# UAV Cluster-Assisted Task Offloading for Emergent Disaster Scenarios
## 3 System Model
### UAV Mobile Model  
This paper constructs the system region as a three-dimensional right-angle coordinate system, and for computational convenience divides the time equally into \(T\) time slices, i.e., \(t\in\mathcal{T}=\{1,2,\ldots,T\}\), where the length of each time slice \(t\) is \(\xi\). Using \(L_{g}(t)=[x_{g}(t),y_{g}(t)]\) to denote the coordinates of the ground user, assuming that the UAV cluster is flying in the air at a fixed height \(h\), then the projected coordinates of the  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Notations** & **Description** \\ \hline \(G\) & Number of ground users \\ \(U\) & Number of UAVs \\ \(T\) & Number of time slices \\ \(\xi\) & The length of time slice \\ \(L_{g}\) & The coordinates of ground user \(g\) \\ \(h\) & The UAV flight height \\ \(L_{u}\) & The projected coordinates of UAV \(u\) \\ \(v_{u}\) & The horizontal flight speed of UAV \(u\) \\ \(E_{u}^{fly}\) & The propulsion energy consumption of UAV \(u\) \\ \(m_{uav}\) & The mass and load of UAV \\ \(f_{g}\) & The computational task of ground user \(g\) \\ \(M_{g}\) & The amount of task data for user \(g\) \\ \(T_{g}\) & The task deadline of user \(g\) \\ \(s_{g}\) & Number of CPU cycles per bit of data to be executed for the task of user \(g\) \\ \(\lambda_{g1}\) & The proportion of task offloads for ground users \(g\) \\ \(\lambda_{g2}\) & The proportion of ground user \(g\) tasks forwarded via UAVs \\ \(T_{g}^{loc}\) & The local computation delay of ground user \(g\) \\ \(f_{g}\) & Number of CPU cycles per second that can be processed by ground user \(g\) \\ \(E_{g}^{loc}\) & The local computing energy consumption of ground user \(g\) \\ \(\mu\) & The effective switching capacitance \\ \(h_{u,g}\) & The channel gain between UAV \(u\) and ground user \(g\) \\ \(h_{0}\) & The average path gain at a reference distance of 1 meter \\ \(P\) & The transmit power \\ \(r_{u,g}\) & The communication rate between UAV \(u\) and ground user \(g\) \\ \(B\) & The available bandwidth \\ \(\sigma\) & The thermal noise power \\ \(h_{u^{\prime},u}\) & The channel gain between UAV \(u^{\prime}\) and UAV \(u\) \\ \(r_{u^{\prime},u}\) & The communication rate between UAV \(u^{\prime}\) and UAV \(u\) \\ \(\alpha_{g,u}\) & The task offload state of ground user \(g\) \\ \(\beta_{g,u,u^{\prime}}\) & The state of ground user \(g\) forwarding tasks via UAV \\ \(T_{g,u,u^{\prime}}^{trans}\) & The transmission delay of UAV-assisted task offloading \\ \(T_{g,u,u^{\prime}}^{com}\) & The computational delay of UAV-assisted task offloading \\ \(f_{g,u}\) & The computational resources obtained by ground user \(g\) from UAV \(u\) \\ \(f_{u,u^{\prime}}\) & The computational resources obtained by UAV \(u\) from UAV \(u^{\prime}\) \\ \(T_{g,u,u^{\prime}}^{turb}\) & The total delay of UAV-assisted task offloading \\ \(E_{g,u,u^{\prime}}^{auto}\) & The total energy consumption of UAV-assisted task offloading \\ \(T_{g,u,u^{\prime}}^{total}\) & The total task processing delay of ground user \(g\) \\ \(E_{g,u,u^{\prime}}^{total}\) & The total task processing energy consumption of ground user \(g\) \\ \(d_{\min}\) & The minimum safe distance between UAVs \\ \(V_{\max}\) & The maximum flight speed of UAVs \\ \hline \hline \end{tabular}
\end{table}
Table 1: Table of notations.  
UAV on the ground at moment \(t\) can be expressed as \(L_{u}(t)=[x_{u}(t),y_{u}(t)]\). Therefore, the horizontal flight speed of the UAV in time slice \(t\) can be expressed as:  
\[v_{u}(t)=\|L_{u}(t+1)-L_{u}(t)\|/\xi. \tag{1}\]  
The primary energy overhead of the UAV in flight is the flight propulsion energy consumption, and by calculating the flight speed, the propulsion energy of the UAV in each time slice can be expressed as follows:  
\[E_{u}^{fly}(t)=k(v_{u}(t))^{2}, \tag{2}\]  
where \(k=0.5m_{uav}\xi\) and \(m_{uav}\) denotes the mass and load of the UAV.