# Routing with Renewable Energy Management in Wireless Sensor Networks
## 3 REBORN-Renewable Energy-Based Routing Algorithm
\[\mu=\frac{(\alpha-\varphi)\bigg{(}\frac{\beta-\delta}{\varphi-\delta}+\frac{ \varphi-\lambda}{\rho-\lambda}\bigg{)}+2\varphi}{2} \tag{6}\]

To control how both the charge level of the battery and the solar intensity are perceived during the harvesting process, a parameter \(K\) was adopted to give more freedom to the algorithm and manage the packets sent with the priority of choice between the solar intensity and battery energy. This parameter is a configuration value that can be set during the network initialization or changed during operation. All nodes have the same \(K\) value

Figure 6: Solar intensity vs. Time. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variable** & **Standard Value** & **Function** & **Unit** \\ \hline \(\alpha\) & 7200 & Maximum interval between sending out packets & s \\ \hline \(\varphi\) & 120 & Minimum interval between sending out packets & s \\ \hline \(\lambda\) & 400 & Maximum solar intensity chosen & W/m\({}^{2}\) \\ \hline \(\rho\) & 0 & Solar intensity threshold to arrive at \(\alpha\) & W/m\({}^{2}\) \\ \hline \(\phi\) & – & Current solar intensity in solar panel & W/m\({}^{2}\) \\ \hline \(\Omega\) & – & Time to send the next packet & s \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Solar intensity equation variables. that can vary from 0 to 1 and is associated with battery usage. For instance, a value of \(K=0.6\) assumes that the node will wait a while before sending its information, which corresponds to 60% of the remaining time of the battery charge, added to 40% of the time of the solar intensity perceived. Finally, the final version of our model is shown in Equation (7). \[\mu=(\alpha-\varphi)\bigg{[}\bigg{(}\frac{\beta-\delta}{\sigma-\delta}\bigg{)}K +\bigg{(}\frac{\phi-\lambda}{\rho-\lambda}\bigg{)}(1-K)\bigg{]}+\varphi \tag{7}\]

By using a value of \(K=0.85\) and the values adopted in our simulations, the corresponding time intervals are depicted in Figure 6(b), implying that the battery remaining has more importance than solar intensity. ## 4 Performance Evaluation

In this section, we evaluate the performance of our proposed REBORN algorithm and compare it to three other algorithms. The first of the three algorithms used as a basis for comparison was the GAF-EH (explained in Section 3.2). This algorithm does not have any type of packet-sending control mechanism. The second is the REBORN-BAT, which uses only the residual energy information of the node (as described in Section 3.3.1). The third one, called REBORN-SI, is based only on the solar intensity information perceived in the environment (as described in Section 3.3.2). Finally, the last algorithm, named REBORN-both, is our proposed solution that uses both residual energy and solar intensity (as shown in Section 3.3.3). The main reason to compare our final REBORN algorithm to both REBORN-BAT and REBORN-SI is to better understand the impact of each part of the algorithm. In all algorithms, the minimum interval between data packet transmissions to the network was 2 min. With the exception of GAF-EH, all algorithms were able to send their packets at intervals of no more than 2 h. In this sense, if the battery had a high charge level and the solar intensity on a high level, the data would be sent every 2 min. Furthermore, if the solar intensity was weak or nonexistent and the battery level was low, the node would send its data every 2 h.

### Methodology

The simulations were carried out using the Sinalgo simulator [39], which provides a complete environment for the simulation of distributed algorithms. We assumed that each simulation round corresponds to 1 s for a total of 72 h (i.e., three days of simulation). The dawn of a new day began at 06:00 a.m. while dusk was at 06:00 p.m. This assumption is relevant because it defines the beginning and end of the energy harvest each day. The algorithm was set to start running at 00:00 a.m., and end at 11:59 p.m. on the third day. Figure 7: Relation between packet sending times.