## 5 Methodology
### Max-Min Fairness Oriented Offloading Approach
Given the potential SVs set of \(u_{0}\) as \(\mathbf{SV}=\{sv_{1},sv_{2},\ldots,sv_{K}\}\), we firstly divide \(\mathbf{SV}\) into \((2^{K}-1)\) subsets and check if the sum of the maximum acceptable offloading proportions of vehicles in each subset meets the requirement of the task \(T_{0}\). After then, we apply the Max-Min fairness allocation one by one on subsets that satisfy the required computation amount of \(T_{0}\), to determine the specific proportions that should be offloaded to vehicles in the subsets. Finally, we calculate the total price \(u_{0}\) should pay on each selected subset, and choose the one with the minimum cost as the final vehicle set to execute the computation offloading. More specifically, assume there is a vehicle set \(\mathbf{sb_{i}}\), which satisfies the requirement of task \(T_{0}\), that is \(\sum_{sv_{j}\in\mathbf{sb_{i}}}O_{j}^{max}\geq 1\), the specific Max-Min fairness oriented offloading decision process is as follows. It is observed from Equation (7) that the total delay of the computation offloading system achieves the lowest when each SV in the system has the same delay, that is \(t_{1}=t_{2}=\ldots=t_{|\mathbf{d}|}=t_{op}\), thus, we propose to use a Max-Min fairness allocation method for the multi-round task allocation. Denote \(t_{j}^{1}\) and \(t_{op}^{1}\) as the delay of vehicle \(sv_{j}\) and the optimal delay in the first round allocation, respectively. Set \(t_{1}=t_{2}=\ldots=t_{op}\), considering Equations (4)-(6) jointly, the optimal delay in the first round allocation can be written as:  
\[ \begin{split} t_{op}^{1}&=\frac{O_{1}^{1}\cdot D_{ 0}}{R}+\frac{O_{1}^{1}\cdot D_{0}\cdot G_{0}}{f_{1}},\\ &=\frac{O_{2}^{1}\cdot D_{0}}{R}+\frac{O_{2}^{1}\cdot D_{0}\cdot G _{0}}{f_{2}},\\ &=\ldots\\ &=\frac{O_{|\mathbf{sb_{i}}|}^{1}\cdot D_{0}}{R}+\frac{O_{|\mathbf{sb_{i }}|}^{1}\cdot D_{0}\cdot G_{0}}{f_{|\mathbf{sb_{i}}|}},\end{split}  \tag{22}\]  
where \(O_{j}^{1}\) represents the proportion of the requested task that should be offloaded to vehicle \(sv_{j}\) in the first round allocation. From Equation (22), it can be deduced that the general form of \(O_{j}^{1}\) can be expressed as:  
\[O_{j}^{1}=O_{1}^{1}\cdot\frac{f_{j}\cdot(f_{1}+G_{0}\cdot R)}{f_{1}\cdot(f_{ j}+G_{0}\cdot R)}. \tag{23}\]  
Moreover, according to constraint C2, \(\sum_{j=1}^{|\mathbf{sb_{i}}|}O_{j}^{1}=1\), thus:  
\[O_{1}^{1}=\frac{1}{\sum\limits_{j=1}^{|\mathbf{sb_{i}}|}\frac{f_{j}\cdot(f_{1}+G_{ 0}\cdot R)}{f_{1}\cdot(f_{1}+G_{0}\cdot R)}}. \tag{24}\]  
Once \(O_{1}^{1}\) is determined, the values of \(O_{2}^{1},O_{3}^{1},\ldots,O_{|\mathbf{sb_{i}}|}^{1}\) can be calculated according to Equation (23). However, the calculated optimal offloading proportions are obtained without considering the impacts of vehicles' moving characteristics, and it needs to be adjusted accordingly. From the above analysis, we have obtained the maximum acceptable offloading proportion of vehicle \(sv_{j}\) under the practical conditions as \(O_{j}^{max}\). The adjustment is performed by comparing the optimal allocation proportion with the actual maximum acceptable offloading proportion of each vehicle. For any vehicle \(sv_{j}\), if the calculated optimal allocation proportion is not larger than the maximum acceptable offloading proportion, which is \(O^{1}_{j}\leq O^{max}_{j}\), then the final proportion allocated on \(sv_{j}\) is \(O^{final}_{j}=O^{1}_{j}\). Otherwise, \(O^{final}_{j}=O^{max}_{j}\), and the extra proportion of task that \(sv_{j}\) cannot process is collected for a new round allocation, which is performed on the vehicles in the same set with extra capabilities to handle these proportion of task. The second round allocation process is similar to the first round allocation process, a new optimal delay \(t^{2}_{op}\) is calculated and proportions should be allocated to vehicles are calculated the same way in the first round. After that, if there are still some extra proportions to be allocated, a third-round allocation is initiated. The process repeats until there are no extra proportions of tasks.