## 3 Problem Formulation
### Computational Model  
In the multi-UAV Mobile Edge Computing (MEC) system, the offloading strategy adopts a partial offloading approach consistent with the single-UAV MEC system. Assume that mobile device (MD) \(l\) is served by UAV \(u\) during time slot \(t\). Let \(D_{l}(t)\) denote the total computational task volume of MD \(l\) at time slot \(t\), and let \(\alpha_{l,u}(t)\) represent the offloading ratio of tasks from MD \(l\) to UAV \(u\). Consequently, \(1-\alpha_{l,u}(t)\), \(u(t)\), represents the proportion of tasks processed locally. Thus, the local processing delay of MD \(l\) at time slot \(t\) can be expressed as  
\[t_{l,u}^{local}(t)=(1-\alpha_{l,u}(t))D_{l}(t)S/f_{md}, \tag{12}\]  
where \(S\) denotes the number of CPU cycles required to process one unit of data, and \(f_{md}\) represents the computational capability of the MD's processor.  
The processing delay for tasks offloaded from MD \(l\) to UAV \(u\) consists of two components--transmission delay and computational delay--formulated as follows:  
\[t_{l,u}^{tr}(t)=\alpha_{l,u}(t)D_{l}(t)/r_{l,u}(t), \tag{13}\]  
\[t_{l,u}^{comp}(t)=\alpha_{l,u}(t)D_{l}(t)S/f_{u}(t), \tag{14}\]  
Since the computational results generated by MEC are typically small, the transmission delay of returning results via the downlink is negligible. In Equations (6)-(11), UAV \(u\) can dynamically adjust its operating frequency using Dynamic Voltage and Frequency Scaling (DVFS) technology. The CPU frequency of UAV \(u\) at time slot \(t\), denoted as \(f_{u}^{uav}(t)\), is given by  
\[f_{u}(t)=k_{u}(t)f_{max}^{uav}, \tag{15}\]  
where \(f_{max}^{uav}\) is the maximum CPU frequency of the UAV, and \(k(t)\) is the CPU frequency adjustment factor at time slot \(t\).  
For the task volume \(D_{l}(t)\) generated by MD \(l\), the total processing delay is determined by the maximum of the local processing delay and the UAV processing delay. Therefore, the processing delay of UAV \(u\) for MD \(l\) is defined as  
\[t_{l,u}^{de}(t)=max\{t_{l,u}^{local}(t),t_{l,u}^{tr}(t)+t_{l,u}^{comp}(t)\}, \tag{16}\]  
For multiple UAVs at time slot \(t\), the overall task processing delay is determined by the maximum delay among all UAVs. Thus, the task processing delay at time slot \(t\) is defined as  
\[t^{delay}(t)=max\{t_{l,u}^{delay}(t)\},\forall u\in\{1,2,\ldots,M\}, \tag{17}\]  
The energy consumption of UAVs consists of two components: flight energy consumption and energy consumed by the MEC server during task computation. Let \(M_{uav}\) denote the mass of the UAV. At time slot \(t\), UAV \(u\) flies at a constant speed \(v(t)\in[0,v_{max}]\), with an adjustment angle \(\theta_{uav}\in[0,2\pi]\), moving from its initial position to its final position over a duration \(\tau_{fly}\). The energy consumed during this flight is given by  
\[e_{fly}(t)=\phi||v_{u}(t)||^{2}, \tag{18}\]  
where \(\phi=0.5M_{uav}\tau_{fly}\) represents the energy consumption coeffient. Additionally, the energy consumed by the MEC server of UAV \(u\) during computation is  
\[p_{u}(t)=\kappa[f_{u}(t)]^{3}, \tag{19}\]where \(\kappa\) is a constant coefficient. Therefore, the energy consumed by UAV \(u\) for computing tasks offloaded from MD \(l\) at time slot \(t\) is  
\[e_{comp}(t)=p_{u}(t)t_{l,u}^{comp}(t)=\kappa[f_{u}(t)]^{2}\alpha_{l,u}(t)D_{l}(t)S. \tag{20}\]  
Given the small data size of computational results, the energy consumption for transmitting results back to the MD is negligible [41]. Thus, the total energy consumption of UAV \(u\) at time slot \(t\) is  
\[e_{to}(t)=e_{fly}(t)+e_{comp}(t), \tag{21}\]  
In summary, the total energy consumption of all UAVs is  
\[E_{to}(t)=\sum_{t}\sum_{u}e_{to}, \tag{22}\]  
This model provides a comprehensive framework for optimizing task offloading and resource allocation in multi-UAV MEC systems, balancing both processing delays and energy consumption.