## 5 Performance Evaluation
### Performance Evaluation  
Figure 6 shows the distribution of individual hop distance \(d_{i}\) under different multi-hop routes, as is discussed in Equation (9) and Table 2. Given the source to BS distance \(d=800\), there are several multi-hop route options with hop number \(n\in[2,8]\) (see Table 3). Finally, we will choose 8-hop route since each node consumes the least energy. It is worth noting that the practical \(d_{1}(8)\) will be larger than the theoretical value under random network topology. In this way, the energy consumption for all the 8 sensor nodes is the minimal than other \(n\) hop route where \(n\in[2,7]\). Therefore, both energy efficiency and energy balancing is achieved. \begin{table}
\begin{tabular}{|c|c|} \hline
**Parameter** & **Value** \\ \hline Network size & 300 \(\times\)300 m\({}^{2}\) \\ \hline Node number & 300 \\ \hline Radius & 150 m \\ \hline Data length & 2,000 bits \\ \hline Initial energy & 2 Joule \\ \hline \(E_{\mathit{e}\mathit{i}\mathit{e}\mathit{i}\mathit{e}}\) & 50 nJ/bit \\ \hline \(\varepsilon_{\mathit{e}\mathit{i}\mathit{e}\mathit{i}\mathit{e}}\) & 0.001 pJ/bit/m\({}^{4}\) \\ \hline \(\Delta\) & [20,50] m \\ \hline BS & inside or outside \\ \hline \end{tabular}
\end{table} 
Table 4: Simulation environment. Figure 6: Distribution of hop distance under different multi-hop routes. Figure 7 shows the average energy consumption for four routing algorithms under 100 different network topologies. The simulation environment is that there are 300 nodes randomly placed in a 300 \(\times\) 300 m\({}^{2}\) area network. We set \(R=150\) and \(\Delta=40\) here. We can see from Figure 7 that direct transmission algorithm consumes the largest amount of energy since the average source to sink node distance is relatively long and multi-path model is used here. Our DEAR algorithm consumes the least energy due to it distance-based nature. The performance of greedy and MRE algorithm is in the middle under 100 simulations. From here we can see that DEAR can not only balance energy consumption for all sensor nodes but also reduce energy consumption comparing to other algorithms. Figures 8 and 9 show the total energy consumption when BS is placed either inside or outside. The simulation environment is similar to Figure 7 where there are 300 nodes randomly deployed in a 300 \(\times\) 300 m\({}^{2}\) area. We set \(R=130\) and \(\Delta=20\) here. From both figures, we can see a similar trend of energy consumption for the four routing algorithms where the direct transmission algorithm consumes the largest energy while our DEAR algorithm consumes the least energy. The total energy means the summation of energy consumption for each algorithm up to the current simulation round. Besides, we can see that the total energy consumption increases sharply when BS is placed outside at (150, 400) since the average source to BS distance is much larger than before. Figure 10 shows network lifetime under the same network environment as in Figure 7. Here, network lifetime is defined as the time when the first node dies out of energy since this might cause network partition or isolated area quickly afterwards. Figure 7: Average energy consumption. As can be seen from Figure10, direct transmission usually has the shortest lifetime in a large scale network scenario or when the average source to sink node distance is large. For the MRE algorithm, a node chooses its next hop based on the remaining energy which is irrelevant to the distance distribution. Therefore, the final multi-hop route might has too many short hop number which consumes more average energy, as is shown in previous Figure 7. For a greedy routing algorithm, each node will prefer to choose its next hop with distance close to \(R\) in order to make greediest progress toward the sink node. Thus, more energy consumption is caused with relatively short network lifetime. Again we can see the DEAR algorithm has the longest network lifetime due to its energy efficiency and balancing nature. Figure 8: Total energy consumption when BS is inside.