# 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 average DI values for all algorithms in the LD scenarios were 37.41463, 31.419, and 27.98235 for RK-Means, K-Means++, and OK-Means, respectively. The average DI values for all algorithms in the HD scenarios were 8.8585, 8.195225, and 7.2028 for RK-Means, K-Means++, and OK-Means, respectively. The overall DI results were 23.13656 for RK-Means, 19.80711 for K-Means++, and 17.59258 for OK-Means. The overall improvements made by RK-Means represented a 16.8% increase compared with K-Means++ and a 31.5% increase compared with OK-Means. Therefore, the proposed algorithm was more efficient than the other evaluated algorithms, especially in LD scenarios, but also in terms of the overall evaluation results. ### Stability Analysis

In this subsection, cluster stability is explained. The effectiveness of using a CRS in the proposed clustering technique was made clear in the vehicle distribution based on multiple parameters, especially vehicle speed. In each cluster, we tried to calculate the average speed value and the standard deviation. The CRS classified the vehicles with a small standard deviation of speed, which meant that all vehicles had approximately equal cluster leaving times, and the clusters would dynamically move forward with the same vehicles. Thus, the cluster lifetime was high, and the clustering change rate was low. Figure 16 shows the RK-Means standard deviation of speed in the low-density scenarios. For the LD1 scenario, as shown in Figure 16a, the minimum STD value was 0.355499648 (for cluster No. 7), and the maximum STD value was 0.367654729 (for cluster No. 2); the other STD values were within this range, and the difference between them was very small. For the LD2 scenario, as shown in Figure 16b, the minimum STD value was 0.429344109 (for cluster No. 13), and the maximum STD value was 1.333829075 (for cluster No. 3); the other STD values were within this range, and the difference between them was small. The same was true for the LD3 and LD4 scenarios described in Figure 16c,d, respectively, which indicates the high stability of our proposed model. Figure 17 shows the RK-Means standard deviation of speed in high-density scenarios. For the HD1 scenario, as shown in Figure 17a, the minimum STD value was 0.284018779 (for cluster No.10), and the maximum STD value was 0.314635087 (for cluster No. 1); the other STD values were within this range, and the difference between them was very small. For the HD2 scenario, as shown in Figure 17b, the minimum STD value was 0.156418243 (for cluster No. 12), and the maximum STD value was 0.374165739 (for cluster No. 4); the other STD values were within this range, and the difference between them was small. The same was true for the HD3 and HD4 scenarios described in Figure 17c,d, respectively, which indicates the high stability of our proposed model. Figure 16: RK-Means standard deviation of speed in low-density scenarios. Table 11 shows the comparison of the standard deviations of RK-Means, K-Means++, and OK-Means in both scenarios. The small value of the standard deviation in the proposed model indicates that the cluster lifetime was high, because all vehicle locations changed within a small duration. The new clusters contained the same vehicles, so the cluster member changing rate was low. ## 6 Conclusions

In this paper, a new RK-Means clustering algorithm was proposed to decrease the difficulty of calculating the clustering numbers and improve the clustering results of K-Means clustering algorithms. The RK-Means clustering algorithm was applied to create a vehicle