# UAV Cluster-Assisted Task Offloading for Emergent Disaster Scenarios
## 3 System Model
### Computational Process Model  
First, the computational task of ground user \(g\) is described as \(J_{g}(t)=(M_{g}(t),T_{g}(t))\), where \(M_{g}(t)\) denotes the data size of the task and \(T_{g}(t)\) denotes the deadline of the task. If the current task cannot be completed within the specified deadline, it will be considered a failed execution. Define \(s_{g}\) to denote the number of CPU cycles required to execute each bit of data for the task of user \(g\). It is used to describe the complexity of the task. Next, the variable \(\left\{0\leq\lambda_{g2}(t)\leq\lambda_{g1}(t)\leq 1\right\}\) is defined to denote the proportion of data offloaded by the task, where \(\lambda_{g1}(t)\) denotes the proportion of ground user \(g\) that offloads part of the task data \(M_{g}(t)\) to UAV \(u\), and \(\lambda_{g2}(t)\) denotes the proportion of data that UAV \(u\) forwards to other UAVs \(u^{\prime}\) for collaborative computation from the part of the task data offloaded by ground user \(g\). Then the proportion of task data performed locally by the ground user device is \(1-\lambda_{g1}(t)\), the proportion of tasks offloaded to UAV \(u\) is \(\lambda_{g1}(t)-\lambda_{g2}(t)\), and the proportion of tasks forwarded from UAV \(u\) to UAV \(u^{\prime}\) is \(\lambda_{g2}(t)\). The calculation process of task offloading is divided into two parts, which are local calculation by ground user devices and UAV cluster-assisted offloading calculation. (1) Local calculation: The computation of the task is conducted by the ground user device itself, and the size of the task data it needs to compute is \((1-\lambda_{g1}(t))M_{g}(t)\), then the local computation delay of the ground user \(g\) can be expressed as:  
\[T_{g}^{loc}(t)=\frac{(1-\lambda_{g1}(t))}{f_{g}}s_{g}M_{g}(t), \tag{3}\]  
where \(f_{g}\) denotes the number of CPU cycles per second that the ground user device can process. Therefore, the local computing energy consumption of the ground user is:  
\[E_{g}^{loc}(t)=\mu_{1}(f_{g})^{3}T_{g}^{loc}(t), \tag{4}\]  
where \(\mu_{1}\) is the effective switching capacitance associated with the chip architecture of the device itself [33]. (2) UAV cluster-assisted offloading calculation: Usually, the communication channels between UAV clusters and ground user devices are modeled as large-scale and small-scale fading. However, in the scenario considered in this paper, the channel between the UAV cluster and ground users is usually dominated by the line-of-sight component, and the communication link has a strong line-of-sight range, so the effect of small-scale fading can be negligible. Therefore, the channel gain between the UAV \(u\) and ground user \(g\) at moment \(t\) can be expressed as:  
\[h_{u,g}(t)=h_{0}\bigg{(}\sqrt{\big{\|}L_{u}(t)-L_{g}(t)\big{\|}^{2}+h^{2}} \bigg{)}^{-2}, \tag{5}\]  
where \(h_{0}\) is the average path gain at a reference distance of 1 meter and \(h\) is the UAV flight height. Assuming that the communication between the UAV and the ground user always uses \(P\) as the transmit power, the instantaneous communication rate between the UAV \(u\) and the ground user \(g\) is expressed as:  
\[r_{u,g}(t)=B\log_{2}\biggl{(}1+\frac{Ph_{u,g}(t)}{\sigma^{2}}\biggr{)}, \tag{6}\]  
where \(B\) denotes the available bandwidth. \(\sigma\) denotes the thermal noise power, which is linearly proportional to the assigned bandwidth. Similarly, the channel gain between the UAVs in the cluster can be obtained as:  
\[h_{u^{\prime},u}(t)=h_{0}\biggl{(}\sqrt{\left\|L_{u^{\prime}}(t)-L_{u}(t) \right\|^{2}+h^{2}}\biggr{)}^{-2}. \tag{7}\]  
The communication rate between UAVs is:  
\[r_{u^{\prime},u}(t)=B\log_{2}\biggl{(}1+\frac{Ph_{u^{\prime},u}(t)}{\sigma^{2 }}\biggr{)}. \tag{8}\]  
We assume that the offloading behavior of ground user devices follows an offloading policy at each moment, where ground users perform task offloading at the beginning of each time slice.