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The use of Air traffic management (ATM) simulators for planing and operations can be challenging due to their modelling complexity. This paper presents XALM (eXplainable Active Learning Metamodel), a three-step framework integrating active learning and SHAP (SHapley Additive exPlanations) values into simulation metamodels for supporting ATM decision-making. XALM efficiently uncovers hidden relationships among input and output variables in ATM simulators, those usually of interest in policy analysis. Our experiments show XALM's predictive performance comparable to the XGBoost metamodel with fewer simulations. Additionally, XALM exhibits superior explanatory capabilities compared to non-active learning metamodels. Using the `Mercury' (flight and passenger) ATM simulator, XALM is applied to a real-world scenario in Paris Charles de Gaulle airport, extending an arrival manager's range and scope by analysing six variables. This case study illustrates XALM's effectiveness in enhancing simulation interpretability and understanding variable interactions. By addressing computational challenges and improving explainability, XALM complements traditional simulation-based analyses. Lastly, we discuss two practical approaches for reducing the computational burden of the metamodelling further: we introduce a stopping criterion for active learning based on the inherent uncertainty of the metamodel, and we show how the simulations used for the metamodel can be reused across key performance indicators, thus decreasing the overall number of simulations needed.

This White Paper sets out to explain the value that metamodelling can bring to air traffic management (ATM) research. It will define metamodelling and explore what it can, and cannot, do. The reader is assumed to have basic knowledge of SESAR: the Single European Sky ATM Research project. An important element of SESAR, as the technological pillar of the Single European Sky initiative, is to bring about improvements, as measured through specific key performance indicators (KPIs), and as implemented by a series of so-called SESAR 'Solutions'. These 'Solutions' are new or improved operational procedures or technologies, designed to meet operational and performance improvements described in the European ATM Master Plan., Comment: White Paper of the NOSTROMO, an exploratory research project funded by the SESAR Joint Undertaking (SJU) under the European Union's Horizon 2020 research and innovation programme

This paper presents results from the SESAR ER3 Domino project. Three mechanisms are assessed at the ECAC-wide level: 4D trajectory adjustments (a combination of actively waiting for connecting passengers and dynamic cost indexing), flight prioritisation (enabling ATFM slot swapping at arrival regulations), and flight arrival coordination (where flights are sequenced in extended arrival managers based on an advanced cost-driven optimisation). Classical and new metrics, designed to capture network effects, are used to analyse the results of a micro-level agent-based model. A scenario with congestion at three hubs is used to assess the 4D trajectory adjustment and the flight prioritisation mechanisms. Two different scopes for the extended arrival manager are modelled to analyse the impact of the flight arrival coordination mechanism. Results show that the 4D trajectory adjustments mechanism succeeds in reducing costs and delays for connecting passengers. A trade-off between the interests of the airlines in reducing costs and those of non-connecting passengers emerges, although passengers benefit overall from the mechanism. Flight prioritisation is found to have no significant effects at the network level, as it is applied to a small number of flights. Advanced flight arrival coordination, as implemented, increases delays and costs in the system. The arrival manager optimises the arrival sequence of all flights within its scope but does not consider flight uncertainties, thus leading to sub-optimal actions., Comment: 20 pages, 6 figures, Journal of Air Transport Management

The development of trajectory-based operations and the rolling network operations plan in European air traffic management network implies a move towards more collaborative, strategic flight planning. This opens up the possibility for inclusion of additional information in the collaborative decision-making process. With that in mind, we define the indicator for the economic risk of network elements (e.g., sectors or airports) as the expected costs that the elements impose on airspace users due to Air Traffic Flow Management (ATFM) regulations. The definition of the indicator is based on the analysis of historical ATFM regulations data, that provides an indication of the risk of accruing delay. This risk of delay is translated into a monetary risk for the airspace users, creating the new metric of the economic risk of a given airspace element. We then use some machine learning techniques to find the parameters leading to this economic risk. The metric is accompanied by an indication of the accuracy of the delay cost prediction model. Lastly, the economic risk is transformed into a qualitative economic severity classification. The economic risks and consequently economic severity can be estimated for different temporal horizons and time periods providing an indicator which can be used by Air Navigation Service Providers to identify areas which might need the implementation of strategic measures (e.g., resectorisation or capacity provision change), and by Airspace Users to consider operation of routes which use specific airspace regions., Comment: 19 pages, 14 figures

This article presents a new, holistic model for the air traffic management system, built during the Vista project. The model is an agent-driven simulator, featuring various stakeholders such as the Network Manager and airlines. It is a microscopic model based on individual passenger itineraries in Europe during one day of operations. The article focuses on the technical description of the model, including data and calibration issues, and presents selected key results for 2035 and 2050. In particular, we show clear trends regarding emissions, delay reduction, uncertainty, and increasing airline schedule buffers.

This article presents a model for the economic value of extra capacity at an airport. The model is based on a series of functional relationships linking the benefits of extra capacity and the associated costs. It takes into account the cost of delay for airlines and its indirect consequences on the airport, through the loss or gain of aeronautical and non-aeronautical revenues. The model is highly data-driven and to this end a number of data sources have been used. In particular, special care has been used to take into account the full distribution of delay at the airports rather than its average only. The results with the simple version of the model show the existence of a unique maximum for the operating profit of the airport in terms of capacity. The position of this maximum is clearly dependent on the airport and also has an interesting behaviour with the average number of passenger per aircraft at the airport and the predictability of the flight departure times. In addition, we also show that there exists an important trade-off between an increased predictability and the punctuality at the airport. Finally, it is shown that a more complex behavioural model for passengers can introduce several local maxima in the airport profit and thus drive the airport towards suboptimal decisions.

In ATM systems, the massive number of interacting entities makes it difficult to identify critical elements and paths of disturbance propagation, as well as to predict the system-wide effects that innovations might have. To this end, suitable metrics are required to assess the role of the interconnections between the elements and complex network science provides several network metrics to evaluate the network functioning. Here we focus on centrality and causality metrics measuring, respectively, the importance of a node and the propagation of disturbances along links. By investigating a dataset of US flights, we show that existing centrality and causality metrics are not suited to characterise the effect of delays in the system. We then propose generalisations of such metrics that we prove suited to ATM applications. Specifically, the new centrality is able to account for the temporal and multi-layer structure of ATM network, while the new causality metric focuses on the propagation of extreme events along the system.

We consider the simplified model of strategic allocation of trajectories in the airspace presented in a previous publication. Two types of companies, characterized by different cost functions, compete for allocation of trajectories in the airspace. We study how the equilibrium state of the model depends on the traffic demand and number of airports. We show that in a mixed population environment the equilibrium solution is not the optimal at the global level, but rather than it tends to have a larger fraction of companies who prefer to delay the departure time rather taking a longer routes. Finally we study the evolutionary dynamics investigating the fluctuations of airline types around the equilibrium and the speed of convergence toward it in finite populations. We find that the equilibrium point is shifted by the presence of noise and is reached more slowly., Comment: 20 pages, 13 figures

Networks of elastic beams can deform either by stretching or bending of their members. The primary mode of deformation (bending or stretching) crucially depends on the specific details of the network architecture. In order to shed light on the relationship between microscopic geometry and macroscopic mechanics, we characterize the structural features of networks which deform uniformly, through the stretching of the beams only. We provide a convenient set of geometrical criteria to identify such networks, and derive the values of their effective elastic moduli. The analysis of these criteria elucidates the variability of mechanical response of elastic networks. In particular, our study rationalizes the difference in mechanical behavior of cellular and fiber networks., Comment: v2 version of arXiv:0805.4712 was misplaced, as it correponds to a different work and different publication from v1 and v3 versions. This new submission correponds to the work originally published in arXiv:0805.4712v2

In this paper we present a simulator allowing to perform policy experiments relative to the air traffic management. Different SESAR solutions can be implemented in the model to see the reaction of the different stakeholders as well as other relevant metrics (delays, safety, etc). The model describes both the strategic phase associated to the planning of the flight trajectories and the tactical modifications occurring in the en-route phase. An implementation of the model is available as open-source and freely accessible by any user. More specifically, different procedures related to business trajectories and free-routing are tested and we illustrate the capabilities of the model on airspace implementing these concepts. After performing numerical simulations with the model, we show that in a free-routing scenario the controllers perform less operations although they are dispersed over a larger portion of the airspace. This can potentially increase the complexity of conflict detection and resolution for controllers. In order to investigate this specific aspect, we consider some metrics used to measure traffic complexity. We first show that in non-free-routing situations our simulator deals with complexity in a way similar to what humans would do. This allows us to be confident that the results of our numerical simulations relative to the free-routing can reasonably forecast how human controllers would behave in this new situation. Specifically, our numerical simulations show that most of the complexity metrics decrease with free-routing, while the few metrics which increase are all linked to the flight level changes. This is a non-trivial result since intuitively the complexity should increase with free-routing because of problematic geometries and more dispersed conflicts over the airspace.

We present a stylized model of the allocation of resources on a network. By considering as a concrete example the network of sectors of the airspace, where each node is a sector characterized by a maximal number of simultaneously present aircraft, we consider the problem of air companies competing for the allocation of the airspace. Each company is characterized by a cost function, weighting differently punctuality and length of the flight. We consider the model in the presence of pure and mixed populations of types of airline companies and we study how the equilibria depends on the characteristics of the network., Comment: 13 pages, 6 pages

We show that the European airspace can be represented as a multi-scale traffic network whose nodes are airports, sectors, or navigation points and links are defined and weighted according to the traffic of flights between the nodes. By using a unique database of the air traffic in the European airspace, we investigate the architecture of these networks with a special emphasis on their community structure. We propose that unsupervised network community detection algorithms can be used to monitor the current use of the airspaces and improve it by guiding the design of new ones. Specifically, we compare the performance of three community detection algorithms, also by using a null model which takes into account the spatial distance between nodes, and we discuss their ability to find communities that could be used to define new control units of the airspace., Comment: 22 pages, 14 figures

The rigidity of a network of elastic beams crucially depends on the specific details of its structure. We show both numerically and theoretically that there is a class of isotropic networks which are stiffer than any other isotropic network with same density. The elastic moduli of these \textit{stiffest elastic networks} are explicitly given. They constitute upper-bounds which compete or improve the well-known Hashin-Shtrikman bounds. We provide a convenient set of criteria (necessary and sufficient conditions) to identify these networks, and show that their displacement field under uniform loading conditions is affine down to the microscopic scale. Finally, examples of such networks with periodic arrangement are presented, in both two and three dimensions.