## 6 Results
### Experimental Results
#### 6.2.2 Comparison of Clustering Methods  
After completing the selection of parameters, Algorithm 1 was tested in 100 different simulation environments. Table 4 shows the comparison between Algorithm 1 and the TDCR clustering algorithm in 100 tests.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Framework** & **Average Value** & **Max Value** & **Min Value** & **Median Value** \\ \hline \multirow{2}{*}{Cluster Keep Time} & CTDHR & 35.07 & 50.00 & 24.00 & 34.50 \\  & TDCR & 38.48 & 51.00 & 28.00 & 38.00 \\ \hline \multirow{2}{*}{Number of Clusters} & CTDHR & 13.90 & 16.00 & 11.00 & 14.00 \\  & TDCR & 20.00 & 20.00 & 20.00 & 20.00 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Statistics on the stability of clusters and the number of clusters for CTDHR and TDCR.  
Figure 5: (**a–c**) are the effects of changing the \(\alpha,\beta,d_{limit}\), respectively, on the stability of clusters; (**d–f**) are the effects of changing the \(\alpha,\beta,d_{limit}\), respectively, on the number of clusters  
In TDCR, the method of spatial sampling is used to cluster vehicles, and the sampling radius is half of the DSRC communication radius (when \(R\) is 400 m, the sampling radius is 200 m), so the number of clusters in TDCR is constant, 20. In the clustering method of CTDHR, the parameter \(d_{limit}\) is used to control the size of the cluster, so the coverage of the cluster is not fixed. When \(d_{limit}\) is determined to be 170, the theoretical maximum coverage of the cluster is 340 m. Therefore, the clustering method of CTDHR can obtain fewer clusters. Moreover, in the clustering method of this paper, the one-hop connection between the CM and the CH is also realized. The small number of clusters means that the number of hops in the VANET link can be reduced as much as possible. When there is no congestion in the network, fewer hops make each packet forward as few times as possible, thereby reducing the total delay in the network. Moreover, fewer clusters mean fewer communication resources of the cellular network are required. Fewer clusters also facilitate cluster management and reduce the consumption of communication resources.  
Due to the speed difference between vehicles, the vehicle may change its current state at any time. Therefore, the more vehicles in the cluster, the worse the stability of the cluster. When the number of vehicles on the road is the same, the smaller the number of clusters, the higher the average number of vehicles in the cluster. Therefore, the cluster stability of CTDHR is slightly worse than that of TDCR. In Equation (1), \(Y_{ij}\) considers merging clusters that can stay connected longer, while \((R-d_{ij})^{-1}\) restricts the merging of clusters at the edge of the mutual DSRC communication radius. Therefore, the stability of CTDHR is also fully guaranteed, and the loss of various statistical features is within an acceptable range compared with TDCR. In addition, the number of vehicles in a single CTDHR cluster will not exceed \(N\), which avoids the situation that the number of CMs in a single cluster is too much to exceed the communication capability of the CH. However, this situation may appear in TDCR.