## 2 System Model and Problem Formulation  
### Vehicle Platooning  
A cellular V2X Vehicular framework based on Multi-access Edge Computing is considered. The framework comprising multi-platoon architecture and its system model are shown in Figure 1. A wide crossroads scenario with vehicles traveling on a twin-track is presumed. The framework is deployed with RSUs equipped with edge servers positioned in the middle of the crossroad. The group of platoons featured with connected vehicles is denoted as \(\mathcal{P}=\{1,2,\ldots,P\},P\in\mathbb{V}\). A platoon's total number of vehicles is given by \begin{table}
\begin{tabular}{l l} \hline \hline
**Primary Notations** & **Explanation** \\ \hline \(\mathbb{V}\) & group of positive integers \\ \(P/\mathcal{P}/i\) & number/group/array of platoons \\ \(V_{i}/\mathcal{V}_{i}/n\) & number/group/array of vehicles in platoon \(i\) \\ \(B/B/b\) & number/group/array of subchannels \\ \(g_{i}[b]\) & small-scale fading dependent frequency \\ \(\alpha_{i}\) & large-scale fading independent frequency \\ \(\underline{c}\) & location of RSU \\ \(\underline{\sigma}_{i,b}^{t}\) & indicates the allocation of subchannel \\ \(\phi_{i}^{t}\) & indicates the selection of inter/intra-platoon mode \\ \(p_{i}^{t}[b]\) & power required by CV \(i\) \\ \(C_{i,\underline{c}}^{t}[b]\) & data rate in the subchannel \(b\) linking the CV \(i\) and RSU \\ \(C_{i,\underline{c}}^{t}[b]\) & data rate in the subchannel \(b\) linking the CV \(i\) and its FV \\ \(h_{i,\underline{c}}[b]\) & channel gain in the subchannel \(b\) linking the CV \(i\) and RSU \\ \(h_{i,\underline{c}}[b]\) & channel gain in the subchannel \(b\) linking the CV \(i\) and its FV \\ \(AoI_{i}^{t}\) & AoI of CV till the start of the scheduling window \(t\) \\ \(\aleph_{i}\) & CV \(i^{\prime}\)’s CAM message size \\ \(C_{i,\underline{c}}^{min}\) & CV’s least capacity requirement \\ \(\mathbb{E}\) & collection of edge nodes \\ \(\mathbb{CT}\) & the group of computing task \\ \(\mathfrak{P}_{n}\) & Processing power of edge nodes \\ \(\phi_{i}^{t}(x)\) & Boolean factor for discovering the vehicle location \\ \(L\) & total latency for executing \(CT\) \\ \(es_{n},er_{n}\) & caching space and computational resources required by edge nodes \\ \(c_{stm},cr_{m}\) & caching space and computational resources required by computation tasks \\ \hline \hline \end{tabular}
\end{table} 
Table 1: List of primary notations and explanations. \(\mathcal{V}_{i}=\{1,2,\ldots,V_{i}\},V_{i}\in\mathbb{V}\), and \(i\in\mathcal{P}\), which are numerically progressing from CV as one to \(V_{i}\). The available time slots are scheduled equally in length \(\Delta t\), indexing to a positive integer \(t\in\mathbb{V}\), and the bandwidth is orthogonally partitioned into \(W\)-sized subchannels, indexing to \(b\in\mathcal{B}=\{1,2,\ldots,B\}\). Essentially, a platooning system has two modes of communication:  
In the inter-platoon mode, V2I links are utilized for communicating safety and control information from RSU to all the other platoons. This communication mode is crucially responsible for informing the status of other platoons and crossroads traffic scenarios among all the platoons. However, in intra-platoon mode, V2V links are utilized for communicating the CAM messages between the connected vehicles in each platoon at regular intervals to guarantee familiarity with dynamics and decisions of associated platoon members and platoon captains in particular. The vital purpose of this mode is to achieve the property of string stability in platoons, i.e., the perpetuating distortions are not intensified throughout the string of vehicles. The technical report on 3 GPP guidelines [5] states that the broadcasting frequency of CAMs ought to be 100 Hz for driving maneuver coordination, and the CAM message size is denoted as \(\aleph_{i}\). Orthogonal Frequency Division Multiplexing (OFDM) is leveraged to address the challenges of frequency selective channels.