## 5 Simulation and Performance Evaluation
### Comparison of RSC with Fan-Shaped Clustering  
The RSC results were compared against the existing FSC in [PERSON] et al. [28] to analyze the performance of RSC since both the algorithms applied angular clustering and aimed to increase energy efficiency and to reduce reclustering costs in large-scale networks. The existing algorithm FSC was compared with HEED to find the number of alive nodes with 2000 rounds, i.e., 2000 seconds and produced the results as 42% live nodes with more than 40% live nodes left in FSC compared to 1/3 of nodes with 10% energy in HEED. Since the existing work is already compared with the state-of-the-art algorithm, FSC alone was taken for comparison and simulation. Both RSC and FSC were executed up to 3500 rounds. Similarly, the existing work was compared with HEED for the evaluation of total residual energy and packet collection rate. In most of the scenarios, it was executed up to 2000 rounds. To achieve better results with long duration and large-scale network, the FSC was compared with RSC for 3500 rounds for the above two parameters. The results of RSC and FSC were analyzed based on the total live nodes. Initially, the number of nodes was stable in both the cases. In FSC, the number of nodes started to decrease at 1800 rounds and reaches 860 at 3500 rounds. Conversely, in RSC, the number of nodes started to decrease at 2800 rounds and reached 920 at 3500 rounds. This indicated that the nodes started consuming energy evenly; they died at almost the same time. Figure 5a shows considerable load balancing up to 3000 rounds. The total residual energy decreased with time, as shown in Figure 5b, as the node had to find a route to reach  
Figure 4: Behavioral analysis of RSC: (**a**) the number of live nodes; (**b**) the residual power level of RSC; and (**c**) the packet received ratio of RSC. the sink node and the reclustering process. RSC performed better because the transmission distance was less than that in FSC. The packet received ratio is considered as the most significant measure because it reveals packet loss and the dead nodes in the network. Packet loss may occur when  
1. none of the nodes is selected as the CH,
2. the CH node could not find the forwarder to reach the sink node, and
3. the distance to reach the relay node is much greater. The packet received ratio was analyzed using statistical measures considering the factors mentioned above and the large scale of the applications [29; 32; 33; 34; 35; 36; 37; 38; 39]. For example, the mean values were considered effective for real-time traffic applications, but event-based applications would prefer median and mode values. Some of the applications and preferred statistical measures were as follows:  
* Mean--power distribution units
* Median--capacity planning or cost predictions
* Mode--power consumption of an entire network operation center
* Maximum--domestic applications/heat transfer
* Standard deviation and/or variance--to trigger a warning or an alarm if a system operates outside an acceptable range  
The packet received ratio comparison of the FSC and RSC is shown in Figure 6. In FSC, the packets received were 0.6, whereas in RSC, the packets received were 0.82, and it started to decrease gradually to 0.8 at 2700 rounds and reached 0.5 at 3500 rounds based on the mean values. This is because the radius of the inner and outer layers is equal for RSC, but FSC produces an inner layer that is twice that of the outer layer, which increases the transmission distance. The uniform size of the layers in RSC constitutes a high mean and median packet collection rate, as shown in Figure 6a. RSC and FSC produced results with slight deviations in the mode and maximum statistical measures. Both the algorithms aim to reduce the frequency of the reclustering cost, which was achieved at 2700 rounds in the FSC and 3000 rounds in RSC, as shown in Figure 6c,d. Subsequently, the packet collection rate decreased rapidly due to the finding of the relay node and transmission distance with the present live nodes.