# FTUC: A Flooding Tree Uneven Clustering Protocol for a Wireless Sensor Network
## 6 Simulation and Analysis
### FTUC Parameterization  
In the first part of the experiments, we evaluate the impact of the FTUC parameters on the lifetime of the network. The initial values of the parameters are set as C = 0.8, C1 = 0.8, C2 = 0.2, T = 0.1, R\({}_{0}\) = 100, \(\alpha\) = 0.4, \(\beta\) = 0.3, and \(\gamma\) = 0.3, and the iteration time T\({}_{\text{R}}\) = 300 s.  
The C parameter controls the computation of the competition radius and determines the number of fCH in the network. We evaluated (Figure 5) the average number of cluster heads elected every 10 rounds of the network lifetime, depending on different values of C. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline \(\text{E}_{\text{elec}}(\text{nJ}/\text{bit})\) & 50 \\ \(\epsilon_{\text{fs}}(\text{pJ}/(\text{bit}/\text{m}^{2}))\) & 6 \\ \(\epsilon_{\text{mp}}(\text{pJ}/(\text{bit}/\text{m}^{2}))\) & 0.0011 \\ \(\text{d}_{0}(\text{m})\) & 87 \\ \(\text{E}_{\text{sen}}(\text{nJ}/\text{bit})\) & 0.001 \\ \(\text{E}_{\text{com}}(\text{nJ}/\text{bit})\) & 0.001 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters for the networks. Figure 4: Cupcarbon simulation of FTUC. Cluster heads are evenly distributed in the network, and unequal clusters are created. As can be seen, at the beginning of the network lifetime, each node has enough energy to elect a sufficient cluster heads number. However, after 50 rounds, the number of cluster heads decreases dramatically as the result of the apparition of dead nodes. Then, a lower number of nodes leads to the generation of less tentative CHs, and these tentative CHs have a higher probability of choosing the same node as the final cluster head in an adjacent area, creating bigger clusters. As can be seen, when C = 0.8, the number of CHs is more uniformly elected. This value is a good trade-off between the size of the competition radius of each node and the number of elected fCH. This number has a great impact on the overall distribution of possible CHs throughout the network. We evaluated the mean residual energy depending on C. In Figure 6, we can find that as the C value increases up to 0.8, \(\mathrm{M_{E}(t)}\) increases too. If C continues to grow, the competition radius near the BS becomes very small, resulting in very large clusters being located farther away. These large clusters in turn see their fCH dying prematurely. Finally, it can be seen that C = 0.8 is the best compromise between the number of elected fCHs and the mean residual energy and has been chosen for the rest of the experiments. Figure 5: Number of elected CH per 10 rounds, depending on the competition radius calculation. Figure 6: Evolution of \(\mathrm{M_{E}(t)}\) depending on the C value. The C1 and C2 parameters enable one to make a trade-off during the CH election between the relative position of the node to the reference circle and its residual energy (see Equation (6)). These parameters should respect the condition C1 + C2 = 1. Figure 7 shows the relation between the mean residual energy of the network and C1 and C2. As can be seen with the increase of C1, the network lifetime also increases. We can see that a bigger C1 values makes the position factor more important than the energy factor to prolong the network lifetime. The results in Figure 7 show that when a final cluster head is elected with a good position, it wastes less energy on inter-cluster communications as the CHs are evenly placed in the network. Therefore, it can prolong the network lifetime efficiently. Figure 8 reports the influence of C1 and C2 values on the energy variance (Equation (7)), but it appears as a different trend when compared to what was previously thought. From this point of view, increasing C1 also increases \(\sigma_{\text{E}}\)(t). This comes from the fact that the residual energy of each fCH decreases faster, thus increasing the network energy variance. When C1  
Figure 8: Variance of residual energy depending on C1 and C2.