## 2 System Model and Problem Formulation
### Network Model  
As shown in Figure 1, we consider a multi-UAV-enabled MEC scenario for the IoV [33]. UAVs can provide computing and caching services for vehicles on the ground. The set of UAVs and vehicles is represented as \(\mathcal{U}=\{1,2,\ldots,u,\ldots,U\}\) and \(\mathcal{N}=\{1,2,\ldots,n,\ldots,N\}\), respectively. Since the take-off and landing times of UAVs are very short, and the energy consumption during these processes is minimal, we can ignore both the time and energy consumption involved in the UAVs' takeoff and landing. For simplicity, it is assumed that the capacity of the wireless backhaul link from the BS to each UAV is equal to \(R_{b}\). In our paper, we adopt the 3D Cartesian coordinate system to represent the positions of UAVs and vehicles. We divide time transmitted from the vehicle to the UAV into a set of discrete time slots \(\mathcal{T}=\{1,2,\ldots,t,\ldots,T\}\), and the size of each time slot is \(\tau\). Thus, the location of UAV \(u\) at time slot \(t\) is denoted as \(\mathbf{I_{u}}(t)=(X_{u}(t),Y_{u}(t),Z_{u}(t))\). The location of vehicle \(n\) at the time slot \(t\) is represented as \(\mathbf{I_{n}}(t)=(X_{u}(t),Y_{u}(t),0)\). We assume that the velocity of the \(u\)-th UAV at time slot \(t\) is denoted by \(V\) and each vehicle \(n\), \(n\in N\), in the \begin{table}
\begin{tabular}{l l} \hline \hline
**Notation** & **Description** \\ \hline \(\mathcal{U}\) & Set of UAVs \\ \(\mathcal{N}\) & Set of vehicles \\ \(\mathcal{T}\) & Set of time slots \\ \(\mathbf{I_{u}}(t)\) & UAV \(u\)’s location at time \(t\) \\ \(\mathbf{I_{n}}(t)\) & Vehicle \(n\)’s location at time \(t\) \\ \(V\) & UAV \(u\)’s instantaneous speed at time \(t\) \\ \(d_{\min}\) & Minimum safe distance between UAVs \\ \(H_{\min}\) & Minimum flight altitude \\ \(H_{\max}\) & Maximum flight altitude \\ \(s_{n}^{d}(t)\) & Task size of vehicle \(n\) \\ \(c_{n}^{d}(t)\) & CPU cycles for task \(n\) \\ \(f_{n}\) & Computation resource of vehicle \(n\) \\ \(f_{u}\) & Computation resource of UAV \(u\) \\ \(a_{u,u}^{d}(t)\) & Offloading decision (V2U) \\ \(x_{u,d}(t)\) & Caching decision for program \(d\) \\ \(x_{u,k}(t)\) & Caching decision for content \(k\) \\ \(R_{n,u}(t)\) & Data transmission rate (V2U) \\ \(T_{n}(t)\) & Total task delay of vehicle \(n\) \\ \(E_{u}^{\mathrm{Hy}}\) & Flight energy consumption of UAV \(u\) \\ \(E_{u}^{\mathrm{Omp}}\) & Computation energy consumption of UAV \(u\) \\ \(E^{\max}\) & UAV \(u\)’s max energy budget \\ \(P(V)\) & Propulsion power at speed \(V\) \\ \(L_{n,u}(t)\) & Distance between vehicle \(n\) and UAV \(u\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of key notations. system generates multiple tasks \(\pi_{n}(t)\) during each time slot \(t\), \(t\in\mathcal{T}\). For UAVs, they are independent and identically distributed, follow the homogeneous Poisson point process (PPP) with density \(\lambda_{u}\), and are represented by set \(\Phi_{s}\). This modeling choice indicates that the initial position of the UAV is randomly and uniformly distributed within the service area. In the scenario studied in this paper, vehicles move along straight paths only, without considering turns or complex road conditions. This setup simplifies the vehicle motion model, allowing us to focus on the communication, computation, and caching scheduling problems during straight-line driving. This is a common simplification in initial studies before considering more complex mobility models [34]. For the multi-UAV cooperative system architecture, we consider the following UAV location constraints to ensure proper system operation:  
Safety Distance Constraint Between UAVs: The distance between each pair of UAVs \(u\) and \(v\) must be greater than or equal to the minimum safe distance dmin in all time slots:  
\[\|\mathbf{I}_{u}(t)-\mathbf{I}_{v}(t)\|\geq d_{min},\quad\forall u\
eq v, \forall t\in\mathcal{T},\forall u,v\in\mathcal{U}, \tag{1}\]  
where \(\mathbf{I}_{u}(t)\) and \(\mathbf{I}_{v}(t)\) denote the positions of UAV \(u\) and UAV \(v\) at the \(t\)-th time slot, respectively.