## 3 System Model  
We consider a square region consisting of a set of MDs, represented by \(\mathbb{D}=\{1,2,3,\ldots,M\}\), and a set of UAVs, denoted by \(\mathbb{U}=\{1,2,3,\ldots,N\}\). Other notations used in the system model are in Table 1. \begin{table}
\begin{tabular}{c c} \hline
**Notation** & **Description** \\ \hline \(M,\mathbb{D}\) & Number and set of MDs \\ \(N,\mathbb{U}\) & Number and set of UAVs \\ \(A_{i,j}\) & User association between the \(i\)th MD and the \(j\)th UAV–MEC server \\ \(\lambda_{i}\) & Task request rate of MD \(i\) \\ \(\mathbf{i}_{i}\) & Input data size (in bytes) of each task of MD \(i\) \\ \(\lambda_{min}\lambda_{max}\) & Minimal, maximal values of task request \\ \(t_{min}t_{max}\) & Minimal, maximal values for the task data size \\ \([x_{i},y_{i},0]\) & Coordinates of the \(i\)th MD \\ \([x_{j}(t),y_{j}(t),h]\) & Coordinates of the \(j\)th UAV–MEC server \\ \(T\) & Cycle period of UAV–MEC server’s ellipsoidal trajectory \\ \(C_{x,j}\) & X-coordinate center of the \(j\)th UAV–MEC server’s ellipsoidal path \\ \(C_{y,j}\) & Y-coordinate center of the \(j\)th UAV–MEC server’s ellipsoidal path \\ \(R_{x,j}\) & Major radius of the \(j\)th UAV–MEC server’s ellipsoidal path \\ \(R_{y,j}\) & Minor radius of the \(j\)th UAV–MEC server’s ellipsoidal path \\ \(\dot{\theta}_{j}\) & Rotation angle in the \(j\)th UAV–MEC server’s ellipsoidal path \\ \(r_{i,j}\) & Ground distance \\ \(d_{i,j}(t)\) & 3D distance between MD \(i\) and UAV–MEC server \(j\) \\ \(PL_{LoS}\) & Path loss of line-of-sight link \\ \(PL_{LoS}\) & Path loss of non-line-of-sight link \\ \(P(LoS)\) & Probability of line-of-sight link \\ \(P(NLoS)\) & Probability of non-line-of-sight link \\ \(a,b\) & Propagation environment constants \\ \(c\) & Speed of light \\ \(f\) & Carrier frequency \\ \(\eta_{\text{LOS}}\eta_{\text{NLoS}}\) & Additional loss for LoS and NLoS propagation modes \\ \(\omega\) & Elevation angle between MD and UAV–MEC server \\ \(PL_{ij}(t)\) & Path loss between MD \(i\) and UAV–MEC server \(j\) \\ \(h\) & Height of the UAV–MEC server \\ \(P_{i}\) & Transmit power of the MD \\ \(\sigma^{2}\) & Noise power \\ \(B\) & Channel bandwidth \\ \(SNR_{i,j}(t)\) & Signal-to-noise ratio between MD \(i\) and UAV–MEC server \(j\) \\ \(R_{i,j}\) & Average data transmission rate \\ \(T_{i,j}^{Trans}\) & Data transmission latency between MD \(i\) and UAV–MEC server \(j\) \\ \(E_{ij,j}^{Trans}\) & Energy consumption for transferring data from MD \(i\) to UAV–MEC server \(j\) \\ \(T_{j}^{total}\) & Total data transmission latency of MDs connected to UAV–MEC server \(j\) \\ \(E_{j}^{total}\) & Total transmission energy consumption of MDs connected to UAV–MEC server \(j\) \\ \(U_{j}\) & Weighted sum of transmission latency and transmission \\  & energy consumption \\ \(\rho\) & Relative weights of transmission latency and transmission energy \\  & consumption of MDs connected to UAV–MEC server \(j\) \\ \hline \end{tabular}
\end{table} 
Table 1: List of Notations. We assume the current location of the MDs is known and that each MD has computation-intensive tasks to execute. The MDs themselves, however, are unable to execute these computation-intensive tasks locally because of limited resources in processing power, memory, or energy. To address this, UAVs are utilized to enhance the delivery of MEC services to ground MDs, allowing them to use more powerful computing resources for efficient task execution. Each MD \(i\) has a task request rate \(\lambda_{i}\) (\(\lambda_{\text{min}}\leq\lambda_{i}\leq\lambda_{\text{max}}\)), and the size of the input data for each task is denoted \(\mathfrak{l}_{i}\) (\(\mathfrak{l}_{\text{min}}\leq\mathfrak{l}_{i}\leq\mathfrak{l}_{\text{max}}\)), where \(\lambda_{\text{min}},\lambda_{\text{max}}\) are the minimum and maximum task request values and \(\mathfrak{l}_{\text{min}},\mathfrak{l}_{\text{max}}\) are the minimum and maximum task data sizes. MDs transfer all their computational task requests to UAV-MEC servers for execution.