# A Green Routing Protocol with Wireless Power Transfer for Internet of Things
## 4 System Model  
An LLN with \(N\) nodes is considered, as shown in Figure 2, while in Table 1 the definitions used in this paper are summarized. Each sensor node in the network is powered by the battery, it is equipped with one antenna and has homogeneous storage and computation capacity. Usually, in a WSN, the nodes are geographically distributed to periodically report measurements towards the sink node. This is the typical use case of the RPL routing protocol in which the predominant type of traffic is of the MP2P type. For this reason, a subset of nodes, particularly those ones closer to the root node, consume more energy of other ones and, therefore, are more vulnerable. Then, it is important to prevent these nodes from running out of energy too quickly, consequently allowing an extension of the whole network lifetime.  
We assume that a limited number of nodes have sufficient power \(P\), e.g., a CH which powers the nodes grouped in its cluster or a relay node or a cellular device in proximity, to recharge their neighbor nodes at the maximum level of battery. For example, in Figure 2, the node 3 has the power \(P\) necessary to recharge the nodes number 6 and number 1 in its surrounding. Moreover, we consider MP2P traffic pattern in RPL where the end-nodes send data messages to the root node, also known as a sink node or LLN Border Router (LBR) node in RPL, creating an upward flow as, e.g., in Figure 2.  
The energy harvested by the \(i\)-th node in the surrounding of the node with power \(P\), called hereinafter the strong node, is  
\[E_{i}=\zeta_{i}h_{i}PT_{r} \tag{1}\]  
where \(0<\zeta_{i}<1\) is the RF-EH efficiency of the nodei, \(h_{i}\) is channel power gain between the strong node and the node \(i\), and \(T_{r}\) is the time necessary to charge at the maximum value the battery of node \(i\). The channel power gain \(h_{i}\) is expressed as:  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Notations** & **Definitions** \\ \hline \(E_{i}\) & Energy harvested by \(i\)-th node \\ P & Maximum Transmission power \\ \(T_{r}\) & Time to recharge nodes at power P \\ \(T_{p}\) & Duration time of a packet \\ G & average power attenuation \\ \(h_{i}\) & channel power gain from strong node and \(i\)-th node \\ \(h_{ij}\) & channel power gain from \(i\)-th node and \(j-th\) node \\ \(d_{i}\) & distance from strong node to \(i\)-th node \\ \(\alpha\) & path loss exponent \\ \(\zeta_{i}\) & RF-EH efficiency of the node \(i\) (child) \\ \(\eta_{j}\) & RF-EH efficiency at node \(j\) (parent) \\ \(P_{c}(t)\) & Consumed power at time \(t\) at the parent \\ \(E_{0}\) & Initial energy level at the parent \\ \(E_{r}\) & Residual energy level at the parent \\ \(P_{h}(t)\) & Harvested power from the energy source \\ \(P_{rx}\) & Received power at the parent \\ \(P_{th}\) & RF-EH sensitivity level at the parent \\ \hline \hline \end{tabular}
\end{table}
Table 1: Notations and Definitions.  
\[h_{i}=Gd_{i}^{-\alpha} \tag{2}\]  
Here, \(d_{i}\) is the distance between the strong node and \(i\)-th node, \(G\) refers to the average power attenuation at a reference distance of 1 m, and \(\alpha\) is the path loss exponent.  
The node \(i\) has a sufficient power to recharge the node \(j\) which has been selected as parent node according to the RPL path selection, during the SWIPT mode operation. For example, as shown in Figure 2, the node 3 recharges the node 1 which has a sufficient power to harvest energy to its parent, now. Then, node 1 can select as parent node 5 or node 7. It chooses node 7 with a lower level of battery than node 5 according to the OF of RPL, detailed in the next Section 5, to recharge it by SWIPT and, as a consequence, for achieving the goal of the global energy balance of the network.  
In the SWIPT mode, the normal sensor functions, i.e., sensing, sending, and receiving, can work together for energy-harvesting. We consider the SWIPT PS receiver where the RF signal is divided into two parts with different power, one for information decoding and the other one for EH.