# Matching of Energy Provisions in Multihop Wireless Infra-Structures
## 6 Numerical Evaluation
### Numerical Results in Scenario-1: Line Topology
We can see that the overall energy consumption of BSs in this evaluation is unbalanced for all networks that utilize the Same-EP. This is because the network traffic is delivered from STAs to the GW by multi-hop relays of wireless links, resulting in the concentrated network traffic at the nodes near the GW. In general, BSs that are close to the GW position have more energy consumption than BSs that are far away from the GW position. However, the topological position of BSs with maximum energy consumption is not in zone(1) but at the center of zone(2), the center of which is around the BS2 at the position of (300, 300). The reason for this phenomenon is the total packet activity, including transmission, receiving and overhearing, at BS2 is largest. From the figure, we see that Matching-EP \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Items** & **BS(1)** & **BS(2)** & **BS(3)** & **BS(4)** & **Accuracy** \\ \hline Time average value of simulation value \(Diff_{M}(i)\) result & 1.09 & 1.33 & 0.97 & 0.61 & 1 \\ _Diff(i)_ for uniform energy consumption & 1 & 1 & 1 & 1 & 0.751 \\ _Diff(i)_ from _TX-RX-OH_ analysis & 1.074 & 1.218 & 0.975 & 0.733 & 0.925 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The accuracy of energy differentiation analysis in line-topology WMI based on _TX_, _RX_, _OH_ relations among BSs. Figure 10: An example of energy differentiation of BSs in the line-topology WMI with 4 BSs. enables much better energy balance among BSs. The average matching degree of networks employing Matching-EP is much higher than the network with uniform initial energy deployment. Figure 11(a) shows the results of the network lifetime of the WMI. Comparing with Same-EP approach, the Matching-EP approach enables 27%-41% improvement of network lifetime. From the result, it can be seen that the networks with smaller number of BSs result in larger lifetime. This is because there are smaller amounts of STA traffic in networks with smaller number of BSs. Figure 11(b) illustrates the amount of successful packet delivery with varying BS number. Matching-EP results in a larger amount of packet delivery with a improvement ratio ranging from 22% to 41% for packet delivery during the network lifetime. The improvement is significant at the networks with a larger BS number. This is because that there is a larger difference of energy consumption with Same-EP in a network with a larger BS number. Figure 11(c) shows the average value of Matching Degree, the matching of energy provision to energy consumption. For the network with 4 BSs, the average energy matching degree of BSs increases from 0.81 to 0.938 with an improvement of 15.9%. For the network with 8 BSs, the energy matching degree of BSs increases from 0.71 to 0.90. For the network with 12 BSs, the energy matching degree  
Figure 11: Energy consumption distribution and energy mapping in scenario-1 (Line Scenario). of BSs increases from 0.67 to 0.88. For the network with 16 BSs, the energy matching degree of BSs increases from 0.63 to 0.85 with an improvement of 34.6%.