# UAV Cluster-Assisted Task Offloading for Emergent Disaster Scenarios
## 3 System Model
### Computational Process Model
Therefore, it is assumed that each ground user can select at most one UAV for data transmission in each time slice, so the transmission scheduling should satisfy the following constraints:  
\[\sum_{u=1}^{U}\alpha_{g,u}(t)\leq 1,\quad\forall t,g, \tag{9}\]  
where \(\alpha_{g,u}(t)\) is a binary variable indicating the task offload state of ground user \(g\) at moment \(t\). If \(\alpha_{g,u}(t)=1\), it means that at moment \(t\) ground user \(g\) offloads the task data to UAV \(u\) for assisted computation, otherwise it is 0. In other words, each ground user can offload the task to at most one UAV. Due to the large amount of computationally intensive task data, a single UAV may not be able to store it entirely and needs to forward part of the task data to other UAVs in the cluster for collaborative computation. Therefore, this paper assumes that in each time slice, UAV \(u\) can only forward the computational tasks offloaded by ground user \(g\) to one other UAV \(u^{\prime}\), so the UAV forwarding policy needs to satisfy the following constraints:  
\[\sum_{u^{\prime}=1}^{U}\beta_{g,u,u^{\prime}}(t)\leq 1,\quad\forall t,g,u, \tag{10}\]  
where \(\beta_{g,u,u^{\prime}}(t)\) are binary variables, \(\beta_{g,u,u^{\prime}}(t)=1\) if the UAV \(u\) forwards its own task data, and \(\beta_{g,u,u^{\prime}}(t)=0\) if the computation of the task is conducted by it independently. Since the amount of uploaded data for computationally intensive tasks is much larger than that for the return transmission of computation results, the delay and energy consumed for the return transmission of computation results through the downlink are ignorable. Therefore, the total transmission delay of introducing the UAV cluster for assisted task-offloading consists of two parts: the transmission delay of the ground user \(g\) to offload the task data to the UAV \(u\) on the one hand, and the transmission delay of the UAV \(u\) to forward the task data to the UAV \(u^{\prime}\) on the other hand. Thus, the total transmission delay of UAV-assisted task offloading can be expressed as follows:  
\[T_{g,u,u^{\prime}}^{trans}(t)=\alpha_{g,u}(t)\biggl{[}\frac{\bigl{(}\lambda_{g 1}(t)-\lambda_{g2}(t)\bigr{)}M_{g}(t)}{r_{u,g}(t)}+\beta_{g,u,u^{\prime}}(t) \frac{\lambda_{g2}(t)M_{g}(t)}{r_{u^{\prime},u}(t)}\biggr{]}. \tag{11}\]The computational delay is similarly composed of the processing delay of the UAV \(u\) and the processing delay of the UAV \(u^{\prime}\), denoted as follows:  
\[T^{com}_{g,u,u^{\prime}}(t)=\frac{\left(\lambda_{g1}(t)-\lambda_{g2}(t)\right)}{ f_{g,u}}s_{g}M_{g}(t)+\frac{\lambda_{g2}(t)}{f_{u,u^{\prime}}}s_{g}M_{g}(t), \tag{12}\]  
where \(f_{g,u}\) denotes the computational resources acquired by ground user \(g\) from UAV \(u\) and \(f_{u,u^{\prime}}\) denotes the computational resources acquired by UAV \(u\) from UAV \(u^{\prime}\). Therefore, the total delay of the UAV cluster-assisted task offload is the sum of transmission delay and computation delay, expressed as follows:  
\[E_{g}^{loc}(t)=\mu_{1}(f_{g})^{3}T_{g}^{loc}(t), \tag{4}\]0  
The total energy consumption generated is:  
\[E_{g}^{loc}(t)=\mu_{1}(f_{g})^{3}T_{g}^{loc}(t), \tag{4}\]1  
where \(\mu_{2}\) denotes the effective capacitance switch of the UAV CPU. Therefore, the total task processing delay of the ground user \(g\) can be expressed as:  
\[E_{g}^{loc}(t)=\mu_{1}(f_{g})^{3}T_{g}^{loc}(t), \tag{4}\]2  
The total task processing energy consumption consists of three components: ground user local computation energy consumption, UAV cluster-assisted task-offloading energy consumption, and flight energy consumption, denoted as:  
\[E_{g}^{loc}(t)=\mu_{1}(f_{g})^{3}T_{g}^{loc}(t), \tag{4}\]3