# Matching of Energy Provisions in Multihop Wireless Infra-Structures
## 6 Numerical Evaluation  
In this section, we show the evaluation results with respect to the proposal of energy provision and analyses described in Sections 4 and 5. We do network simulations using the discrete event network simulator NS-3 to study the impact of energy provision on the network performance [40]. In a WMI network, battery powered BSs are provided with various amounts of initial energy. The total amount of initial energy in the WMI network is constant. We evaluate the proposed protocol Matching-EP in comparison with the conventional conventional energy provision approach, here called Same-EP, in which all BS have the same initial energy. In the evaluation, we focus on the impact of network sizes, network topology, and routing protocols on the proposed energy deployments. We consider two scenarios for the evaluation. The first scenario, scenario-1, evaluates the basic routing-independent case of the line-topology network. Various size networks are evaluated, as shown in Figure 8. Four cases of networks with different network sizes and different number of static STAs are studied. The second scenario, scenario-2, employs a grid-topology WMI network, that enable us to examine different routing protocols. The network topology for scenario-2 is shown in Figure 9. Mobile STA with random mobility are employed in the network. This scenario lets us to examine the impact of energy deployment in the combined environment of routing and STA mobility. Figure 8: Line topology scenarios (such as WMI for roads). Four routing protocols based on proactive Hybrid Wireless Mesh Protocol (HWMP) in IEEE 802.11s mesh networks are evaluated in the scenario 2. In addition to proactive HWMP in IEEE 802.11s mesh networks, we developed three routing protocols based on HWMP with various routing metrics so as to evaluate the energy matching performances of shortest path, energy and connectivity aware routing protocols [41]. * HWMP proactive routing (HWMP): As defined in IEEE 11s [34], default proactive tree-based routing adopts the airtime cost metric. * Shortest path HWMP routing (SP-HWMP): A proactive HWMP routing with shortest path selection. A cost metric for shortest path selection can be defined for each BS by \(C_{sp}(i)=1\), so that the path cost is the sum of each BS cost \(C_{sp}(i)\) in the path, _i.e._, \(C_{R}(i)=\Sigma C_{sp}(i)\). * Energy aware HWMP routing (E-HWMP): A proactive HWMP routing with residual energy as BS cost metric, given by \(C_{Er}(i)=\dfrac{100}{E_{r}/E_{0}}\) where \(E_{r}\) is the residual energy at BS(\(i\)). * Energy-Connectivity aware HWMP routing (EC-HWMP): A proactive HWMP routing with both residual energy and network connectivity as the cost metric. The cost metric is given by \(C_{EC}(i)=C_{Er}(i)\times H_{GW}(i)\) where \(H_{GW}(i)\) is the hop distance from the BS(\(i\)) to the GW. Main evaluation metrics in the simulation are shown in Table 5. The metrics in our evaluations include: network lifetime, successfully received packets, matching degree between energy consumption and energy provisions, _etc._ \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt}} \hline \hline
**Network Lifetime** & The duration from the start time of the network to the time when the first BS runs out of its energy \\ \hline
**Successfully Received Packets** & The total number of successfully received packets at the GW \\ \hline
**Node Energy** & The remaining energy at each BS \\ \hline
**Matching Degree** & As defined in Equation (2) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Evaluation Metrics. Figure 9: Grid network topology model in scenario-2. Unless otherwise stated, the simulation is set up as shown in Table 6. The simulation environment includes not only packet level routing operations, but also MAC Protocols dealing with carrier sensing, packet collisions, packet retransmission. This allows us to obtain realistic results with regard to energy consumption in the network. The simulation adopts the log-distance path loss model as the default propagation loss model.