## 4 Performance Evaluation
### Evaluation of FL-ECC/D  
A comparative evaluation of FL-ECC/D is performed using many scenarios, to illustrate and validate its behavior under different densities, sparse, moderate, or dense, and through different positions of the BS. The comparison is based on the metric of energy balancing and network lifetime in terms of FND, 10 PND, QND, and HND. All nodes in the scenarios are randomly distributed over an area of \(200\times 200\) meters. The proposed _FL-ECC/D_ is comparatively evaluated for the case of positioning the BS at the center of WSN. Figures 8-11 compare the achieved average lifetime of FL-EEC/D for FND, 10 PND, QND, and HND, respectively, against the achieved average lifetime of LEACH, FL[1]/D, and _K_-means-LEACH. The network sizes are \(50,100,200,300\), and \(400\) nodes. Figure 8: FND of FL-ECC/D against LEACH, _K_-means-LEACH, and FL[1]/D (BS at the center of WSN). Figure 7: Lorenz curve and the line of equality for the distribution of wealth. It is clear from these four figures that the proposed FL-EEC/D achieved a longer average of network lifetime for each of the terms FND, 10 PND, QND, and HND, for all network sizes. For example, considering Figure 8, we see that the network lifetime achieved by FL-EEC/D in terms of FND for the network of 50 nodes was approximately 4.48-, 3-, and 1.6-times the average of that achieved by LEACH, \(K\)-means-LEACH, and FL[1]/D, respectively. Figure 12 demonstrates the overall achieved enhancement of the proposed FL-EEC/D against LEACH, FL[1]/D, and \(K\)-means-LEACH for the network lifetime metric in terms FND, 10 PND, QND,  
Figure 11: HND of FL-EEC/D against LEACH, \(K\)-means-LEACH, and FL[1]/D (BS at the center of WSN). Figure 10: QND of FL-EEC/D against LEACH, \(K\)-means-LEACH, and FL[1]/D (BS at the center of WSN). Figure 9: 10 PND of FL-EEC/D against LEACH, \(K\)-means-LEACH, and FL[1]/D (BS at the center of WSN). and HND, for the five WSN sizes. The average improvement diminishes as the rounds progress, and this indicates that we are achieving a good balance in the distribution of energy an extending the time before the events of FND, 10 PND, and QND occur. We further evaluate the proposed _FL-EEC/D_ for the same metrics, but change the position of the BS to the corner of the WSN. Figures 13-16 present the achieved average network lifetime in terms of FND, 10 PND, QND, and HND, respectively, for the different WSN sizes. Figure 14: 10 PND of FL-EEC/D against LEACH, _K_-means-LEACH, and FL[1]/D (BS at corner of WSN). Figure 12: Average improvement percentage of FL-EEC/D over LEACH, _K_-means-LEACH, and FL[1]/D for network lifetime (BS at the center of WSN). Figure 13: FND of FL-EEC/D against LEACH, _K_-means-LEACH, and FL[1]/D (BS at the corner of WSN). It is obvious from these figures that FL-EEC/D highly outperformed its counterparts. However, placing the BS at a farther position resulted in a faster depletion of the nodes, for all schemes. Here, the advantage of FL-EEC/D is more prevalent, as its enhancement over the other schemes became higher, as demonstrated in Figure 17.  
The improvements achieved by the FL-EEC/D scheme point to the ability of balancing the energy through the nodes. This is a result of better selection of the CHs and interchanging the load over the nodes in a more balanced approach. Figure 16: HND of FL-EEC/D against LEACH, \(K\)-means-LEACH, and FL[1]/D (BS at the corner of WSN). Figure 7:0 Average improvement percentage of FL-EEC/D over LEACH, \(K\)-means-LEACH, and FL[1]/D for network lifetime (BS at the corner of WSN). Figure 7:1 QND of FL-EEC/D against LEACH, \(K\)-means-LEACH, and FL[1]/D (BS at the corner of WSN). As shown in Figures 12 and 17, the improvement of network lifetime starts high for FND and then gradually decreases for 10 PND, QND, and HND, respectively. This sequence is evidence of the strength of collaboration between different sensors to take loads of CH operations. Thus, most of the nodes operate together for the longest possible duration and then almost die together.