# A Green Routing Protocol with Wireless Power Transfer for Internet of Things
## 6 Results Analysis  
In order to validate the proposed routing approach, we resorted to numerical simulations performed over the Cooja framework, which has been proven to be an accurate, flexible, and high fidelity tool for the simulation of RPL in WSNs [39]. In particular, we consider the parameters for the simulations as in ref. [36] and reported in Table 2. In addition, we focused on a worst case condition, where devices are not allowed to be in sleep mode, as it usually happens for emergency situation. The scenario under investigation is comprised of 50 nodes randomly deployed over an area of 200 \(\times\) 200 m\({}^{2}\), where a specific node acts as the sink, that is the device in charge of collecting data from the other sensors, as well as the DODAG Root. It has been supposed the presence of one node endowed with an additional power supply able to recharge its neighboring motes; in addition, it is located far enough from the sink node to enhance the benefits. For the sake of simplicity, the initial energy level \(E_{0}\) is the maximum value which is associated with the maximum battery level \(B_{\max}\) for all the devices. Further, the energy-harvesting process has been modeled as a closed system, i.e, without any outer energy \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Communication pattern & MP2P \\ L3 Protocol & RPL \\ L2 Protocol & IEEE 802.15.4 \\ Transceiver & CC2420 \\ \(E_{0}\) & 25 (I) \\ Data message rate & 1 (msg/min) \\ \hline DIO & 16 (bytes) \\ DAO & 16 (bytes) \\ DAO-ACK & 4 (bytes) \\ DIS & 2 (bytes) \\ Data Packet & 30 (bytes) \\ \(P\) & 100 mW \\ \(P_{h}\) & 10 mW \\ \(\alpha\) & 2.5 \\ \(\zeta\) & 0.6 \\ \(\eta\) & 0.2 \\ \(T_{r}\) & 5 s \\ \(T_{p}\) & 1 s \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters adopted in performing numerical simulations. source, where the battery recharging is performed on the basis of the received RF signal. In particular, a fraction \(\eta\) of the received power is successfully convoyed to the battery, without any additional loss, according to (6). Considering the features of IEEE 802.15.4 standard and the specific network deployment, we assumed that \(\eta=0.2\). In Figures 3-5, the residual normalized battery level as a function of the time normalized to the frame duration for the different _groups_ of devices that are interconnected with RPL protocol with the OF0, OF1, or OF2 metric, is pointed out, respectively (The battery level of the DODAG Root A has not been depicted as its behavior is fairly trivial). In particular, each group has been associated with the corresponding rank, that is the minimum number of hops towards the root, so that the \(i\)-th set of nodes is \(i\)-hops far from its destination. It can be noticed that the proposed approach is able to prolong the network lifetime (i.e., the time interval within which all the network nodes are active) with a gain approximately equal to 54% and 14% w.r.t. the RPL endowed with OF0 or OF1 metric, respectively. This is due to the fact that OF0 metric does not take into account battery level, while OF1 metric relies only on the nodes' battery levels, without taking into account the opportunity of being recharged by neighboring nodes. In addition, the node with rank equal to 2 or 3 benefits from the proposed approach, thus lowering the DODAG disconnection probability. Figure 3: Residual normalized battery level time evolution of different groups of devices connected with RPL objective function zero (OF0). Figure 4: Residual normalized battery level time evolution of different groups of devices connected with RPL OF1. Figure 5: Residual normalized battery level time evolution of different groups of devices connected with RPL OF2. Finally, in Figure 6, the [PERSON]'s Fairness Index for the WPAN nodes' battery level is depicted as a function of time for the RPL protocol based on OF0, OF1, and OF2 metrics. Specifically, the raw data obtained from the Cooja simulator has been accurately post processed to derive this parameter, which is defined as ref.