# A Robust and Energy-Efficient Weighted Clustering Algorithm on Mobile Ad Hoc Sensor Networks +
## 5 Simulation Results and Discussion  
Firstly, the performance of RE\({}^{2}\)WCA algorithm is evaluated. For purpose of generality, it is assumed that one thousand nodes are placed into a filed which ranges 2000 m \(\times\) 2000 m. In addition, the iteration threshold is set to 0.0005 [10; 11; 13]. Equation (10) implies that the max iteration times of RE\({}^{2}\)WCA protocol is 12. In the process of initialization, _CH\({}_{prob}\)_ = \(\mathcal{C}_{prob}\)_ = 5% is set for all nodes in the network, where only in sixth iteration, nodes with high energy will exit RE\({}^{2}\)WCA protocol. It means that if the residual energy of nodes is higher, they will terminate RE\({}^{2}\)WCA more earlier. The performance of DWCA and EDWCA are evaluated to demonstrate more straightforward and convincing. Therefore, from the aspects [3; 10] listed as follows, RE\({}^{2}\)WCA is compared with EMDWCA and DWCA protocols. (1) Ratio of the number of clusters to the number of all nodes; (2) Ratio of non-single node clusters to the number of clusters; (3) Standard deviation of the number of nodes in a cluster and maximum number of nodes in a cluster; (4) Average residual energy of CHs elected in each cluster. Figure 9a shows that both in three algorithms, when the radius of cluster increases, the percentage of cluster heads decrease respectively. When the radius of cluster reaches 400 m, it is not surprised that only one cluster head exists in the mobile network. With cluster radius increasing, the percentage of cluster heads of RE\({}^{2}\)WCA is larger than DWCA and EDWCA algorithms. Because group mobility is considered where the nodes with similar motion pattern can maintain the original structure of cluster when the network topology changes. Thus, the number of cluster heads can be decreased a little slowly in RE\({}^{2}\)WCA protocol. In Figure 9b, RE\({}^{2}\)WCA protocol does not perform very well compared with DWCA and EMDWCA. When the radius of cluster reaches 25 m, the average residual energy of three protocols are nearly same. Figure 9b implies that with the radius of cluster increasing, the average residual energy increases. However, the residual energy of DWCA and EDWCA protocols is higher than RE\({}^{2}\)WCA. The difference between RE\({}^{2}\)WCA and EMDWCA is about 13%. Compared with DWCA is approximately 10%. It demonstrates that the _CH_ residual energy selected by RE\({}^{2}\)WCA is high and is not far lower than the EMDWCA and DWCA. Application requirement meets different types of cost function when selecting _CH_. If the protocol needs to be utilized in high node density network, the standard deviation will larger. If considering load balance, the standard deviation will be much smaller. In EMDWCA, the protocol considers the \(1/node\)_degree_. Clearly, the maximum degree cost will increase the standard deviation. However, DWCA considers the minimum degree cost, that is, _node degree_, which demonstrates the standard deviation is relatively smaller. In RE\({}^{2}\)WCA, we consider a compromise between two extremes which is load balancing and cluster density respectively. Another vital property of cluster is percentage of non-single node clusters. It demonstrates the feature of minimize the node into a cluster. In Figure 10b, the percentage of non-single nodes of three protocols increase with the radius of cluster becomes larger. Theoretically, if the radius of cluster is large enough, the percentage of non-single nodes nearly reaches to 100% with all nodes forming into one cluster. It also implies that the percentage non-single nodes of RE\({}^{2}\)WCA is much higher compared with two other protocols. From Figure 1c, we can see the ratio of maximum number of nodes RE\({}^{2}\)WCA to EMDWCA is lower than other two types of cost. The number of nodes will surely larger than minimum node degree and AMRP. In fact, this figure shows similar facts with Figure 10a. They all demonstrates the different types of cost will form into various clusters. More requirements need considering in the actual application.