# 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
\begin{table}
\begin{tabular}{c l c c c} \hline \hline
**Scenario** & **Algorithm** & **Maximum** & **Average** & **Minimum** \\ \hline \multirow{3}{*}{LD1} & RK-Means & 10.0281 & **7.1953** & **2.8043** \\  & K-Means++ & 22.3953 & 13.0426 & 9.7661 \\  & OK-Means & **10.0102** & 7.5284 & 2.9302 \\ \hline \multirow{3}{*}{LD2} & RK-Means & **6.1243** & **3.7182** & **1.9843** \\  & K-Means++ & 11.7042 & 10.1505 & 9.8902 \\  & OK-Means & 13.3535 & 3.7293 & 2.9646 \\ \hline \multirow{3}{*}{LD3} & RK-Means & **8.4965** & **7.8033** & **6.8341** \\  & K-Means++ & 15.0121 & 13.3145 & 11.7047 \\  & OK-Means & 16.6213 & 13.6447 & 11.1972 \\ \hline \multirow{3}{*}{LD4} & RK-Means & **7.9712** & **4.5561** & **3.5431** \\  & K-Means++ & 9.7351 & 7.4745 & 6.4503 \\  & OK-Means & 11.3739 & 8.9334 & 6.7684 \\ \hline \multirow{3}{*}{HD1} & RK-Means & **15.0285** & **11.5614** & **8.0535** \\  & K-Means++ & 17.4779 & 13.0422 & 9.7661 \\  & OK-Means & 22.7448 & 16.4297 & 11.4612 \\ \hline \multirow{3}{*}{HD2} & RK-Means & **10.7905** & **9.8075** & **7.8421** \\  & K-Means++ & 11.8499 & 10.0278 & 8.5043 \\  & OK-Means & 17.4678 & 17.0153 & 16.4298 \\ \hline \multirow{3}{*}{HD3} & RK-Means & 18.0311 & **8.8341** & **1.8682** \\  & K-Means++ & **13.7679** & 9.7783 & 4.0764 \\  & OK-Means & 16.5879 & 14.3458 & 12.2135 \\ \hline \multirow{3}{*}{HD4} & RK-Means & 17.4466 & 14.8739 & 11.4529 \\  & K-Means++ & **16.5129** & **13.3536** & **7.8224** \\ \cline{1-1}  & OK-Means & 21.1495 & 19.7686 & 16.4615 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: RMSE numerical results. Figure 12: RMSE comparison results. Figure 14: DB comparison results. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Scenario** & **Algorithm** & **Maximum** & **Average** & **Minimum** \\ \hline \multirow{3}{*}{LD1} & RK-Means & **0.9884** & **0.9672** & **0.9511** \\  & K-Means++ & 0.9793 & 0.9559 & 0.9143 \\  & OK-Means & 0.9595 & 0.9489 & 0.9093 \\ \hline \multirow{3}{*}{LD2} & RK-Means & **0.9944** & 0.9515 & 0.9463 \\  & K-Means++ & 0.9861 & **0.9572** & **0.9489** \\  & OK-Means & 0.9877 & 0.9498 & 0.9398 \\ \hline \multirow{3}{*}{LD3} & RK-Means & 0.9387 & 0.9184 & **0.8963** \\  & K-Means++ & **0.9539** & **0.9275** & 0.8827 \\  & OK-Means & 0.8979 & 0.8837 & 0.8625 \\ \hline \multirow{3}{*}{LD4} & RK-Means & **0.9698** & 0.8826 & **0.8801** \\  & K-Means++ & 0.9491 & 0.9109 & 0.8593 \\  & OK-Means & 0.9585 & **0.9276** & 0.8746 \\ \hline \multirow{3}{*}{HD1} & RK-Means & **0.9895** & **0.9227** & 0.7542 \\  & K-Means++ & 0.9861 & 0.8931 & **0.7633** \\  & OK-Means & 0.9488 & 0.8839 & 0.7437 \\ \hline \multirow{3}{*}{HD2} & RK-Means & **0.9892** & 0.9623 & 0.9382 \\  & K-Means++ & 0.9723 & **0.9631** & **0.9553** \\  & OK-Means & 0.9715 & 0.9599 & 0.9451 \\ \hline \multirow{3}{*}{HD3} & RK-Means & **0.8664** & **0.8548** & **0.8492** \\  & K-Means++ & 0.8212 & 0.8156 & 0.8003 \\  & OK-Means & 0.8151 & 0.8028 & 0.7948 \\ \hline \multirow{3}{*}{HD4} & RK-Means & 0.9583 & 0.9499 & 0.9271 \\  & K-Means++ & **0.9745** & **0.9567** & **0.9355** \\  & OK-Means & 0.9313 & 0.9186 & 0.9082 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: SC numerical results. Figure 13: SC comparison results. The minimum average RMSE value in the HD scenario (HD1, HD2, HD3, and HD4) was 10.7905 for RK-Means, 11.8499 for K-Means++, and 16.5879 for OK-Means. The bold underlined RMSE values in Table 7 represent good results and indicate that the proposed algorithm had high similarity compared with the others. The RMSE value of the proposed model in the LD scenario was better than that of the K-Means++ and OK-Means models, though it demonstrated only small improvements compared with OK-Means. In the HD scenario, the proposed model demonstrated improvements compared with the others, indicating that it performed most effectively in the high-density scenario when the evaluation was based on the minimum average value. The effectiveness in high-density scenarios was the primary challenge.