# A Semi-Random Elliptical Movement Model for Relay Nodes in Flying Ad Hoc Networks
## 2 Related Work
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  
Figure 1: Representative examples of FANET mobility model categories. Six UAV nodes are simulated, and their trajectories are visualized using different colors to distinguish their individual paths and movement behaviors. 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.