## 4 Model
### Vehicle Cluster Model and Algorithm
\begin{table}
\begin{tabular}{c l} \hline \hline
**Notation** & **Implication** \\ \hline \(G(\mathcal{V},\mathcal{E})\) & Topological diagram composed of CH and RSU \\ \(\mathcal{V}\) & The set of CHs and RSU \\ \(\mathcal{E}\) & The set of edges in \(G(\mathcal{V},\mathcal{E})\) \\ \(a_{i}\) & The \(i\)-th CH in the \(\mathcal{V}\) \\ \(e(i,j)\) & Edge between \(a_{i}\) and \(a_{j}\) \\ \(\mathcal{C}\) & The set of clusters \\ \(c_{i}\) & The \(i\)-th cluster in the \(\mathcal{C}\) \\ \(R\) & Communication radius of DSRC \\ \(D^{cluster}\) & Merge parameter used to measure whether two clusters can be merged \\ \(D^{vehicle}\) & Used to measure whether two vehicles can establish communication \\ \(D^{vehicle}_{threshold}\) & If \(D^{vehicle}\geq D^{vehicle}_{threshold}\), the two vehicles can establish stable communication \\ \(Y_{ij}\) & The remaining time that \(c_{i}\) and \(c_{j}\) are within the DSRC communication radius \\ \(d^{cluster}_{ij}\) & The distance between the two clusters and the distance between the two vehicles \\ \(d_{limit}\) & Maximum mergeable distance \\ \(N\) & Maximum number of CMs that can be included in a single cluster \\ \(v^{min},v^{max}\) & Maximum and minimum speed of CMs in a cluster \\ \(v^{vehicle}\) & The speed of the vehicle \\ \(Path_{i}\) & VANETs communication link from \(a_{i}\) to RSU \\ \(\mathcal{B}_{i}\) & Data packet buffer of \(a_{i}\) \\ \(b_{ik}\) & \(k\)-th packets in \(\mathcal{B}_{i},i\in\{1,\ldots,M\}\) \\ \(\tilde{S}_{ik}\) & Size of \(b_{ik}\) \\ \(f^{CV2X}\), \(f^{DSRC}\) & The transmission rates of DSRC and C-V2X, respectively \\ \(\omega_{ik}\) & Weight of \(b_{ik}\) \\ \(l_{ik}\) & Maximum delay allowed for \(b_{ik}\) \\ \(l^{min},l^{max}\) & The upper and lower boundaries of \(l^{k}_{j}\) \\ \(T\) & The weighted delay generated in the system per unit time \\ \(p\) & Price per MB of cellular data \\ \(p\) & Communication costs incurred in the system per unit time \\ \(q^{CV2X}_{ik}\) & Sum of queuing delay and processing delay when \(b_{ik}\) is sent through C-V2X \\ \(q^{m}_{ik}\) & The sum of queuing delay and processing delay generated when \(b_{ik}\) \\ \(q^{m}_{ik}\) & is forwarded at \(m\)-th of \(Path_{i}\) \\ \(r\) & Vehicle’s data generation rate \\ \(u^{CV2X}_{i}\) & The average delay generated by the packets sent using C-V2X in \(a_{i}\) \\ \(u^{DSRC}_{i}\) & The average delay generated by the packets sent using VANETs in \(a_{i}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Notation Table. distance between \(c_{i}\) and \(c_{j}\). \((R-d_{ij}^{cluster})^{-1}\) can describe whether \(c_{i}\) and \(c_{j}\) are on the edge of each other's DSRC communication range. The detailed definition of \(D_{ij}^{cluster}\) is as follows:  
\[D_{ij}^{cluster}=\left\{ \begin{array}{l}\alpha Y_{ij}+\frac{\beta}{R-d_{ij }^{cluster}},d_{ij}^{c}\leq d_{limit}\\ 0,d_{ij}^{c}>d_{limit}\end{array} \right. \tag{1}\]  
When \(c_{i}\) and \(c_{j}\) are at the edge of each other's DSRC communication range (that is, when \(d_{ij}^{cluster}\) is close to \(R\)), if the speed (the speed here refers to the average speed of all vehicles in the cluster) difference between \(c_{i}\) and \(c_{j}\) increases, it will cause \(c_{i}\) and \(c_{j}\) to quickly leave the DSRC communication range. Therefore, in Equation (1), the difference between \(R\) and \(d_{ij}^{cluster}\) is used to limit the merging of clusters at the edge of the DSRC communication range. \(\beta\) is a negative value whose absolute value is greater than 1. When \((R-d_{ij}^{cluster})\) becomes smaller, \((R-d_{ij}^{cluster})^{-1}\) increases, \(D_{ij}^{cluster}\) becomes smaller. \(d_{limit}\) is the maximum allowed distance that clusters can merge. \(\alpha\) is the weight of \(Y_{ij}\), and the calculation formula of \(Y_{ij}\) is:  
\[Y_{ij}=\frac{R\pm d_{ij}^{cluster}}{\max\Bigl{\{}\Bigl{|}v_{i}^{max}-v_{j}^{ min}\Bigr{|},\Bigl{|}v_{j}^{max}-v_{i}^{min}\Bigr{|}\Bigr{\}}} \tag{2}\]  
where \(v^{max}\) and \(v^{min}\) represent the maximum speed and minimum speed, respectively, of the CMs in the cluster.