIRE ATCOs to check that the selected variables can characterise air traffic, and thus be able to calculate its complexity.The results of this workshop were positive and these variables were indeed selected for the indicator.-Subsequently, a workshop was held with these same ATCOs to review and approve the relative weights used in the weighted sum.Although these weights were determined thanks to the use of machine learning tools, ENAIRE ATCOs validated both the structure of the models and the objectives they produced.Through these workshops, the ATCOs involved were able to provide feedback on the development of the complexity indicator, and validate it for applicability in a real-life scenario.

Methodology of patterns analysis with EDA
Once it has been determined how air traffic complexity is to be measured, it is also necessary to identify how this complexity is to be characterised along with air traffic behaviour.According to [10], the EDA has the function of presenting the information of a data series in simple graphs.Applying this, considering both the variables that define the impact and complexity, as well as the impact or complexity itself, data series, its behaviour can be studied by means of EDA.
Specifically, in [10], the three graphs that are simplest to represent, but allow more information to be obtained from the data series, appear in [10]: -Dot Plot. -Histograms.
-Boxplot.Thanks to these three graphs, it is possible to produce an EDA that allows the different sectors to be characterised according to their complexity.But the complexity indicator developed has the advantage of being based on the impact of flows, and ultimately of operational variables obtained directly from flight plans.The methodology for characterising sectors and flows through the indicator is therefore developed in the following phases: -Characterisation of group of ATC sectors: The first step of the methodology is to be able to compare the ATC sectors by their complexity.For this purpose, a comparative complexity analysis of the different sectors is carried out.-Selection of ATC sector for further analysis: After the comparative analysis, one or several sectors can be chosen for a more detailed analysis of their complexity.-Analysis of complexity parameters: This is the detailed complexity analysis of the sector(s) chosen.
-Comparative impact analysis of different air traffic flows: Within the selected sector, it is not only important to know the complexity and how it behaves.The complexity indicator developed is based on the behaviour of the main traffic flows in the sector.For this reason, within the methodology, once the complexity has been analysed, the impact of the main traffic flows is studied.Firstly, a comparative analysis of the impact of the traffic flows is carried out.-Analysis of impact parameters: A detailed analysis of the selected flows is carried out with the aim of finding out the patterns of their impact and how the variables that make up the impact influence this parameter.This is the last step of the methodology.

Results
Following the methodology developed, the complexity indicator is applied to the operation of 4 ATC sectors.The data on operations of the whole year 2019 have been used.The data have been obtained based on ENAIRE radar traces and have been provided to the authors after processing and validation by the company CRIDA.
In addition to applying the complexity indicator, to be able to analyse the results in detail, the EDA characterisation methodology has been used.At the first tier, sectors are evaluated and compared by their daily complexity.In this first case, the representation is done by a dot diagram representing each of the daily complexity tiers, and by a boxplot which serves to present the global information in a summarised form.The four ATC sectors and the analysis is presented in Fig. 2.

Figure 2. Analysis of different ATC sectors complexity.
Thanks to the EDA, the complexity of each of the sectors can be analysed both globally, with the boxplot, and specifically with the dot plot.Within the sectors analysed, two trends can be observed.
-The GCCCRNE and LECMPAU sectors are sectors with stable operation during the year.This is reflected in the complexity.The complexity of these sectors is level 3 on most of the days that the sectors operate.This can be seen in the boxplot, with the box having only level 3 complexity.
And it can also be seen in the dot plot.-The sectors LECBCCC and LECBBAS are highly variable sectors.These sectors include the TMA (Terminal Maneuvering Area) of Barcelona and Palma de Mallorca airports.These airports are popular holiday destinations, so the operation in summer in these sectors is much more complex than in winter.This can be seen both in the boxplot with more variable boxes centred on complexity level 4, and in the dot plot where on summer days the LECBCCC sector has complexity level 4 and the LECBBAS sector has complexity level 5.This comparative analysis of complexity allows conclusions to be drawn about the different sectors, but to be able to analyse this complexity in more detail, the second part of the methodology is proposed (see Fig. 2).Continuing with the application case, it has been decided to study the detail of the complexity of LECBBAS.This sector has been considered the most interesting as it has variability between summer and winter seasons and reaches the highest complexity levels.Fig. 3 shows part of the detailed analysis of the complexity of LECBBAS, by means of a dot plot of the number of flows and a boxplot of the number of entry and exit points.Both the number of flows and the number of entry and exit points of aircraft follow the complexity pattern in LECBBAS.In addition, the number of flows has been related to complexity.A direct relationship with complexity can be seen in both cases.Since, as the number of flows increases, the entry and exit points to the sector will be more in order to handle the higher amount of traffic.These reasons increase the complexity of the sector.In the winter season (January-April and November-December), the complexity in LECBBAS is level 3 or 2, and the variables analysed have a limited range.However, in summer these variables increase, reaching complexity levels of 5 on most days.
With this analysis, the complexity can be justified.This can provide the ATC service with possible courses of action to reduce complexity if necessary.In order to be able to identify areas of conflict in more detail, the analysis of air traffic flows is added to the characterisation methodology.In the LECCBAS sector, the most important flows according to the number of days open, the number of aircraft in the flow throughout the year, and the impact of these flows, are 4.These flows, together with the comparative analysis of the impact are presented in Fig. 4. In this case, the impact of the four flows follows the trend observed in the sector.The impact of all flows is greater in summer than in winter.This is due to the high seasonality of the sector.However, two trends can be distinguished in the flows.
-Flows 169_LECBBAS_CL, 1_LECBBAS_CL and 7_LECBBAS_CL are sector overflight flows.These flows have summer complexity level 4, due to the fact that they do not involve so much effort for the ATC service.Specifically, flow 7_LECBBAS_CL is a flow with operation to Ibiza airport, which is a usual holiday destination.This means that the impact increases in general, with impact level 5 days appearing.-Flow 9_LECCBAS is a descent flow to Palma de Mallorca airport.This causes flights to be approach flights, increasing the difficulty for the ATC service.This flow has a higher average impact than the rest, and in summer it reaches impact level 5 on most days.All patterns analysed with the impact graphs are consistent with the previous analyses performed.Furthermore, based on the operational knowledge of the operation in the LECBBAS sector, the results obtained are meaningful.
Finally, the detailed analysis of the variables defining the impact is presented.The aim is to analyse in detail why the impact follows the patterns of behaviour seen.
According to the conclusions obtained, it has been determined that the flow of most interest is flow 9_LECBBAS_CL because of its different nature from the rest of the flows.A sample of the detailed analysis is presented in Fig. 6.It has been decided to present the most representative variable for each of the four fields defining the impact (see Table 1).Specifically, flights per day, the number of FLs (Flight Levels), the percentage of hourly activity and the percentage of regulated flights are presented in Fig. 5.The number of flights and hourly activity follow the expected pattern of behaviour.In summer, the number of flights is higher, and these flights are spread over more hours.This makes the work of the ATC service more difficult, resulting in higher impact levels in the summer season.
The number of FLs has a bimodal distribution.The first mode is 1 FL, due to the winter operation, where the number of flights is considerably lower, and therefore can be distributed over a single flight level.The second mode, at 5 or 6 FLs, is due to the summer operation where more FLs are needed to handle the higher number of flights Finally, the percentage of regulated flights follows a similar trend to the rest of the variables.In summer there are usually more regulated flights.Due to the increased complexity in summer, more ATFCM regulations appear to help the ATC system cope with the demand.In winter, it is not necessary to put in place as many regulations.However, on some winter days, all flights are regulated.This is because the ATC service resources are lower in winter, so regulations must be put in place to balance this demand, which, although lower, has to be adapted to the ATC service resources.
Firstly, it can be stated that the complexity indicator seems to correctly characterise the operation of the sectors.After having applied this indicator to four different ATC sectors, it can be seen that the complexity corresponds to the operational knowledge of the sectors.
In terms of characterisation methodology development, the methodology allows characterisation of the operation at different levels of detail.All this is achieved by means of simple graphs only, so that the process can focus on drawing conclusions rather than interpreting the graphs.This makes this characterisation methodology a great complement to the complexity indicator, thanks to the EDA.But in this aspect, there is also room for improvement.These will be developed in future work.
-Although the EDA approach is to represent information by means of very simple graphs.In order to improve the characterisation methodology, other types of graphs that are better adapted to the variables should be considered, while maintaining the objective of simplicity.-A dynamic and interactive methodology should be developed, allowing users to select the periods or sectors of analysis in a simple way.In this way, the application of the complexity indicator and the characterisation methodology is simpler in the real operation.Regarding the validation of the process, the results have shown, from an operational point of view, that the complexity indicator can correctly describe air traffic.Even so, an additional workshop with ENAIRE ATCOs is planned in order to have a final validation process of both the final indicator and the results obtained.In this workshop, the development proposed in this paper will be presented to the ATCOs, to see if they really meet the objectives initially proposed, although these results are promising.

Figure 1 .
Figure 1.Scheme of development of complexity indicator based on Air Traffic situation.This complexity indicator is based on the data present in the flight plans.Therefore, traffic density, vertical density, temporal distribution and the influence of ATFCM (Air Traffic Flow and Capacity Management) regulations can be evaluated.Within these four initial fields, different variables, obtained after the analysis of[3] and[9], are considered and presented in Table1.From these variables, the values of the variables and the variability coefficients (Eq.(1)) are used.

Table 1 .
Initial variables to define the impact indicator.