# Flight allocation in flight-centric air traffic control: A MILP model approach

Andreas Guitart, Daniel Delahaye

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Andreas Guitart, Daniel Delahaye. Flight allocation in flight-centric air traffic control: A MILP model approach. International Air Transportation Research and Development Symposium, Eurocontrol FAA, Jun 2025, Prague (République Tchèque), Czech Republic. hal-05128499

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# Flight allocation in flight-centric air traffic control: A MILP model approach

Andréas Guitart and Daniel Delahaye

OPTIM

Ecole Nationale de l'Aviation Civile
Toulouse, France

andreas.guitart@enac.fr, daniel@recherche.enac.fr

**Abstract**—This study addresses flight allocation in a flight-centric air traffic management framework using two Mixed-Integer Linear Programming (MILP) models. The first model minimizes maximum complexity to balance workload, while the second minimizes interactions between flights assigned to different controllers. Tests over the Brest airspace show that the first model, despite achieving workload balance, leads to impractical allocations by assigning distant, non-interacting flights to the same controller. The second model, though more operationally feasible, results in workload imbalances, with some controllers managing high-complexity traffic while others remain underloaded. Despite this limitation, it better preserves spatial coherence and allows for fast adjustments to traffic changes. Future work should integrate conflict detection and resolution to optimize allocations while considering real-time controller actions.

**Keywords**—flight allocation; MILP model; flight-centric; controller schedule

## I. INTRODUCTION

Air Traffic Management (ATM) is undergoing significant transformation, driven by research initiatives such as the NextGen program of the United States Government Accountability Office [16] and the Single European Sky ATM Research (SESAR) program [4]. These programs aim to overhaul ATM to increase the capacity of Air Traffic Control (ATC) services through advanced automation, enabling efficient management of the anticipated growth in air traffic ([15]).

A key innovation in this area is the development of Trajectory-Based Operations (TBO) ([11]). TBO seeks to address the imbalance between airspace capacity and demand during strategic planning while minimizing the need for reactive decision-making by ATC during tactical operations. To support this, new tools are being developed, as showcased at the Global TBO Symposium organized by Eurocontrol in Brussels in June 2024 [3]. These tools facilitate the end-to-end management of flights from origin to destination, leveraging Time-Based Management (TBM), System-Wide Information Management (SWIM) for sharing aeronautical, meteorological, and flight data, and aircraft capabilities to fly precise four-dimensional trajectories (3D+T).

The introduction of TBO is expected to enhance the predictability of air traffic operations, leading to increased flight efficiency, reduced airline costs, minimized environmental impact, expanded airspace capacity, and improved airport throughput—all contributing to reduced delays. At the tactical level, TBO has inspired the concept of Flight Centric ATC (FCA), which reimagines airspace configuration and the roles of ATC personnel ([18]). FCA eliminates the traditional division of airspace into fixed sectors, replacing it with traffic-oriented divisions, creating more uniform structures across larger airspace regions ([9]). Several studies have already been carried out on the FCA concept to optimize operations [8, 12, 17].

Conventional air traffic control operates using a sector-based approach, where the airspace is divided into sectors, each managed by two air traffic controllers (ATCOs). As an aircraft moves through conventional airspace, it typically crosses multiple sectors and is handed over from one controller to another. In contrast, the flight-centric approach eliminates the division of airspace into sectors. Instead, ATCOs collectively manage the entire airspace, and each aircraft entering this airspace is assigned to a single controller who oversees it throughout its entire journey within the flight-centric zone (see Figure 1). Coordination between controllers (either directly or via automated systems) is required to resolve potential conflicts between aircraft. Within the FCA framework, controllers are tasked with monitoring and managing specific sets of flights across extended areas. To ensure an equitable distribution of workload, flights are assigned to controller teams based on traffic characteristics and complexity. These controllers are responsible for maintaining safe separation within their assigned flights by identifying and resolving potential conflicts. Additionally, they must collaborate with other controllers to address conflicts involving flights under their respective assignments. The challenge of assigning flights to controllers has recently gained attention, with some initial, straightforward solutions already proposed to address this emerging issue ([5, 6, 7, 9]).

This work is conducted within the framework of the SESAR project HYPERSOLVER. The HYPERSOLVER project aims to advance Air Traffic Management (ATM) by proposing a significant redesign of its structural paradigm, focusing on optimizing the integration and benefits of in-
<figure><img src="image_2.png" /><figcaption>(a) Conventional air traffic control: each controller is assigned to a given sector.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>(b) Flight centric concept: each controller manages a group of aircraft.</figcaption></figure>

<caption>Figure 1: Comparison sector and flight centric</caption>

novative AI solutions. By leveraging advanced Deep Reinforcement Learning (DRL) AI agents, the project seeks to address air traffic hotspots and conflicts across multiple time horizons, from Air Traffic Flow Management (ATFM) to Air Traffic Control (ATC). This technological innovation is complemented by a strong emphasis on Human-AI collaboration, defining high-level scenarios and processes to ensure effective interaction and synergy between human operators and AI systems. Transitional steps are planned to facilitate a gradual and smooth shift from current practices to a more efficient and adaptable framework, fostering trust and enhancing decision-making while maintaining operational safety. This work consists in developing a framework for allocating flights to controllers, which will be integrated into the HYPERSOLVER system.

This paper is organized as follows: Section II introduces the two MILP models for flight allocation. Section III describes the generation of controller schedule data. Section IV presents the results of applying both models to the Brest airspace.

## II. MATHEMATICAL MODEL

This section presents two optimization models designed for flight allocation in a flight-centric ATC framework. The first aims to minimize the maximum workload of controllers, and the second minimizes the interaction between aircraft which are assigned to different controllers. The model is an iterative process in which allocations are revised as the number of available controllers evolves. As new aircraft enter the airspace, new conflicts may arise, overloading one or more controllers. Therefore, some flights must be reallocated to other controllers who may or may not already be in charge of other flights (see Figure 2). In this study, we denote by $F$, the set of flights, $C$, the set of controllers and $T$ the time step set.

<figure><img src="image_4.png" /><figcaption>(a) Traffic situation at time $t$ (b) Traffic situation at time $t+1$</figcaption></figure>

<caption>Figure 2: Controller allocation change: the new flights imply reallocation to a new controller.</caption>

### A. Decision variables

At each time step $t \in T$, a new model is created from the new traffic situation. For each controller $c \in C$ and each flight $f \in F$ we define $x_{c,f}$ the binary decision variable corresponding to whether the flight $f$ is assigned to the controller $c$. We further define for each controller $c \in C$ and each flight $f \in F$, $y_{c,f}$ the binary variable representing whether the affection has changed. And finally, we define $w^{\max}$ a continuous variable that represents the maximum controller workload.

### B. Constraints

The first constraint is that each flight is assigned to one and only one controller. It can be written as follows:

$$ \sum_{c \in C} x_{c,f} = 1 \qquad f \in F. \qquad (1) $$

The second constraint is to limit the number of flights assigned to a controller. It is defined as follows:

$$ \sum_{f \in F} x_{c,f} \leq n^{f,\max} x_{c,t} \qquad c \in C, \qquad (2) $$

where $x_{c,t}$ indicates if the controller $c$ is available and $n^{f,\max}$ is maximum number of flights that can be assigned to a controller. The final constraint is to limit the workload of each controller by minimizing the maximum complexity of
controllers ($w^{\max}$). The maximum is linearized using the following constraints:

$$ \sum_{f \in F} s_{f,t} x_{c,f} \leq w^{\max} \quad c \in C, \quad (3) $$

where $s_{f,t}$ is the control score (complexity) of a flight $f$ that represents the level of difficulty to control this flight.

In the context of operational control, our goal is to identify a workload metric that accurately quantifies the difficulty experienced by air traffic controllers in managing a group of aircraft within a region of interest. This complexity metric is solely determined by the geometry of the trajectories, $\Gamma$, in the controlled area, as well as the uncertainties in positions, speeds, and future locations of the aircraft. It serves as an approximation of the challenge controllers face when managing air traffic. The complexity, $w_p$, associated with the discretized spatiotemporal positions, $p \in \mathbb{R}^4$, along a trajectory $\gamma \in \Gamma$, corresponds to the complexity of the region of interest surrounding the position $p$. Numerous metrics have been developed, some based on aircraft convergence [2], others on dynamical systems [1]. More recently, a geometrical metric has been proposed to evaluate the total conflict duration with continuous time uncertainties [13]. This metric is used in this study to evaluate the score $s_{f,t}$ of a flight $f$ at a time $t$.

### C. Objective functions

The objective function is composed of two different criteria. The first is the minimization of the maximum workload assigned to controller temas $w^{\max}$ and the second is the minimization of the allocation changes. The second criterion can be written as follows:

$$ \sum_{c \in C} \sum_{f \in F} |x_{c,f} - x_{c,f}^{\text{last}}|, \quad (4) $$

where $x_{c,f}^{\text{last}}$ indicates if the flight $f$ was allocated to the controller $c$ at the previous time step. To linearize the model, the binary variables $y_{c,f}$ are introduced and the following constraints are added:

$$ y_{c,f} - x_{c,f} \geq -x_{c,f}^{\text{last}} \quad c \in C, f \in F, \quad (5) $$

and

$$ y_{c,f} + x_{c,f} \geq x_{c,f}^{\text{last}} \quad c \in C, f \in F. \quad (6) $$

To summarize, the objective function can be written as follows:

$$ w^{\max} + \alpha \sum_{c \in C} \sum_{f \in F} y_{c,f} x_{c,t}, \quad (7) $$

where $\alpha$ is a penalty value representing the impact of an allocation change.

This model is an initial representation of the allocation problem. However, as it is written, it can assign very distant aircraft to the same controller even though they do not interact with each other. On the other hand, some aircraft in close proximity could be allocated to two different controllers. This is why we propose a new model that takes into account the interactions between aircraft.

### D. New model

In this new model, we keep the variables $x_{c,f}$ and $y_{c,f}$ and the associated constraints 1, 2, 5 and 6. We introduce the set $F^{(2)} = \{(f_1, f_2) \in F^2, f_1 \neq f_2\}$. The new variables are the following: for each controller $c \in C$ and flights $(f_1, f_2) \in F^{(2)}$, $x_{c,f_1, f_2}$ a binary variable representing whether $f_1$ and $f_2$ are assigned to the same controller $c$. These new variables impose constraints 9b, 9c and 9d. Flight allocation is also constrained by a maximum distance $d^{\max}$. If two flights $f_1$ and $f_2$ are allocated to the same controller, the average distance $d_{f_1, f_2}^{\text{mean}}$ during the time period must be less than $d^{\max}$ (Constraint 9e). Maximum workload $w^{\max}$ is no longer an objective but a constraint (9f). The metric used to evaluate this workload is the same as in the previous model.

To define the new objective function, we need to define the interaction $i_{f_1, f_2}$ between two flights $f_1$ and $f_2$. The interaction between two aircraft is the complexity of the two aircraft without considering the rest of the traffic. This interaction is evaluated using the complexity metric of the previous model.

The conflict duration sensitivity [13] to heading maneuvers with continuous time uncertainty is the total conflict duration for heading maneuvers between $-\Psi$ and $\Psi$, integrating all possible positions of aircraft $f_1$ and $f_2$ around the reference with a constant speed and a continuous time uncertainty:

$$ i_{f_1, f_2} = \int_{-\Psi}^{\Psi} \mathcal{T}_{f_1, f_2}(\psi) \, d\psi, \quad (8) $$

where $\mathcal{T}_{f_1, f_2}(\psi)$ is the integral for a specific heading change and equals:

$$ \mathcal{T}_{f_1, f_2}(\psi) = kT(z(\bar{u})) - kT(z(\underline{u})), $$

where $k$ is the conflict duration's ellipse area divided by $\pi$, $z(\underline{u})$ (resp. $z(\bar{u})$) is linked to the minimal (resp. maximal) time uncertainty and:

$$ T(z) = \begin{cases} 0 & \text{if } z \le -1 \\ \frac{2+z^2}{3}\sqrt{1-z^2} + z\frac{\pi}{2} + z \arcsin(z) & \text{if } z \in (-1, 1) \\ \pi z & \text{if } z \ge 1 \end{cases} $$

More details about this metric may be found in [13].

Consequently, the new model can be written:

$$ \min_x \sum_{(f_1, f_2) \in F^{(2)}} i_{f_1, f_2} \left( 1 - \sum_{c \in C} x_{c, f_1, f_2} \right) + \alpha \sum_{c \in C} \sum_{f \in F} y_{c, f} x_{c, t} \quad (9a) $$

subject to:

$$ x_{c,f_1, f_2} \leq x_{c,f_1} \quad (f_1, f_2) \in F^{(2)}, c \in C \quad (9b) $$

$$ x_{c,f_1, f_2} \leq x_{c,f_2} \quad (f_1, f_2) \in F^{(2)}, c \in C \quad (9c) $$

$$ x_{c,f_1, f_2} + 1 \geq x_{c,f_1} + x_{c,f_2} \quad (f_1, f_2) \in F^{(2)}, c \in C \quad (9d) $$

$$ d_{f_1, f_2}^{\text{mean}} \leq d_{f_1, f_2}^{\text{max}} x_{c, f_1, f_2} + M(1 - x_{c, f_1, f_2}) \quad (f_1, f_2) \in F^{(2)}, c \in C \quad (9e) $$
$$ \sum_{f \in F} s_{f,t} x_{c,f} \le w^{\max} \qquad c \in C \quad (9f) $$

$$ x_{c,f} \in \{0, 1\} \qquad c \in C, f \in F \quad (9g) $$

$$ x_{c,f_1, f_2} \in \{0, 1\} \qquad (f_1, f_2) \in F^{(2)}, c \in C \quad (9h) $$

$$ y_{c,f} \in \{0, 1\} \qquad c \in C, f \in F \quad (9i) $$

### III. CONTROLLER SCHEDULE GENERATION

As the controllers' schedule is not known, we propose to generate our scenario taking into account the constraints of working time and breaks, as well as the minimum number of controllers required. To generate this scenario, we propose to solve an optimization problem. For each controller $c \in C$ and each time $t \in T$, we define $x_{c,t}$ the binary variable corresponding to whether controller $c$ works at time $t$. We further define for each controller $c \in C$, $x_c$ the binary variable representing whether the controller $c$ works on this day. To model working hours, we have assumed that controllers have two work slots with a minimum break in between. To specify these working times, we therefore introduce for each controller $c$ and each time $t \in T$, the binary variables $y_{c,t}^1$ and $y_{c,t}^2$ corresponding to the beginning of the first and second working periods respectively. In this model, the objective is to minimize the number of controllers who work this day. The model can be written as follows:

$$ \min_{x} \sum_{c \in C} x_c \qquad (10a) $$

subject to:

$$ \sum_{c \in C} x_{c,t} \ge n^{\min} \qquad t \in T \quad (10b) $$

$$ \sum_{t \in T} y_{c,t}^1 = x_c \qquad c \in C \quad (10c) $$

$$ \sum_{t \in T} y_{c,t}^2 = x_c \qquad c \in C \quad (10d) $$

$$ \sum_{\tau=t}^{t+t^w-1} x_{c,\tau} \ge t^w y_{c,t}^1 \qquad t \in T, c \in C \quad (10e) $$

$$ \sum_{\tau=t}^{t+t^w-1} x_{c,\tau} \ge t^w y_{c,t}^2 \qquad t \in T, c \in C \quad (10f) $$

$$ \sum_{t \in T} x_{c,t} \le |T| x_c \qquad c \in C \quad (10g) $$

$$ \sum_{\tau=0}^{t+t^w+t^r} (1 - y_{c,\tau}^2) \ge (t + t^w + t^r) y_{c,t}^1 \qquad c \in C, t \in T \quad (10h) $$

$$ \sum_{t \in T} x_{c,t} \le 2t^w \qquad c \in C \quad (10i) $$

$$ x_c \in \{0, 1\} \qquad c \in C \quad (10j) $$

$$ x_{c,t} \in \{0, 1\} \qquad c \in C, t \in T \quad (10k) $$

$$ y_{c,t}^1 \in \{0, 1\} \qquad c \in C, t \in T \quad (10l) $$

$$ y_{c,t}^2 \in \{0, 1\} \qquad c \in C, t \in T \quad (10m) $$

Constraint 10b ensures a minimum number of controllers $n^{\min}$ for each time $t \in T$. Constraints 10c and 10d link the variables $y_{c,t}^1$ and $y_{c,t}^2$ with $x_c$ to ensure that if the controller is not on duty ($x_c = 0$), all $y_{c,t}^1$ and $y_{c,t}^2$ are set to zero and if he is working there is a single start time for each work slot. Constraints 10e and 10f impose a continuous working time of $t^w$ for the two work slots. Constraint 10g links the variables $x_{c,t}$ with $x_c$. Constraint 10h imposes a minimum rest time of $t^r$.

## IV. RESULTS

### A. Case study

We propose to test our algorithm on the Brest control center in France on June 1, 2023. 1634 aircraft trajectories have been simulated from flight plans (see Figure 3).

<figure><img src="image_5.png" /><figcaption>Figure 3: Brest airspace trajectories.</figcaption></figure>

Table I shows the input parameters of the study. Using this data and the proposed controller planning generation model, a schedule of 90 controllers is generated. The working hours are based on French practices [14] and can be adapted to any working system. In all simulations, the allocations are updated every 20 minutes. The computer used for the experiments is equipped with an Intel Core-i9 processor, with 64 Go RAM. The resolution of our optimization problem formulation is made using the MIP solver Gurobi, version 11.0.0 with Java API [10]. The computation time for each allocation update ranges from a few milliseconds in the case with few aircraft to around 15 seconds in the extreme case with almost 100 aircraft.

<table><caption>TABLE I. Input parameters</caption><thead><tr><th rowspan="2">Parameters</th><th colspan="3">Data generation</th><th colspan="2">Resolution</th></tr><tr><th>n<sup>min</sup></th><th>t<sup>w</sup> (min)</th><th>t<sup>r</sup> (min)</th><th>d<sup>max</sup> (NM)</th><th>w<sup>max</sup></th></tr></thead><tbody><tr><td>Value</td><td>10</td><td>120</td><td>40</td><td>100</td><td>w<sup>total</sup>/150</td></tr></tbody></table>

### B. Model comparison

The first test evaluates the initial model, which focuses solely on minimizing the maximum complexity across controllers. Figure 4 illustrates traffic situations alongside the corresponding controller allocations generated by solving
this model. In this figure, aircraft positions are represented by lines, where colors indicate altitude, and the assigned controller is denoted by a number. If the controller number is displayed in red, it means that the allocation has changed compared to the previous time step.

A key observation from Figure 4 is that the initial model induces frequent reallocations to redistribute workload among controllers, ensuring a more balanced workload. However, this rebalancing comes at the cost of operational feasibility. Specifically, the allocation often results in controllers managing aircraft that are geographically dispersed and unrelated in terms of interaction. For instance, a single controller may be responsible for aircraft located in the north, south, west, and east of the airspace simultaneously (see Figure 4a), which is impractical from an air traffic management perspective.

A more striking example appears in the north of the airspace (Figure 4d), where two aircraft at the same altitude, seemingly on converging paths, are assigned to different controllers (25 and 57). Such an allocation contradicts standard operational principles, as conflict resolution typically requires the same controller to manage interacting aircraft to ensure situational awareness and efficient deconfliction. This highlights a major shortcoming of the model: while it effectively distributes workload, it disregards spatial coherence and operational constraints, making it unsuitable for real-world implementation.

Further insights can be drawn from Figure 5, which presents the total complexity and the number of flights assigned to each controller at three different time steps. As anticipated, the allocation undergoes frequent modifications to achieve a more balanced complexity distribution. However, the absence of spatial consistency in these reassignments reinforces the need for a more refined model that incorporates additional operational constraints, such as geographical continuity and local traffic interactions, to ensure practical feasibility.

The second test evaluates the performance of the second proposed model. Figure 6 presents traffic situations along with the corresponding controller allocations generated by solving this model. Unlike the first model, where controllers were assigned geographically dispersed and non-interacting aircraft, this second model exhibits a more structured and spatially coherent allocation. Specifically, flights assigned to a given controller are generally confined within a well-defined airspace region, reducing the cognitive load and improving situational awareness for air traffic controllers.

Moreover, this second model better accounts for aircraft interactions. Controllers are more likely to manage aircraft that are at the same altitude and in close proximity to one another, facilitating conflict detection and resolution. A clear example of this improvement is illustrated in Figure 6d. Unlike the first model (Figure 4d), where two aircraft on a converging path in the northern sector of the airspace were assigned to different controllers (leading to coordination challenges), the second model correctly assigns both aircraft to the same controller (N°8). This decision aligns with operational best practices, ensuring that potential conflicts are handled within a single sector without the need for inter-controller coordination.

Despite these advantages, this model introduces a new challenge: an uneven distribution of workload among controllers. Figure 7 highlights a significant disparity in complexity levels. Some controllers experience an excessive workload, managing highly complex traffic situations, while others are assigned to regions with minimal activity and near-zero complexity. This imbalance could lead to excessive strain on certain controllers, potentially impacting performance and safety, while under using others.

This outcome suggests that while the second model successfully enhances spatial coherence and operational realism, it does so at the expense of workload unbalance. To address this issue, further refinements are necessary, such as incorporating additional constraints to enforce a more balanced distribution of complexity while preserving the geographical consistency of assignments.

### C. Influence of the allocation change parameter

The third test addresses the influence of the parameter $\alpha$ on the number of controller reassignments over time. Figures 8 and 9 illustrate how the number of changes varies as a function of $\alpha$ for the first and second models, respectively.

In Figure 8, which corresponds to the first model, we observe a strong dependence on $\alpha$. Specifically, increasing $\alpha$ significantly reduces the number of controller changes. When $\alpha = 100$, reassignments become almost negligible, occurring only at the beginning and end of a controller's shift. This outcome is expected, as a higher $\alpha$ penalizes frequent changes more heavily, leading the optimization process to favor consistency in controller assignments over time. This behavior is particularly important in an operational setting, as excessive reassignments can disrupt controller workload continuity and increase coordination efforts.

Conversely, in Figure 9, which represents the second model, the effect of $\alpha$ is noticeably weaker. The number of controller changes remains relatively stable regardless of the $\alpha$ value. This can be attributed to the spatial constraints imposed in the second model. In particular, Constraint 9e enforces geographical proximity, necessitating reassignments when aircraft are too far apart. As a result, even a low $\alpha$ value is sufficient to prevent unnecessary controller switches while still allowing essential reassignments dictated by spatial constraints.

### D. Controller workload

The final analysis focuses on the relationship between controller workload, measured by the number of assigned aircraft, and complexity levels. Figure 10 presents the average number of flights per controller and the corresponding average complexity at each time step. The results indicate that, on average, a controller is responsible for fewer than 8 aircraft at any given moment, with the typical workload hovering around five aircraft per controller.

A notable observation is the presence of two distinct peaks in complexity: one occurring between 4:00 and 5:00 AM and another between 8:00 and 11:00 AM. These peaks correspond to key phases in transatlantic traffic flow—the first peak aligns with the early morning wave of inbound flights arriving from
<figure><img src="image_6.png" /><figcaption>(a) 7:39.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>(b) 7:41.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>(c) 7:59.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>(d) 8:01.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>(a) Allocation from 7:40 to 8:00.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>(b) Allocation from 8:00 to 8:20.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>(c) Allocation from 8:20 to 8:40.</figcaption></figure>

<caption>Figure 5: Complexity and number of flights for each controller at 3 time steps with the first model: several allocation changes are made to balance the workload (flight numbers assigned to the controllers are written on the red bars).</caption>
<figure><img src="image_13.png" /><figcaption>Figure 6: Traffic situations and associated allocation generated with the second model.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Figure 7: Complexity and number of flights for each controller at 3 time steps with the second model: several allocation changes are made to reduce interactions between flights allocated to different controllers (flight numbers assigned to the controllers are written on the red bars).</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>Figure 8: Number of changes at each time depending on $\alpha$ with the first model.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Figure 9: Number of changes at each time depending on $\alpha$ with the second model.</figcaption></figure>

North America, while the second peak corresponds to the high departure volume of outbound transatlantic flights.

Figure 11 further reinforces this observation by depicting the maximum number of aircraft assigned to any individual controller over time. The trends in this figure mirror those in Figure 10, reflecting the same increases in traffic volume. However, a critical difference emerges: the maximum number of controlled aircraft is frequently at its upper limit, suggesting that at least one controller is consistently operating at full capacity. Additionally, the maximum complexity is more than twice the average complexity, confirming a significant imbalance in workload distribution across controllers.

To address workload imbalance among controllers, one potential approach is to integrate the maximum complexity directly into the objective function. By explicitly penalizing high-complexity assignments, the optimization process could encourage a more even distribution of workload across controllers. However, this approach is significantly constrained by the spatial limitations imposed by the model, particularly the requirement that aircraft assigned to the same controller remain within a certain proximity.

These constraints limit the extent to which workload can be balanced because air traffic complexity is inherently space-dependent. In practice, certain regions of the airspace natu-

<figure><img src="image_17.png" /><figcaption>Figure 10: Average number of flights and average complexity for each time step (with second model).</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>Figure 11: Maximum number of flights and maximum complexity for each time step (with second model).</figcaption></figure>

rally have higher traffic density and more intricate interactions between aircraft, leading to unavoidable complexity disparities. Even under conventional air traffic control, controllers are sometimes assigned different levels of workloads because of the distribution of traffic at a given moment.

Furthermore, air traffic complexity is not just a function of the number of aircraft but also of their relative positions, flight levels, and interaction patterns. High-density clusters of converging or crossing trajectories create localized complexity hotspots that cannot always be evenly distributed among controllers.

V. CONCLUSION

This study has focused on the problem of flight allocation in a flight-centric air traffic management framework. We proposed two distinct Mixed-Integer Linear Programming (MILP) models aimed at optimizing the assignment of flights to controllers. The first model minimizes the maximum complexity assigned to any controller, with the objective of balancing workload across all controllers. The second model prioritizes minimizing interactions between flights assigned to different controllers while ensuring that flights allocated to the same controller remain within a predefined maximum distance.
Both models were tested in a realistic traffic scenario within the Brest airspace in France. The results highlight key differences between the two approaches. The first model, while effective at balancing complexity among controllers, introduces significant operational challenges. Specifically, it assigns flights that are spatially distant and do not interact to the same controller, leading to impractical allocations that increase coordination overhead and degrade situational awareness. Conversely, the second model produces more operationally feasible assignments by ensuring that flights with potential conflicts are managed by the same controller. This improves conflict resolution efficiency and better aligns with real-world air traffic control practices.

However, a notable drawback of the second model is the significant imbalance in complexity among controllers. Some controllers experience high workload levels, managing dense clusters of interacting aircraft, while others are assigned much lower complexity. Despite this imbalance, the second model remains the more promising approach, as it maintains spatial coherence in allocations and allows for rapid reassignment in response to evolving traffic conditions. This flexibility is crucial for adapting to dynamic airspace environments where traffic density and complexity fluctuate over time.

One extension to enhance this approach would be to integrate controller actions into the optimization process. One potential avenue for improvement is to connect the allocation algorithm with a conflict detection and resolution (CD&R) module. By incorporating real-time conflict information, the model could dynamically adjust assignments not only based on spatial proximity and complexity but also on the need for controllers to intervene in specific conflict scenarios.

## ACKNOWLEDGMENT

The authors would like to express their gratitude to the SESAR 3 Joint Undertaking (JU), as the software - en-compassing both the simulator and algorithm implementation was developed within the framework of HYPERSOLVER, an exploratory research project under the SESAR program. The opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not reflect the views of SESAR 3 JU.

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