A Semi-Random Elliptical Movement Model for Relay Nodes in Flying Ad Hoc Networks

Abstract

This study presents a semi-random mobility model called Semi-Random Elliptical Movement (SREM), developed for relay-oriented Flying Ad Hoc Networks (FANETs). In FANETs, node distribution has a major impact on network performance, making the mobility model a critical design element. While random models offer simplicity and path diversity, they often result in unstable relay paths due to inconsistent node placement. In contrast, planned path models provide alignment but lack the flexibility needed in dynamic environments. SREM addresses these challenges by enabling nodes to move along elliptical trajectories, combining autonomous movement with alignment to the relay path. This approach encourages natural node concentration along the relay path while maintaining distributed mobility. The spatial characteristics of SREM have been analytically defined and validated through the Monte Carlo method, confirming stable node distributions that support effective relaying. Computer simulation results show that SREM performs better than general mobility models that do not account for relaying, offering more suitable performance in relay-focused scenarios. These findings suggest that SREM provides both structural consistency and practical effectiveness, making it a strong candidate for improving the realism and reliability of FANET simulations involving relay-based communication.

1. Introduction

While reliance on pre-established networks may be effective in many situations, in practice, it often encounters challenges related to deployment complexity, cost, and time consumption [1]. Particularly in unforeseen scenarios such as natural disasters, accidents, or intentional interference, existing network infrastructures are highly vulnerable and may collapse entirely. For instance, in disaster zones where communication infrastructure has been destroyed, or in combat zones where rapid network deployment is infeasible, traditional static infrastructure-based networks are rendered unusable. In this context, there is a growing demand for network solutions that require no prior installation, leading to the emergence of the Mobile Ad hoc Network (MANET) concept [2].

MANETs are a type of wireless network that are spontaneously formed, wherein mobile nodes autonomously establish and maintain communication without relying on fixed infrastructure. MANETs possess self-healing capabilities, allowing the network to recover dynamically from node or link failures [3]. These networks operate without centralized control, and each node functions simultaneously as a transmitter, receiver, and router. The defining characteristic of a MANET lies not in the type of nodes it employs, but in their ability to perform essential networking functions.

Research on MANETs predates the widespread adoption of wireless LAN technologies such as IEEE 802.11 (Wi-Fi), and numerous implementations based on the IEEE 802.11 standard have since been proposed. Notable examples include power-efficient communication control mechanisms [4], media access schemes supporting multicast functionality [5], protocol enhancements for performance optimization [6], and adaptive algorithms designed to respond flexibly to environmental changes [7].

FANET is an extension of MANET that is distinguished by its use of autonomously flying UAVs (Unmanned Aerial Vehicles) to form networks in real-time within dynamic three-dimensional space, where altitude, speed, and position constantly change [8]. These characteristics make FANETs highly promising for time-sensitive and flexible applications such as military operations [9], disaster response, surveillance [10], and reconnaissance. However, due to the high mobility of UAVs—typically flying at speeds between 30 and 460 km/h [11]—FANETs experience rapidly changing network topologies and frequent link disconnections, presenting major challenges in maintaining consistent connectivity in latency-sensitive and reliability-critical environments.

Various FANET-specific routing protocols have been proposed, but most focus on theoretical performance and lack sufficient validation in real-world conditions [12]. Given FANETs’ high-speed mobility and dynamic environments, effective communication requires not only robust routing design but also mobility models that accurately reflect UAV behavior and adapt to changing conditions [13]. As FANET applications expand, selecting appropriate mobility models for specific experimental goals is becoming increasingly important [14].

Mobility models used in FANET simulations are generally classified into four types: group-based, path-planned, time-dependent, and random-based, each designed for various application purposes [15]. Existing research has primarily focused on improving energy efficiency or supporting UAV-based search operations [16]. In contrast, research on mobility models tailored for relay-based communication—one of the core applications of FANETs—remains relatively limited. In relay network scenarios, it is crucial for nodes to remain stably distributed along communication paths; however, existing models often fail to adequately reflect such requirements in terms of spatial structure and path alignment, resulting in limitations in the accuracy of network performance evaluation.

This study proposes SREM, a mobility model suitable for FANET experiments applicable to relay networks. SREM is designed by placing waypoints along the perimeter of an ellipse, allowing UAVs to move in straight lines between each waypoint. By defining the major axis as the relay axis, nodes are naturally aligned along this path. This design enables the analysis of communication metrics in a manner well-suited for relay scenarios and adaptable to diverse environments. The main contributions of this paper are as follows: (1) the proposal of a mobility model for relay network experiments; (2) empirical analysis of node spatial distribution using the Monte Carlo method; and (3) performance comparison with existing models, demonstrating that SREM is more suitable for relay network experiments.

This paper is structured into six sections. Section 2 classifies existing mobility models used in FANET experiments into four categories and compares their respective strengths and weaknesses. Section 3 describes the design and implementation of the proposed SREM model, along with its potential applications. Section 4 analyzes the spatial distribution of nodes using numerical analysis and the Monte Carlo method. Section 5 evaluates the communication performance of SREM in comparison with existing models using the NS-3 simulator. Finally, Section 6 presents a discussion based on the overall findings and outlines future research directions by addressing the structural limitations of the current model.

2. Related Work

This section analyzes the strengths and limitations of existing mobility models to highlight the need for a new model suitable for relay-based FANET environments and to establish the rationale for proposing SREM. As shown in

Table 1. Comparison of mobility models for flying ad hoc networks.

Mobility Model Type	Purpose in      Simulation	Representative Models	Experimental Use Cases	Strengths	Limitations
Group-based	Collaborative flight, swarm, leader-based movement	RPGM, CLMN, ECR	Measure group cohesion, link stability, collision avoidance	Well-suited for formation flying, robust to internal coordination	Not suitable for individual relay testing
Planned path	Mission-oriented scanning or patrol with fixed routes	PPRZM, MG	Evaluate coverage uniformity, path efficiency	Realistic mission replication, predictable node paths	Inflexible for dynamic path reconfiguration
Time-dependent	Realistic inertia-based directional change	GM, ST	Analyze path continuity, delay fluctuation, connectivity maintenance	Captures motion realism, useful for inertia-based aircraft	Lacks path customization for targeted relay zones
Random	Baseline testing, exploratory mobility patterns	RW, RWP, RD	Test routing resilience, assess distribution randomness	Simple to implement, supports wide variability	Poor realism, lacks communication path alignment

, existing FANET mobility models are categorized into four major types, each possessing its own unique advantages and drawbacks [17].

Group-based models are well-suited for simulating scenarios in which multiple UAVs operate cooperatively in formation or swarm configurations. These models are particularly effective in FANET applications that require coordinated group behavior, such as military missions, multi-UAV reconnaissance, and collaborative area coverage tasks.

The Reference Point Group Mobility (RPGM) model, as shown in Figure 1a, has each node follow a group leader with random deviations. This model is suitable for scenarios such as military operations and disaster response [18]. The Column (CLMN) model describes UAVs advancing along a reference line while oscillating or rotating around it, making it well-suited for linear-area scanning tasks such as agricultural monitoring [19]. The Exponential Correlated Random (ECR) model captures the movement of UAV swarms using an exponentially correlated probability function, enhancing collision avoidance and link stability, and it is appropriate for large-scale UAV formation [20].

These group-based models are highly effective for analyzing inter-node distance maintenance, group cohesion, and intra-group link stability [21]. They are frequently used to evaluate collective mobility behaviors or to measure communication retention within coordinated swarms. However, since UAVs move as part of a formation, it is difficult to simulate autonomous path selection or relay path alignment for individual nodes.

Planned path mobility models involve UAVs repeatedly following predefined trajectories and are commonly used in applications such as reconnaissance, surveillance, environmental monitoring, and mission-oriented data collection. Since UAV movement paths are predetermined, these models offer high trajectory predictability, along with strong repeatability and spatial uniformity. As a result, they are highly advantageous for quantitative simulation experiments, such as coverage analysis, scan evaluation, and path efficiency measurement.

A representative example is the Paparazzi model (PPRZM), shown in Figure 1b, in which UAVs repeatedly fly along a fixed path. This model is optimized for systematically covering specific areas [22]. Another example is the Manhattan Grid (MG) model, illustrated in Figure 1c, where UAVs move vertically or horizontally along a grid structure modeled after urban road networks, with random direction selection at each intersection [23]. This model is suitable for industrial FANET applications, such as urban communications.

Planned path models offer high repeatability and predictability, making them effective for experiments focused on reconnaissance or area coverage. However, their fixed trajectories limit flexibility in generating diverse scenarios. Therefore, integration with more adaptable mobility structures is required to support dynamic network optimization [24].

Time-dependent mobility models determine a UAV’s current state based on its previous velocity and direction, thereby preventing abrupt changes in trajectory or speed. This structure effectively simulates the inertia-driven flight characteristics of UAVs and provides advantages over purely random models by preserving trajectory continuity, enabling gradual directional changes, and producing more realistic movement patterns. As a result, such models are particularly useful in FANET simulations for accurately evaluating path persistence, delay variation, and the duration of inter-node connectivity.

A representative example in this category is the Gauss–Markov (GM), in which a node’s velocity and direction are updated through a linear combination of its previous state and a random component [25]. The structure is shown in Figure 1d, and it is well-suited for experimentally simulating various UAV maneuvering scenarios by flexibly adjusting the balance between randomness and continuity [26]. Another notable model is the Smooth Turn (ST), which features a structure where UAVs rotate or change direction around a reference point, generating smoother trajectories by considering vertical acceleration [27]. In the ST model, UAVs periodically change direction with exponentially distributed wait times, making it suitable for simulating mobility in IoT-integrated networks [28].

Time-dependent models such as these are effective for experimental objectives involving connectivity maintenance, delay performance evaluation, and continuous path generation in FANETs [29]. However, they present limitations when applied to scenarios requiring node alignment along relay paths or the deliberate placement of relay nodes.

Random-based mobility models determine the direction and speed of node movement probabilistically at each time step. Due to their simplicity and flexibility in configuring various experimental conditions, these models are among the most widely used foundational types in FANET simulations.

Representative examples include the Random Walk (RW) model, a memoryless model in which nodes move by selecting a random direction and speed at each time step [30]. The Random Waypoint (RWP) model, as illustrated in Figure 1e, allows nodes to randomly choose a destination, pause upon arrival, and then repeat the process, creating an alternating pattern of movement and idleness [31]. In the Random Direction (RD) model, nodes select a destination on the boundary of the simulation area, stop upon reaching it, and then randomly choose a new destination again [32].

Random-based models are widely used in the early stages of FANET experiments and in evaluating the performance of routing algorithms. They offer the advantage of generating unbiased node distributions and enabling a wide range of relative positions, making them suitable for experiments such as propagation speed analysis and traffic capacity evaluation [33]. However, the resulting trajectories are inadequate for modeling specific experimental scenarios.

One approach proposed to address the structural limitations of purely random models is the Semi-Random Circular Movement (SRCM) model. SRCM is designed to balance randomness with structured mobility. As shown in Figure 1f, it enables nodes to semi-randomly select start and end points along the arc of a circular trajectory within a fixed radius and to move accordingly [34].

SRCM enables the model to preserve the diversity of random movement while ensuring more uniform coverage across the entire area. Unlike simple random models, SRCM can be effectively applied to purpose-driven experiments such as scanning. Moreover, compared to path-based models that enforce repetitive trajectories, it offers the advantage of generating a wider variety of experimental scenarios. However, while SRCM is effective for scanning-oriented experiments, it has limitations in FANET scenarios requiring relay path alignment, making it unsuitable for relay-based communication experiments.

3. SREM Model

3.1. Design of SREM

As discussed in Section 2, existing mobility models are not well-suited for relay-based network experiments. To address this gap, we propose the the SRCM model. While SREM retains SRCM’s core strength—balancing structured repetition with random mobility—it is modified to better suit relay-centric FANET scenarios. The structural design of SRCM proves effective for scanning-oriented applications. However, due to its constraint of circular trajectories, SRCM is limited in its ability to naturally align nodes along linear paths, such as those between a source and destination. SREM replaces the circular trajectory with an elliptical one, allowing the spatial distribution of nodes to naturally align along the relay axis. This design modification makes SREM well-suited for relay-centric FANET experiments.

As illustrated in Figure 2, the SREM model defines the major axis of the ellipse along the straight line connecting the source and destination nodes, positioning the center of the ellipse at the midpoint of this communication path. In the context of this study, we refer to this straight-line path as the relay axis, which serves as the primary geometric reference for UAV movement and packet forwarding.

Within the SREM framework, multiple nodes are assumed to rotate counterclockwise around the center O of a two-dimensional elliptical space $\Omega$, which has a major axis length of $2a$ and a minor axis length of $2b$. The values of a and b can be configured depending on the simulation objectives. By aligning the elliptical trajectory with the relay axis, the model promotes a natural spatial distribution of UAV nodes along the intended communication route, thereby enhancing connectivity and facilitating efficient relay operations in FANET scenarios.

All nodes are assumed to fly at a fixed altitude, and takeoff and landing phases are excluded from the simulation. Each node $n_i$ is initially positioned at $P_i^{\left(0\right)}=(x_i^{\left(0\right)},y_i^{\left(0\right)})$, and its location can be expressed in Cartesian coordinates according to the equation of an ellipse, as follows:

$$x_i^{\left(0\right)}=a·cos\left({\theta }_i^{\left(0\right)}\right),y_i^{\left(0\right)}=b·sin\left({\theta }_i^{\left(0\right)}\right)$$

(1)

Here, ${\theta }_i^{\left(0\right)}$ denotes the initial angle. Each node selects its next destination $P_i^{\left(1\right)}$ randomly within a defined angular range along its initial elliptical trajectory $E_i^{\left(0\right)}$ and moves in a straight line toward that point with velocity $v_i$. After completing one full revolution along the elliptical path, the node selects a new elliptical trajectory $E_i^{\left(1\right)}$, defined by a different pair of semi-major and semi-minor axes while keeping the center O fixed, and repeats the same movement process. During this transition, the node adjusts its radial position toward the center before entering the new trajectory.

The conventional SRCM model assumes that UAVs move continuously along a circular path with a constant angular velocity $\omega$. However, in the case of elliptical movement, the curvature varies depending on the location along the ellipse. Under constant angular velocity, the distance traveled per unit time is not uniform—nodes travel farther per angular increment along the major axis and shorter along the minor axis. This leads to longer residence times in the minor-axis regions, resulting in an imbalanced spatial distribution that does not reflect realistic UAV navigation dynamics.

In practice, UAV platforms generally operate based on linear speed, covering a fixed distance over a given time. This distance-based speed control is also standard in widely used simulation frameworks such as NS-3, PX4, and ArduPilot [35,36]. Accordingly, the SREM model in this study adopts a constant linear speed assumption, rather than constant angular velocity. Furthermore, unlike SRCM, where UAVs move continuously along a curve, SREM constructs mobility paths by randomly selecting points on the ellipse and connecting them via straight-line segments. This approach provides the following advantages:

• Similarity to real-world navigation: UAVs typically follow straight-line paths using waypoint-based navigation, which aligns with the proposed structure.
• Spatial control with flexible routing: Elliptical boundaries constrain movement, while diverse waypoint combinations enable adaptable paths.
• Simplified analysis: Straight-line movement simplifies distance calculation, relay assessment, and path optimization.

Therefore, SREM functions as a high-precision mobility model that is well-suited to both real-world UAV operations and simulation frameworks, enhancing the overall reliability and applicability of FANET simulations.

Table 2. Comparison between SRCM and SREM mobility models.

Feature	SRCM [34]	SREM (Proposed)
Trajectory shape	Circular path	Elliptical path
Movement style	Curved movement along circular arc	Straight-line movement between random points on the ellipse
Node speed	Constant angular velocity ($\omega$)	Constant linear velocity (v)
Position bias	None	None
Purpose	Uniform area surveillance	Relay alignment along the relay axis
Flexibility	Limited control over spatial distribution	Directional density adjustable via ellipse parameters

presents a comparative summary of the SRCM model and the proposed SREM model, highlighting the key differences discussed above.

3.2. Implementation of SREM

In the SREM model, the major axis of the ellipse is aligned with the relay path, and UAVs move in straight lines between randomly selected points along the ellipse boundary. This point-to-point movement pattern naturally produces a relay-centric node distribution, while the elliptical boundary serves as a structural constraint that defines the UAVs’ operational space. To ensure uniform coverage of the entire area, the SREM model periodically adjusts the size of the ellipse after a fixed number of movements, preventing nodes from remaining confined to a single elliptical trajectory. This approach helps maintain a balance between randomness and structural constraints while enhancing spatial diversity.

As outlined in Algorithm 1, each UAV begins by randomly selecting an initial angular position on the elliptical boundary, then it determines a new target angle and moves in a straight line toward the corresponding point. This procedure is repeated throughout the simulation to maintain spatial diversity and prevent pattern stagnation. The algorithm incurs minimal computational overhead, as each UAV performs a small set of operations—namely, generating random angles and computing their corresponding coordinates via trigonometric functions. These steps are executed in constant time per UAV, yielding a per-node computational complexity of $𝒪\left(1\right)$. Consequently, for a network of N UAVs operating concurrently, the total computational complexity per iteration scales linearly as $𝒪\left(N\right)$, making the algorithm efficient and well-suited for simulating large-scale FANET scenarios.

Algorithm 1: SREM implementation algorithm.

Figure 3 visualizes the distribution of node trajectories across different simulation steps under the proposed SREM model. In (a), only 10 steps are performed, and each UAV travels in straight lines between randomly selected points on the ellipse boundary, forming relatively constrained paths within a limited area. In (b), after 50 steps, the nodes begin to cover a broader region of the ellipse, resulting in more diverse trajectory patterns and a denser spatial distribution. Finally, (c) shows the distribution after 200 steps, where the trajectories of each node are uniformly spread across the entire elliptical area. This demonstrates that SREM is a model that effectively combines structured repetitive linear movement, relay-centric spatial alignment, and spatial diversity.

3.3. Application of SREM

SREM is a mobility model optimized for scenarios where relay-based communication is essential. By aligning the major axis of an ellipse with the straight line connecting the source and destination and guiding UAVs to move semi-randomly along the elliptical path, SREM naturally concentrates relay nodes along the relay route. This enables SREM to provide more structured node alignment than random models and greater flexibility than path-based models. Such a configuration enhances the probability of maintaining relay paths, making it well-suited for realistic relay-based FANET experiments.

Key parameters of SREM—such as the semi-major and semi-minor axes $(a,b)$, angular range $\theta$, and velocity v—can be tuned to flexibly control the degree of concentration along the communication path, the spatial distribution range, and the frequency of trajectory shifts. These structural features distinguish SREM from the SRCM model, which was more suitable for coverage-oriented uniform distribution analysis, and they position SREM as a more appropriate model for controlling relay node distribution and optimizing communication performance in FANET simulations.

Beyond its application in relay-centric FANET simulations, the SREM model is also highly effective for adaptive modeling in irregular spatial diffusion scenarios. For instance, in maritime search-and-rescue operations where the estimated location of a distress target expands elliptically due to currents and wind, SREM can be used to align the major axis of the ellipse with the central search line (e.g., between the last known and predicted locations). By deploying FANET drones along the elliptical trajectory, the search effort can be concentrated along the most probable path, maximizing coverage efficiency with limited resources.

Similarly, in disaster situations such as rapidly spreading wildfires or toxic gas leaks, SREM enables strategic deployment by aligning the major axis of the ellipse with the primary direction of hazard propagation. FANET drones can be densely positioned at the forward edge of the spread to ensure fast data collection and real-time monitoring while maintaining a naturally dispersed layout in the rear area to optimize resource allocation.

In summary, SREM serves not only as a mobility model optimized for evaluating communication-path alignment in FANETs but also as a flexible tool for adaptive FANET coverage planning that reflects physical environmental changes. By leveraging the geometric properties and mathematical tractability of ellipses, SREM enhances both the scalability and precision of FANET deployment strategies across various application domains, including maritime search, disaster response, and perimeter surveillance.

4. Node Distribution in SREM

4.1. Numerical Analysis

The SREM model is a mobility framework designed to effectively induce node density aligned along the communication path in FANET environments. Each node moves in straight lines between two points located on the boundary of an ellipse. Given an ellipse with semi-major axis $a>0$ and semi-minor axis $b>0$, the position of a node on the boundary can be parameterized by an angular value $\theta \in [0,2\pi )$. The n-th waypoint of UAV i is thus defined as $P_i^{\left(n\right)}=\left(acos{\theta }_i^{\left(n\right)},bsin{\theta }_i^{\left(n\right)}\right)$. At each time interval, the UAV selects the next waypoint $P_i^{(n+1)}$ and moves at constant speed along a straight line from $P_i^{\left(n\right)}$ to $P_i^{(n+1)}$.

To theoretically approximate node density along the elliptical path in SREM, we consider the infinitesimal arc length:

$$ds\left(\theta \right)=\sqrt{a^2{sin}^2\theta +b^2{cos}^2\theta }d\theta$$

(2)

Assuming uniform angular motion, UAVs tend to cluster in regions where the arc length is shorter. Thus, the node density is inversely proportional to the arc length, leading to the following approximation: $\rho \left(\theta \right)\propto {\displaystyle \frac{1}{ds\left(\theta \right)}}.$ This implies higher node concentration near the endpoints of the major axis ($\theta =0,\pi$) and lower density near the minor axis ($\theta ={\displaystyle \frac{\pi }{2}},{\displaystyle \frac{3\pi }{2}}$), supporting SREM’s design objective of aligning mobility patterns with the relay path. Although this provides a rough estimate of node distribution, more accurate modeling would require incorporating detailed mathematical formulations and additional parameters.

To obtain an accurate probability estimate, the probability density function $f_{XY}(x,y)$, which represents the likelihood that a node is located at a specific position $(x,y)$, is defined as the cumulative contribution of all possible linear trajectories that pass through that point. This formulation leads to the following double integral expression:

$$f_{XY}(x,y)\propto {\int }_0^{2\pi }{\int }_0^{2\pi }\mathrm{Ind}\left[(x,y)\in \overline{P_i^{\left(n\right)}{P}_i^{(n+1)}}\right]·{\displaystyle \frac{1}{∥\overline{P_i^{\left(n\right)}{P}_i^{(n+1)}}∥}}·{\displaystyle \frac{1}{L^2}}d{\theta }_i^{(n+1)}d{\theta }_i^{\left(n\right)}$$

(3)

• $\mathrm{Ind}\left[(x,y)\in \overline{P_i^{\left(n\right)}{P}_i^{(n+1)}}\right]$: An indicator function that returns 1 if the point $(x,y)$ lies on the line segment $\overline{P_i^{\left(n\right)}{P}_i^{(n+1)}}$, and 0 otherwise.
• ${\displaystyle \frac{1}{∥\overline{P_i^{\left(n\right)}{P}_i^{(n+1)}}∥}}$: A weighting factor inversely proportional to the segment length, reflecting that UAVs spend more time on shorter paths.
• ${\displaystyle \frac{1}{L^2}}$: A normalization constant assuming that departure and arrival angles are independently and uniformly sampled along the elliptical perimeter L.

However, due to the inclusion of the indicator function and the double integral over all possible line segments, this formulation presents significant analytical challenges. Deriving a closed-form expression for the spatial distribution at a given point becomes intractable. A similar structure is observed in the SRCM model, where a UAV selects departure and destination points randomly along a circular trajectory and moves at a constant speed. For the circular case, an approximate closed-form probability density function in polar coordinates can be derived as follows:

$$f_{XY}(x,y)=\mu \left\{2{\pi }^2{(r-x^2-y^2)}^2+4\pi \sqrt{r-(x^2+y^2)}-{\displaystyle \frac{5}{2}}arctan\left({\displaystyle \frac{y}{x}}\right)-{\left[arctan\left({\displaystyle \frac{y}{x}}\right)\right]}^2\right\}$$

(4)

However, as illustrated in Figure 4, the actual visualized distributions exhibit numerical instability, including asymmetry and distortion near the center or boundary—deviating from the ideal circular symmetry. This can be attributed to the numerical instability caused by the $arctan(y/x)$ term, which fluctuates sharply near $x\approx 0$, as well as the limitations introduced by mathematical simplifications such as constant normalization factors and the omission of time-based weighting.

As a result, both SREM and SRCM models face intrinsic limitations when it comes to analytically deriving or precisely interpreting their distribution functions. To overcome these challenges and better understand the actual node density characteristics, we used the Monte Carlo method. By repeatedly sampling node trajectories under various combinations of initial angles ${\theta }_i^{\left(0\right)}$ and angular increments $\delta$, we statistically estimate the frequency of node occurrence at each spatial location.

4.2. Empirical Node Distribution

The SREM model is based on straight-line movements between waypoints defined along the boundary of an ellipse. While the node distribution can theoretically be described using a probability density function, the complexity introduced by the indicator function and the double integral renders closed-form analytical solutions practically intractable. To address this limitation and gain empirical insight into the actual distribution characteristics, we analyze the distribution tendencies of relay nodes under the SREM model using the Monte Carlo method.

Figure 5 visualizes the node distribution results obtained by repeatedly sampling UAV trajectories generated between randomly selected departure points ${\theta }_i^{\left(n\right)}$ and arrival points ${\theta }_i^{(n+1)}={\theta }_i^{\left(n\right)}+\delta$, where $\delta \in \left[{\displaystyle \frac{\pi }{6}},{\displaystyle \frac{\pi }{2}}\right]$, along the elliptical boundary. In this experiment, the size of the ellipse was fixed to ensure consistency in node scale, and all trajectories were constrained to a single elliptical path. This setup clearly revealed the spatial tendency of node avoidance near the center and concentration toward the boundary.

To quantitatively analyze the spatial distribution of nodes, we define the midpoint (M) of each straight-line segment representing the UAV’s movement as a representative location. The distance between this midpoint and the center of the ellipse (O) is then normalized by the semi-major axis length a, resulting in a normalized radial distance variable $r_{\mathrm{norm}}$, defined as follows:

$$r_{\mathrm{norm}}={\displaystyle \frac{\parallel M-O\parallel }{a}},\mathrm{where}M={\displaystyle \frac{1}{2}}(P_i^{\left(n\right)}+P_i^{(n+1)})$$

(5)

This variable serves as a quantitative measure of how far each trajectory lies from the center of the ellipse, and it enables consistent comparison across different elliptical scales. The interval $r_{\mathrm{norm}}\in [0,1]$ was uniformly divided, and for each subinterval, the number of segments whose midpoints fell within that range was counted to generate a histogram representing the distribution.

Although using the midpoint of each segment as a representative node location is a simplified approximation, it is theoretically valid under the assumptions of the SREM model, in which UAVs travel at constant speeds along linear trajectories. Since each segment corresponds to a UAV’s position over a fixed period of time, and the velocity is uniform, the segment’s spatial contribution serves as an unbiased estimator of node density [37]. Under the assumption of uniform temporal and spatial distribution, this approach is statistically sound. When a sufficiently large number of segments is sampled, the histogram based on the normalized radial distance variable $r_{\mathrm{norm}}$ functions as a practical statistical indicator that captures the overall bias and concentration tendencies of node distribution.

Figure 6 visualizes the distribution of segment midpoints’ normalized distances from the ellipse center under varying angular increment ranges $\delta$ in the SREM model. Each subplot illustrates how the values of $r_{\mathrm{norm}}$ change depending on the range of $\delta$ used when UAVs determine their next waypoint. In (a), a relatively large angular increment $\delta \in \left[{\displaystyle \frac{\pi }{6}},{\displaystyle \frac{\pi }{2}}\right]$ is applied. Even under this setting, most midpoints do not pass through the center but remain distributed along the ellipse boundary.

As the angular increment range narrows—as shown in (b) with $\delta \in \left[{\displaystyle \frac{\pi }{12}},{\displaystyle \frac{\pi }{6}}\right]$, and in (c) with $\delta \in \left[{\displaystyle \frac{\pi }{24}},{\displaystyle \frac{\pi }{12}}\right]$—the UAV trajectories increasingly adhere to the elliptical path and avoid the center, favoring the outer regions. In particular, subplot (c) reveals a clear distinction in concentration along the major and minor axes, with the center region remaining largely vacant. This numerically confirms the center-avoidance tendency that is structurally embedded within the SREM model.

These simulation-based distribution results empirically support that the SREM model effectively induces dense node alignment along the communication axis in FANET relay scenarios while simultaneously avoiding congestion in the central area, as intended by its design.

5. Performance Evaluation

5.1. Simulation Setup

To evaluate the performance of the proposed SREM model, simulations were conducted using the NS-3 network simulator. The simulation environment was configured as a two-dimensional plane of size $1000\times 1000{\mathrm{m}}^2$, in which a total of 50 UAV nodes were deployed to fly at a fixed altitude. Each UAV was equipped with a communication range of 100 m and assigned a movement speed within the range of 20 to $40\mathrm{m}/\mathrm{s}$. The total simulation duration was 100 s, and to assess variability in mobility behavior, each scenario was executed 10 times. The three mobility models compared were RWP, SRCM, and the proposed SREM.

In the simulation setup, the source node was fixed at coordinate $(0,500)$, located on the left edge of the area, and the destination node was fixed at $(1000,500)$, on the right edge. Since the distance between the two nodes exceeded the communication range, multi-hop relay paths through intermediate UAV nodes were required. The objective of this experiment was to compare the effectiveness of each mobility model in forming relay paths and delivering packets in such a scenario. The key simulation parameters used in this study are summarized in

Table 3. Simulation parameters.

Parameter	Value
Simulation tool	NS-3
Environment size	$1000\times 1000{\mathrm{m}}^2$
Number of UAVs	50
Mobility model	SREM, SRCM, RWP
SREM ellipse (a, b)	$a=500\mathrm{m},b=250\mathrm{m}$
SRCM maximum radius	500 m
RWP pause time	1 s
RWP speed	40 m/s
Source node location	$(0,500)$
Destination node location	$(1000,500)$
Routing protocol	AODV
Traffic model	Constant Bit Rate (CBR)
Traffic type	TCP
Packet size	64 bytes
CBR rate	1 Mbps
HELLO interval	100 ms
MAC protocol	IEEE 802.11a
Antenna type	Omni-directional
UAV velocity	20∼40 m/s
Simulation runtime	100 s

.

All UAV nodes utilized the Ad hoc On-Demand Distance Vector (AODV) routing protocol, dynamically establishing routes through route discovery messages. Packets were discarded if no route could be established, and key performance metrics—including packet delivery ratio, end-to-end delay, and average hop count—were measured accordingly.

Traffic was generated using a Constant Bit Rate (CBR) model, in which the source node transmitted 100 packets of 64 bytes each at a rate of 1 Mbps. The MAC layer was based on the IEEE 802.11a standard, and all UAVs were equipped with omnidirectional antennas. HELLO messages were broadcast every 100 ms. The traffic type was configured as TCP.

In the SREM model, the straight line connecting the source and destination nodes was designated as the major axis of the ellipse, with the center of the ellipse positioned at the center of the simulation area, $(500,500)$. The semi-major and semi-minor axes were set to $a=500\mathrm{m}$ and $b=250\mathrm{m}$, respectively. Each UAV selected two random points on the elliptical boundary and traveled in a straight line between them.

In the RWP model, each UAV randomly selected a destination within the simulation space and moved toward it in a straight line. Upon reaching the target, the UAV paused for one second before immediately selecting a new destination and repeating the process. Initial positions were randomly assigned without synchronization among nodes. In the SRCM model, UAVs selected random start and end points along the boundary of a circle with a maximum radius of $500\mathrm{m}$ and moved along the corresponding circular arc.

To comprehensively evaluate communication stability and efficiency in a FANET environment, the simulation performance assessment was conducted using the following five key metrics:

• Packet Delivery Ratio (PDR): The ratio of packets successfully delivered to the destination.
• Throughput: The total amount of valid data received per unit time.
• Connection Time (CT): The average duration during which two nodes remain within communication range and maintain a valid routing path simultaneously.
• End-to-End Delay (EED): The time it takes for a packet to travel from the source to the destination.
• Hop Count: The number of hops required for a packet to reach its destination.

These quantitative metrics were used to analyze the overall ability of each mobility model to provide stable and efficient relay-based communication in the FANET environment.

5.2. Simulation Results

To clearly present the simulation results, this section provides a quantitative comparison of the relative performance of the three mobility models—SREM, SRCM, and RWP—based on key performance metrics. All simulations were conducted under identical environmental settings and repeated ten times to ensure statistical reliability. The analysis focused on core communication indicators, including PDR, throughput, EED, connection time, and average hop count. A summary of the overall results is presented in

Table 4. Simulation performance of mobility models.

Mobility Model	PDR [%]	EED [s]	Throughput [KB/s]	CT [s]	Hop Count
SREM	91.3	0.061	110.3	23.8	11.2
SRCM	81.4	0.089	98.1	18.1	14.5
RWP	51.7	0.175	61.0	10.4	21.7

.

Figure 7 illustrates the PDR results measured over ten simulation runs for the three mobility models: SREM, SRCM, and RWP. The SREM model consistently maintained a PDR above 90% across all trials, exhibiting both the highest delivery rate and the lowest variability. This performance is attributed to its path-aligned design, which concentrates node movement along the communication axis, thereby minimizing link breakages and sustaining stable relay connections.

The SRCM model demonstrated generally good performance, with PDR values ranging between approximately 75% and 85%, though some variability was observed across runs. While its circular trajectory provides uniform coverage, the lack of alignment with the communication axis likely caused occasional instability in relay paths.

The RWP model showed the lowest and most unstable performance among the three, with PDR fluctuating widely between below 30% and up to 70% depending on the trial. This outcome is primarily due to RWP’s fully random, memoryless mobility pattern, which results in frequent route changes, increased hop counts, link disconnections, and higher packet loss.

The differences in PDR performance are directly reflected in the observed throughput results. The SREM model achieved an average throughput of approximately 110 KB/s, significantly outperforming the other two models under identical simulation conditions. In contrast, the SRCM model recorded about 98 KB/s, while the RWP model demonstrated a considerably lower throughput of around 61 KB/s. This indicates that RWP not only suffers from reduced packet delivery but also exhibits a substantial degradation in overall network data-handling capacity.

Despite all three models operating with the same number of UAVs, within the same simulation area, and under identical speed and communication parameters, SREM consistently achieved the highest throughput. This outcome suggests that the performance gains are not due to differences in network capacity but rather stem from SREM’s path-aligned mobility structure, which enables more stable and efficient relay link formation. In essence, these results demonstrate that even when using the same network resources, structural differences in mobility design can lead to significant variations in performance—highlighting the practical advantages of path-centric relay mobility models in FANET environments.

Figure 8 compares the average EED among the three mobility models: SREM, SRCM, and RWP. The SREM model consistently maintained a very low EED, averaging approximately 0.06 s, with minimal variance across trials, indicating strong temporal consistency. This performance is attributed to the model’s elliptical mobility structure, which aligns node movement along the communication axis and enables more efficient path formation. Consequently, SREM achieved an average hop count of 11.2, contributing to its reduced delay.

The SRCM model exhibited a slightly higher average EED of around 0.09 s, though it remained generally stable. This is likely due to the model’s circular trajectory, which ensures a baseline level of coverage and route availability but lacks alignment with the communication axis. This misalignment occasionally leads to suboptimal relay paths, as reflected in its average hop count of 14.5.

In contrast, the RWP model showed the highest EED, averaging approximately 0.18 s, with the greatest variation among trials. The random and non-deterministic nature of RWP often results in frequent link breaks and repeated route discoveries, degrading the overall consistency of relay network. Its average hop count was 21.7—the highest among the three models.

Connection time, defined as the average duration for which a link between UAVs remains valid, is a key metric for evaluating communication stability in FANETs. The simulation results demonstrate that the differences in mobility structures and alignment strategies across the models lead to substantial variations in average connection time.

The SREM model, which guides UAVs along elliptical trajectories aligned with the communication axis, inherently induces orbital overlap among nodes and results in prolonged periods of contact within communicable ranges. Simulation results demonstrate that SREM achieved the highest average connection time of approximately 23.8 s, indicating its superior capability in maintaining persistent links in FANET environments.

In contrast, the SRCM model, though based on structured circular motion, lacks explicit alignment with the communication axis. While it facilitates occasional node encounters due to its repeated orbital nature, its average connection time was measured at around 18.1 s—lower than SREM—highlighting the limitations of its trajectory structure in sustaining long-term links.

The RWP model exhibited the shortest average connection time, approximately 10.4 s. Due to its random, memoryless movement characteristics, frequent link disruptions and re-establishments were observed. This volatility in node positions and density over time makes it difficult to maintain stable communication paths, leading to reduced link persistence and increased transmission uncertainty.

These findings underscore the importance of structurally aligned mobility models for achieving stable communication in FANET scenarios. Unlike models that merely ensure coverage or path diversity, SREM’s design prioritizes relay-oriented alignment, resulting in higher packet delivery rates, shorter paths, and more persistent connections. Collectively, the results validate SREM as an effective mobility model optimized for relay-based UAV communication networks.

Although this study provides a quantitative evaluation of the SREM model’s communication performance using the NS-3 simulator, numerical results may differ when implemented in other simulation platforms such as PX4 or ArduPilot. These discrepancies can arise from variations in physical-layer modeling, control architectures, and system-level constraints. Factors such as actuator delays, sensor noise, and hardware limitations can influence observed outcomes. Nonetheless, the theoretical analysis of node distribution and the structured properties of the elliptical trajectory presented in this paper offer strong support that SREM is inherently well-suited for relay-centric FANET communications, independent of the simulation environment.

5.3. Sensitivity Analysis of Key SREM Parameters

To evaluate the robustness and adaptability of the proposed SREM model, we conducted a sensitivity analysis focusing on three key parameters: the semi-major axis length a, the aspect ratio $b/a$, and the angular increment $\delta$. Each parameter governs the spatial structure and movement behavior of UAV nodes, which directly affects the model’s performance in relay-based FANET scenarios.

We conducted a sensitivity analysis of the semi-major axis parameter a while maintaining a fixed aspect ratio of $b/a=0.5$. As shown in Figure 9, communication performance varies noticeably depending on the geometric configuration of the elliptical trajectory.

When $a=500\mathrm{m}$, the SREM model achieves optimal performance in terms of PDR, EED, and CT. This is because the major axis of the ellipse aligns exactly with the 1000 m straight-line path between the source and destination nodes, with the center of the ellipse located at $(500,500)$. Such geometric alignment increases the concentration of UAVs along the relay route, enabling efficient packet delivery with fewer hops and lower delay. In contrast, values of a shorter or longer than 500 m either constrain node distribution or disperse it excessively, weakening relay availability and degrading overall communication performance.

An analysis of the aspect ratio $b/a$ of the ellipse revealed that optimal communication performance—measured in terms of PDR, EED, and CT—was achieved when $b/a\approx 0.4$. This ratio provides an effective balance between path alignment and vertical dispersion, preventing excessive node clustering near the center while maintaining strong alignment with the relay axis. When $b/a$ is smaller than 0.4, nodes tend to concentrate excessively around the center, limiting coverage. Conversely, when $b/a$ exceeds 0.4, the elliptical shape approaches a circle, causing nodes to disperse too widely from the main relay path, which degrades connectivity and transmission efficiency.

Lastly, we analyzed the effect of the angular increment $\delta \in [{\theta }_{min},{\theta }_{max}]$, which determines the spacing between waypoints along the elliptical path, on communication performance. The experiment was conducted using three angular ranges: $\left[{\displaystyle \frac{\pi }{6}},{\displaystyle \frac{\pi }{2}}\right]$, $\left[{\displaystyle \frac{\pi }{12}},{\displaystyle \frac{\pi }{6}}\right]$, and $\left[{\displaystyle \frac{\pi }{24}},{\displaystyle \frac{\pi }{12}}\right]$. Although smaller angular increments result in tighter adherence to the elliptical trajectory, they did not lead to meaningful differences in key performance indicators such as PDR, EED, and CT. Extremely small increments may reduce path diversity and limit adaptability in dynamic environments, while excessively large increments can disrupt trajectory consistency. Therefore, the angular increment should be configured to balance path alignment and route diversity.

6. Conclusions

This study introduced the SREM model, a mobility framework tailored to enhance relay-centric communication in FANETs. By aligning the major axis of an ellipse with the intended communication path and guiding UAVs to move between randomly selected points along the elliptical boundary, SREM achieves an effective balance between randomness and structural alignment. A Monte Carlo-based empirical analysis confirmed that this approach naturally concentrates nodes along the relay path, forming stable communication routes.

Simulation results conducted in NS-3 demonstrated that SREM consistently outperformed existing mobility models across key performance metrics, including PDR, EED, and CT. These findings underscore SREM’s suitability for structured relay-based communication scenarios and its value in repeatable and controlled simulation experiments.

However, the structured nature of SREM also introduces inherent limitations. The model’s trajectory rigidity restricts its adaptability in dynamic environments, making it less appropriate for swarm-based cooperative tasks or scenarios requiring precise inter-UAV synchronization. Moreover, SREM does not incorporate essential real-world UAV constraints such as collision avoidance, flight dynamics, or acceleration limits—factors critical for practical deployment. As a result, while SREM serves as a powerful tool for evaluating relay communication under idealized conditions, its direct applicability to real-world operations remains constrained.

Recent advancements in edge computing and lightweight deep learning models have enabled real-time visual-based trajectory adaptation and anomaly detection using UAV-mounted sensors [38]. Future research should focus on integrating such edge-intelligent control capabilities into the SREM framework, allowing UAVs to dynamically adjust their paths in response to changing environments. Furthermore, in swarm-based network scenarios involving cooperative UAV operations, extending SREM to support distributed decision-making and collaborative control could establish it as a foundational mobility framework for next-generation FANET systems [39].