## 4 Problem Formulation  
The task offloading process is mainly divided into three parts: task transmission, task calculation and result return. Since the result is usually small and has little impact on the delay of the whole offloading process, this paper ignores the delay of the result return. Denote the offloading decision as \(\boldsymbol{d}=\left\{O_{1},O_{2},\ldots,O_{j},\ldots\right\}\), where \(O_{j}\) represents the proportion of task that is offloaded to the \(j^{th}\) SV. The task transmission delay for \(u_{0}\) to unload \(O_{j}\) proportion of the task onto vehicle \(sv_{j}\) can be calculated as follows:  
\[t_{j}^{up}=\frac{O_{j}\cdot D_{0}}{R}. \tag{4}\]  
Similarly, the task calculation delay by \(sv_{j}\) to complete the assigned task is calculated as follows:  
\[t_{j}^{cal}=\frac{O_{j}\cdot D_{0}\cdot G_{0}}{f_{j}}, \tag{5}\]  
where \(f_{j}\) is the amount of computing resources that \(sv_{j}\) can lend. Thus, the sub-task completion delay on \(sv_{j}\) can be calculated as:  
\[t_{j}=t_{j}^{up}+t_{j}^{cal}. \tag{6}\]  
The computation task can only be considered as finished until all sub-tasks are completed and the calculation results are returned to the UV. Thus, the total completion time of the task can be written as:  
\[t_{total}=max\Big{\{}t_{1},\ldots,t_{j},\ldots,t_{|\boldsymbol{d}|}\Big{\}}. \tag{7}\]  
Moreover, the pricing decision for the final selected SVs is denoted as \(\boldsymbol{p}=\left\{p_{1},p_{2},\ldots,p_{j},\ldots\right\}\), where \(p_{j}\) is the price that \(sv_{j}\) asks for calculating a unit size of the task. As a result, the total price that \(u_{0}\) should pay for asking SVs to complete the task can be calculated as follows:  
\[P=\sum_{j=1}^{|\boldsymbol{d}|}p_{j}\cdot O_{j}\cdot D_{0}. \tag{8}\]  
The cooperative offloading of multiple vehicles is considered to reduce the task completion delay of the UV. However, vehicles complete tasks with varied lengths of time. Since the final completion delay is the maximum of all completion delays for sub-tasks, it is preferred to minimize the final completion delay by aggregating the completion delays of all sub-tasks. In this way, the completion time of each sub-task is minimized and the overall completion delay of the task is optimized. The resource of each vehicle can be released quickly once the sub-task is finished, thus improving the resource utilization ratio of the system. The resources utilization ratio of the overall offloading system is calculated as the same in [29]:  
\[Utility=\frac{\sum_{j=1}^{|\boldsymbol{d}|}t_{j}}{|\boldsymbol{d}|\cdot t_{ total}}. \tag{9}\]  
Obviously, the resource utilization ratio is a vital metric to describe the efficiency of the offloading system. A high resource utilization ratio indicates that the idle resources on the finally selected SVs are fully exploited, which is welcomed both by the UV and SVs. Meanwhile, the UV also wants to accomplish the computation task with minimum delay and cost, which requires sufficiently exploring the resources of nearby vehicles that ask for a low unit price yet have strong capabilities for providing fast and reliable cooperation. Taking all these aspects into consideration, this paper aims to design a resource- and time-efficient approach for task offloading in VEC networks. Given the definition of resource utilization ratio in Formula (9), the maximization of the resource utilization is stronglycorrelated to the minimization of the completion delay of the task. The optimization problem is formulated as follows:  
\[\textit{maximize}\quad Utility, \tag{10}\]  
s.t. \[C1:0\leq O_{j}\leq 1,\] (10a) \[C2:\sum_{j=1}^{|\mathcal{A}|}O_{j}=1,\] (10b) \[C3:p_{j}>0,\] (10c) \[t_{j}^{cal}=\frac{O_{j}\cdot D_{0}\cdot G_{0}}{f_{j}}, \tag{5}\]0 (10d)  
C1 and C2 state that the portion of the task that is offloaded to a single SV is varied between \([0,1]\), and the sum of the size of offloaded sub-tasks equal to that of the original task. C3 indicates that an SV will only ask for a positive reward.