## 2 System Model and Problem Formulation
### MEC-Aided Platooning  
An MEC-Aided platooning framework with its communication paradigm is shown in Figure 1. As discussed earlier, the \(\mathbb{E}\) edge nodes are installed along the crossroads and are denoted as \(\mathbb{E}=\{e_{1},e_{2},e_{3},\ldots,e_{n}\}\). The effective process of content caching at the edges of the vehicular network is capable of relieving the load on the backhaul links and hastening the transmission. Hitherto, the concept of caching space and computational resources is deployed along the \(n\)th edge node and is denoted as \(es_{n}\) and \(er_{n}\), respectively. The individual connected vehicles \(\mathbb{V}\) have \(i\) computing tasks that are being offloaded to edge nodes. The computing tasks are represented as \(ct\) and are given by \(CT=\{ct_{1},ct_{2},\ldots,ct_{i}\}\). These computational tasks demand caching space and computational resource needs denoted as \(ct_{sn}\) and \(cr_{rn}\), respectively. The RSU installed along the crossroads is given by \(RSU=\{RSU_{1},RSU_{2},\ldots,RSU_{n}\}\). The physical resources of the edge nodes are considered to be resource blocks with equal processing power \(\mathfrak{P}_{n}\). The time of execution is entirely defined by the block's capacity \(C_{n}\), the task's required amount of resource block \(U_{n}\), and the required data rate. Latency Model  
Latency becomes involved as the edge nodes begin the execution of task computation, comprising distinct transmission times such as the following:  
1. The time for a transmission from the initial vehicle to the intended vehicle;
2. The time for task offloading from the intended vehicle to the destination edge node;
3. The time for task execution on the edge node destination;
4. The time for responding to the computational estimations from edge nodes to the initiated vehicle. On the assumed crossroads, each of the vehicles traverse various edge nodes. Considering that Poisson distribution characterizes the vehicle distribution, the reception of task offloading at the MEC server also follows a Poisson process. In order to guarantee the presence of the vehicle at the destination edge node's \(e_{n}\) coverage at the specific instant \(x\), another Boolean factor \(\phi_{i}^{n}(x)\) is used for discovering the location of the vehicle \(V_{i}^{\prime}\) and is determined by  
\[\phi_{i}^{n}(x)= \begin{cases}0,&\text{$V_{i}$ is in the coverage of $e_{n}$}\\ 1,&\text{otherwise}\end{cases}  \tag{5}\]  
The transmission of tasks originates from the initiated vehicle to the intended vehicle that is in the vicinity of the edge node through the multi-hop V2V technique. The primary cause of latency is contributed by computation task transmission time \(trans_{i}(x)\) and is obtained by  
\[trans_{i}(x)=\sum_{n=1}^{N}\sum_{i^{\prime}=1}^{I}\phi_{i}^{n}\cdot(1-\phi_{i ^{\prime}}^{n})\cdot Y_{i}^{i^{\prime}}\cdot\frac{d_{i}}{C_{i,j}^{i}[b]}\cdot (x_{i^{\prime}}+1) \tag{6}\]  
in which \(d_{i}\) is the task offloaded data size and \(C_{i,j}^{t}[b]\) is the rate at which data are transmitted in the network by applying V2V techniques; also, based on the literature, it is assumed to be a constant since V2X users' data transmission occurs in fixed power. \(x_{i^{\prime}}\) is the vehicle number through which the task is traversed from \(v_{i}\) to \(v_{i^{\prime}}\). On the other hand, \(Y_{i}^{i^{\prime}}\) represents the Boolean factor to determine if \(v_{i^{\prime}}\) is the vehicle destination and is determined as  
\[Y_{i}^{i^{\prime}}(x)= \begin{cases}0,&\text{$V_{i^{\prime}}$ is the destination}\\ 1,&\text{otherwise}\end{cases}  \tag{7}\]  
The secondary cause of latency is contributed by \(i\)th task offloading time \(off_{i}(x)\) at the data rate \(C_{i,\Sigma}^{t}[b]\)--the rate between the vehicle and the edge nodes based on V2I technique--and is obtained as  
\[off_{i}(x)=\sum_{e=1}^{N}\phi_{i^{\prime}}^{n}(x)\cdot\frac{d_{i}}{C_{i,\Sigma }^{t}[b]} \tag{8}\]  
The tertiary cause of latency is due to the \(i\)th task execution time executed on the destination edge node.