# An Energy-Efficient Mobile Sink-Based Unequal Clustering Mechanism for WSNs
## 4 Proposed Algorithm
### Cluster Size Optimization  
In the experiments, 300 nodes are uniformly distributed in an area with a radius of 1000 m\({}^{2}\). All sensor nodes have same initial energy. Figure 4 shows the influence of different angles on the total transmission ranges of member nodes located in the last corona in CCWSN. Since in our model 32\({}^{\circ}\) is obtained as the minimum angle from Section 4.2.1, the angles which are less than this value are ignored. Figure 5 shows the comparison between SCWSN and CCWSN with different sector numbers in terms of total data transmission range of nodes. Based on Figure 5, when the network is divided into four sectors, there is the smallest difference between total data transmission range of nodes in SCWSN and CCWSN, thus 90\({}^{\circ}\) is considered as the maximum angle or upper bound of the interval.  
Figure 6 shows the total energy consumption of network in one round. As can be seen, the total energy consumption of the network will rise by increasing the number of sectors. The number of sectors with the maximum and minimum angle and the number of sub-coronas of innermost corona have been calculated with the different number of nodes. Details of this evaluation are shown in Table 2. Since there is a direct relationship between increasing the cluster radius and the increase of the total energy consumption of the 2 nd ring in EBCAG [31], this corona is the critical one in that method. Therefore, Figure 7 demonstrates the total energy consumption of only second corona in different cluster size in EBCAG [31] and CCWSN. As shown, EBCAG and CCWSN behave differently from each other by increasing the cluster size so that increasing the cluster radius in EBCAG leads to increase the energy consumption while it acts to the contrary in CCWSN. However, the energy consumption of 2 nd corona in CCWSN model is lower than EBCAG and the remarkable amount of energy can be saved in our method. Moreover, Figure 8 compares the total energy consumption of network versus simulation time.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline
**Number of nodes (1 st corona)** & 6 & 12 & 18 & 25 & 31 & 37 & 43 & 50 & 56 & 62 & 68 & 75 & 81 & 87 & 93 \\ \hline
**Number of sub-coronas** & 1 & 2 & 2 & 2 & 2 & 3 & 3 & 3 & 3 & 3 & 4 & 4 & 4 & 4 & 4 \\
**Number of sectors with minimum angle** & 6 & 3 & 4 & 6 & 7 & 4 & 4 & 5 & 6 & 6 & 4 & 4 & 5 & 5 & 5 \\
**Number of sectors with maximum angle** & 4 & 3 & 3 & 3 & 3 & 3 & 3 & 3 & 3 & 3 & 3 & 3 & 3 & 3 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Minimum and maximum number of sectors.  
Figure 4: The influence of the angle of sectors on.  
Figure 5: The comparison of data transmission range of MNs in CCWSN and SCWSN.  
Figure 6: Total energy consumption of network in one round.  
Figure 7: Total energy consumption of the second corona.  
From Figure 8, it can be seen that remarkable amount of energy can be saved by applying the clustering on corona-based WSN. Furthermore, since our cluster size optimization method consumes less energy in comparison with DBS [26] strategy, CCWSN is close to the optimal solution.