## 6 Simulation Results and Discussions
### Simulation Scenarios and Results
#### 6.3.4 Simulation Scenario 4: Throughput Evaluation  
In this context, the contributions of our proposed protocol, both without routing and with multi-hop routing, have been verified with respect to throughput when reaching LND. Figure 13 shows the throughput of the network until round \(n\) for the proposed protocol and its counterparts. The results show that in all protocols, larger network area sizes result in lower throughput. Furthermore, our proposed protocol performs substantially better than the other protocols for all network sizes due to the innovative ideas that were previously described. It goes without saying that the proposed protocol not only doubles the network's lifespan but also enhances data transmission rates and energy efficiency. The proposed protocol sustains network functionality for a far longer period of time than previous ones. This results in more data being sent to the sink node, thereby increasing the overall network throughput. A pertinent question that may arise is the extent to which the proposed protocol outperforms other protocols. Complementing this graphical analysis, Table 14 quantifies the improvement ratios of the throughput, offering a precise evaluation of the proposed protocol's efficiency and dominance over alternative approaches.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Items** & **Protocols Considered in Comparision** & \multicolumn{2}{c}{**Improvement Ratio for the Proposed Proposed Protocol Without Routing**} & \multicolumn{2}{c}{**Improvement Ratio for the Proposed Protocol with Multi-Hop Routing**} \\ \hline \multirow{5}{*}{Scenario \#11 Number of Cris: 100\% network area: 100 \(\times\) 100 m\({}^{2}\)} & PSO-EC & \(135\%\) & \(260\%\) \\ \cline{2-4}  & LDIWPSO & \(225\%\) & \(399\%\) \\ \cline{2-4}  & LDIWPSO & \(225\%\) & \(399\%\) \\ \cline{2-4}  & DVPCA & \(133\%\) & \(258\%\) \\ \cline{2-4}  & NFSOP & \(143\%\) & \(273\%\) \\ \cline{2-4}  & Proposed protocol without routing & NA & \(53\%\) \\ \cline{2-4}  & Proposed protocol with multi-hop routing & NA & NA \\ \hline \multirow{5}{*}{Scenario \#1 Number of Cris: 500\% network area: 100 \(\times\) 100 m\({}^{2}\)} & PSO-EC & \(131\%\) & \(254\%\) \\ \cline{2-4}  & LDIWPSO & \(137\%\) & \(264\%\) \\ \cline{2-4}  & DVPCA & \(126\%\) & \(247\%\) \\ \cline{2-4}  & NPSOP & \(130\%\) & \(253\%\) \\ \cline{2-4}  & Proposed protocol without routing & NA & \(53\%\) \\ \cline{2-4}  & Proposed protocol with multi-hop routing & NA & NA \\ \hline \multirow{5}{*}{Scenario \#2 Number of Cris: 100\% network area: 500 \(\times\) 500 m\({}^{2}\)} & PSO-EC & \(194\%\) & \(438\%\) \\ \cline{2-4}  & LDIWPSO & \(190\%\) & \(432\%\) \\ \cline{2-4}  & DVPCA & \(190\%\) & \(432\%\) \\ \cline{2-4}  & NPSOP & \(128\%\) & \(317\%\) \\ \cline{2-4}  & Proposed protocol without routing & NA & \(83\%\) \\ \cline{2-4}  & Proposed protocol with multi-hop routing & NA & NA \\ \hline \multirow{5}{*}{Scenario \#2 Number of Cris: 100\% network area: 500 \(\times\) 500 m\({}^{2}\)} & PSO-EC & \(534\%\) & \(1063\%\) \\ \cline{2-4}  & LDIWPSO & \(573\%\) & \(1133\%\) \\ \cline{2-4}  & DVPCA & \(490\%\) & \(981\%\) \\ \cline{2-4}  & NPSOP & \(468\%\) & \(941\%\) \\ \cline{2-4}  & Proposed protocol without routing & NA & \(83\%\) \\ \cline{2-4}  & Proposed protocol with multi-hop routing & NA & NA \\ \hline \hline \end{tabular}  
* NA: means not available, as the protocol is compared with itself, which is not meaningful.  
\end{table}
Table 13: Comparative analysis of improvement ratios: energy consumption in the proposed protocol versus counterparts.  
Figure 13: Throughput: A comparison with counterpart protocols for Scenarios 1 and 2 (PSO-EEC [39], LDIWPSO [40], OFCA [41], and NPSOP [42]). (**a**) Scenario #1: Network area: 100 \(\times\) 100 m\({}^{2}\) with 100 nodes, 10% and 5% PDFHs. (**b**) Scenario #2: Network area: 500 \(\times\) 500 m\({}^{2}\) with 300 nodes, 10% and 5% PDFHs.