# Modeling and Analysis of New Hybrid Clustering Technique for Vehicular Ad Hoc Network
## 3 Clustering Model
### Covering Rough Set Model
#### 3.1.2 Group Implementation
The drawing functions and data implementing algorithms were created using MATLAB, and the vehicle mobility simulation was carried out using SUMO. In the simulation, the dataset values were tested and modified for certain functions to obtain the most reasonable initial values for the parameters. The parameter settings of the RK-Means, K-Means++, and OK-Means algorithms are shown in \[d_{ij}=d\left(C_{i},C_{j}\right) \tag{23}\]2

The number of clustering iterations was 200 s for the low-density scenario and 380 s for the high-density scenario, and each algorithm was run 20 times independently. The number of clusters in each scenario is shown in \[d_{ij}=d\left(C_{i},C_{j}\right) \tag{23}\]3 \begin{table}
\begin{tabular}{c c c} \hline \hline
**Density** & **SUMO Running Time** & **Timestamp Period** & **Scenario** \\ \hline \multirow{3}{*}{Low-density (60 vehicles)} & 1 to 50 s & LD1 \\  & 51 to 100 s & LD2 \\  & 101 to 150 s & LD3 \\  & 151 to 200 s & LD4 \\ \hline \multirow{3}{*}{High-density (120 vehicles)} & 1 to 95 s & HD1 \\  & 96 to 190 s & HD2 \\  & 191 to 285 s & HD3 \\  & 286 to 380 s & HD4 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Simulation scenarios. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** \\ \hline \multirow{3}{*}{
\begin{tabular}{c} Network topology \\ Mobility simulator \\ Mobility simulation time \\ Vehicle density \\ Vehicle speed \\ Vehicle coverage range \\ \end{tabular} } & Highway (2 Km road length, 4 lanes) \\  & 51 to 100 s & LD2 \\  & 101 to 150 s & LD3 \\  & 151 to 200 s & LD4 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Simulation parameters. Figure 9: Snapshot of the dataset file. The cluster members (CMs) in a cluster are important because a high number of CMs affects the clustering stability, so the clustering algorithm should balance between cluster number and CMs. The proposed algorithm demonstrated better stability than the other algorithms, especially in the low-density scenario, because in the high-density scenario, the vehicles converged and there were many vehicles in a small area. The clustering efficiency is represented by the percentage of clustered vehicles and undefined vehicles (vehicles that do not belong to any cluster). Figures 10 and 11 show the clustering efficiency for all algorithms in the low-density (60 nodes) and high-density (120 nodes) scenarios, respectively. RK-Means assigned 58 nodes to clusters in the LD scenario, with only two undefined nodes, while the K-Means++ and OK-Means algorithms assigned 55 and 56 nodes to clusters, respectively. In the HD scenario, RK-Means was successful in assigning 117 nodes to clusters, leaving only three nodes undefined. The K-Means++ and OK-Means algorithms assigned 114 and 113 nodes to clusters, respectively. low-density and high-density data scenarios are shown in Tables 7-10. A comparison of the average performance of RK-Means, K-Means++, and OK-Means across all scenarios is illustrated in Figures 12-15. As can be seen in Table 7, the proposed RK-Means clustering algorithm was used to obtain the clustering number from a SUMO dataset, which could improve the clustering effectiveness, facilitate the achievement of high cluster similarity, and produce better clustering evaluation results. Regarding the RMSE results, a small value indicates an effective clustering model. For the two scenarios, the RMSE values of RK-Means were lower than those of K-Means++ and OK-Means. The minimum average RMSE value in the LD scenario (LD1, LD2, LD3, and LD4) was 3.7182 for RK-Means, 7.4745 for K-Means++, and 3.7293 for OK-Means.