## 6 Results and Discussion
### Analysis of Network Lifetime and NDR  
The network lifetime is described as the time elapsed between initiating the network operation until the death of its last node. The scenario simulated in our experiments is similar to the topology shown in Figure 1.  
In this scenario, nodes density is also varied from 50 to 500 nodes to analyze the scalability of the three protocols.  
Figures 9 and 10 depict the achieved network lifetime and NDR by DT, LEACH and LEACH-PRO when applied to a WSN with sizes of 50, 100, 200 and 500 nodes respectively. The plotted results show that LEACH-PRO is outperforming the other two protocols. In DT, the source node directly transmits its data to the BS and thus consumes more  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline MATLAB Version & 2015/R \\ Node Deployment Area & 200 m \(\times\) 300 m \\ Network Sizes (Nodes Density) & 50, 100, 200, 500 \\ Initial Energy (J) of each node & 0.5 \\ \(E_{Tx-slice}\) & 50 m/bit \\ \(E_{Rx-slice}\) & 50 n/bit \\ \(\in Lamp\) & 100 pJ/bit/m\({}^{2}\) \\ Control Packet Length & 200 Bits \\ Data Packet Length & 4000 Bits \\ Number of nodes in Cluster & 10 \\ Probability & 0.1 \\ Simulation Rounds & 4000 \\ Position of BS & (100, 300) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Summary of simulation settings.  
transmit power, hence, the death rate of nodes in DT is much higher which makes the network lifetime much shorter as well. In LEACH, instead of direct transmission the data is transmitted via CHs, thus, LEACH achieves longer lifetime than DT, but the blind CHs selection leads to a fast degradation in its performance compared to LEACH-PRO. The supremacy of this latter, in relation to network lifetime and NDR, is mainly due to its efficient probabilistic CH replacement based on maximum residual energy and minimum distance to BS. From Figures 9 and 10 we observe as well that the increase of the network density negatively affects the performance of all protocols, including LEACH-PRO, but this latter is still performing better than DT and LEACH.  
More specifically, Figures 9a and 10a illustrate the network lifetime and NDR for a WSN of size 50. As shown in Figure 10a, the first node dies after 263 rounds, in DT, after 759 rounds, in LEACH and after 1484 rounds in LEACH-PRO. For DT, 50% of nodes die after 502 rounds, and the entire network die after 584 rounds, whereas for LEACH 50% of nodes consume their entire power after 1114 rounds. These results highlight that the death of the first node in LEACH-PRO occurs after the death of 1005 of nodes in DT and 50% of nodes in LEACH. This trend continues when the network size is increased to 100 nodes. However, for a network with 200 nodes, the FND in LEACH-PRO occurs after the death of all nodes in DT but before HND occurrence in LEACH. This trend will hold with a network of 500 nodes. Such significant improvement of performance shown by LEACH-PRO is justified by the stability in finding a node with maximum residual energy to act as a CH.  
Figure 9: The achieved lifetime for varying network densities: Number of dead nodes vs. number of rounds. Network of (**a**) 50, (**b**) 100, (**c**) 200, (**d**) 500 nodes.