# 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
In the HD scenario, there were no improvements, because the high density of nodes in the same area meant that the clusters were close together; however, the results were in the same range for all the algorithms according to the maximum average value, so the average improvements made by RK-Means compared with the other models were substantial across almost all scenarios. Figure 13 shows a comparison of the average SC values for all algorithms in all scenarios. In the low-density scenarios, the average SC value was 0.92993 for RK-Means, 0.93788 for K-Means++, and 0.9275 for OK-Means. In the high-density scenarios, the average SC value was 0.92618 for RK-Means, 0.90713 for K-Means++, and 0.8913 for OK-Means. The overall evaluation results were 0.92618 for RK-Means, 0.9225 for K-Means++, and 0.9094 for OK-Means. The improvements made by the proposed model compared with the other models were substantial across almost all scenarios. Table 9 shows the DB index results; RK-Means, K-Means++, and OK-Means all performed well in the low-density scenarios, and good values were also obtained in the high-density scenarios, even though the vehicles were in converge areas. The bold, underlined DB values in Table 9 represent good results and prove that the proposed algorithm had a high inter-cluster distance compared with the other two algorithms. Among the LD scenarios, the average DB value of RK-Means was 0.2061 in LD1, and the minimum DB result was 0.0977. RK-Means obtained better results for LD1 than K-Means++ and OK-Means. The RK-Means results were in the range of 0.0543 to 0.0806 in LD2. The value variation was small compared with the other algorithms in the same timestamp scenario. Among the HD scenarios, the proposed clustering model had a lower average DB value in HD2 compared with K-Means++ and OK-Means. The improvements made by the proposed model based on the DB index were small, because this index evaluates clustering algorithms based on the distance between centroids. The value of the DB index increases under a high vehicle density because the distance between centroids is decreased. Figure 14 represents a comparison of the average DB values for all algorithms across all scenarios. In the low-density scenarios, the average DB values were 0.32115 for RK-Means, 0.28808 for K-Means++, and 0.30925 for OK-Means. In the high-density scenarios, the average DB values were 0.3832 for RK-Means, 0.42238 for K-Means++, and 0.42143 for OK-Means. The overall evaluation results were 0.35218 for RK-Means, 0.35523 for K-Means++, and 0.36534 for OK-Means. The improvements made by the proposed model compared with the other models were substantial for almost all scenarios, especially in the HD scenarios, for which the proposed model achieved the smallest numerical result variation. Table 10 presents the DI results, which indicate the intra-cluster and inter-cluster similarity and represent a more generalized performance evaluation compared with the RMSE, SC, and DB indexes. The bold and underlined DI values in Table 10 represent good results and indicate that the proposed algorithm had a higher overall performance compared with the other models. Among the low-density scenarios, the maximum DI values for the LD2 timestamp scenario were 180.8782 for RK-Means, 165.1512 for K-Means++, and 174.6099 for OK-Means. A high value indicates that a clustering algorithm has a high similarity and high separation (large distance between closest clusters)

Among the high-density scenarios, the maximum DI values were 14.7284 for RK-Means, 13.3297 for K-Means++, and 10.1819 for OK-Means in the HD2 timestamp scenario. The improvements made by the proposed model compared with the others were substantial in all scenarios. As mentioned above, the value decreased in high-density scenarios because of the small inter-cluster distances. The average values are shown in Figure 15. In all scenarios, the results showed that the proposed clustering model had a high DI value (high internal similarity and large cluster-to-cluster distances).