# Matching of Energy Provisions in Multihop Wireless Infra-Structures
## 6 Numerical Evaluation
### Numerical Results in Scenario-1: Line Topology  
First, in order to evaluate basic performance of energy provision that is independent of routing protocols in multihop wireless networks, we consider line topology scenarios. In this scenario, each BS has an associated STA traffic source generating Poisson traffic. To validate the energy differentiation analysis, we illustrate the result of energy differentiation observed in an example of line-topology WMI with 4 BSs. Table 7 shows results of energy differentiation analysis for the case of a line-topology WMI with four BS. The first row shows \(Diff_{M}(i)\), the time-average value of energy differentiation measured in the simulation evaluation with SP-HWMP routing. The second row shows the value of energy differentiation expected if the energy consumption obeys the uniform energy consumption model. The third row shows the value of energy differentiation expected if the energy consumption obeys the _TX-RX-OH_ relations. The last column shows the accuracy of the models, compared with the \(Diff_{R}(i)\) results obtained by the simulation. The accuracy of the analysis is defined in terms of the analyzed value and the results from the packet-level simulations. The analysis accuracy in regard to energy differentiation at is defined by:  
\[accuracy=1-\frac{\sum_{l=1}^{N}\frac{\mid Diff(i)-Diff_{M}(i)\mid}{Diff_{M}(i)}}{N} \tag{17}\]  
where \(Diff_{M}(i)\) is the averaged differentiation factor of BS(\(i\)) obtained from simulation result over time from the start and to network lifetime. The ideal accuracy of analysis is 1, which indicates that each the analysed differentiation factor is same with the results of energy differentiation factor \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Scenario-1** & **Scenario-2** \\ \hline Simulator & \multicolumn{2}{c}{NS3} \\ MAC/PHY layer model & \multicolumn{2}{c}{IEEE 802.11s [34]} \\ MAC protocol & \multicolumn{2}{c}{CSMA} \\ Propagation loss model & \multicolumn{2}{c}{Log-distance path loss model} \\ Mobility model & static & Random mobility \\ Number of static BSs & 4, 8, 12, 16 & 16 \\ Number of STAs & 4, 8, 12, 16 & 10 \\ Number of GW & \multicolumn{2}{c}{1} \\ Application traffic & \multicolumn{2}{c}{From STAs to GW} \\ Initial energy of Battery & \multicolumn{2}{c}{16 J for Same-EP case} \\ _TX_ current \(I_{TX}\) & \multicolumn{2}{c}{17.4 mA} \\ _RX_ current \(I_{RX}\) & \multicolumn{2}{c}{19.7 mA} \\ _IDLE_ current \(I_{I}\) & \multicolumn{2}{c}{426 \(\mu\)A} \\ Battery energy at BSs & \multicolumn{2}{c}{All BSs} \\ Packet size & \multicolumn{2}{c}{1024 bytes} \\ Data rate & \multicolumn{2}{c}{54 Mb/s} \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Simulation set-up parameters. \(Diff_{M}(i)\). It can be seen that the analysis based on _TX-RX-OH_ relations achieves the high analysis accuracy up to 0.925. _TX-RX-OH_ based analysis improves about 27% accuracy compared with the case of \(Diff(i)=1\) corresponding to uniform energy consumption in the line-topology WMI of 4 BSs. The energy differentiation result is shown in Figure 10. From the results, it can be seen that energy differentiation occurs although each BS has the same initial energy. The energy consumption is correlated with the topological position of each BS. The results show that the BS(1) that is nearest to the GW does not have the largest energy consumption. Instead, we can see that BS(2) has the largest energy consumption. These results are different with previous studies of multihop wireless network such as sensor networks, in which node near the gateway or sink node has the largest energy consumption [19; 33]. To illustrate the position dependency of energy consumption at each BS, we show the relation between the residual energy and position for each BS. Since it is difficult to show the spatial distribution of energy consumption at many moments in time, in Figure 11 we show results for two representative times near the start of network operation and near the end of network lifetime.