## 4 Proposed Routing Protocols
### Proposed Two-Level Phantom with a Pursue Ring Protocol (PhaP)
#### 4.1.1 PHASE 0: Network Configuration
Figure 2: Flowchart of the \(P_{ring}\) computation process in the proposed PhaP protocol. 1.2. PHASE 1: Selection of a First Level Phantom Node (\(P_{\textit{Nsf}}\)) and Packet Routing from Source Node to \(P_{\textit{Nsf}}\)  
After the \(P_{\textit{ring}}\) is configured, the network is ready for packet routing. The proposed PhaP routing algorithm is summarized in Algorithm 1. The packet routing process is done in three phases. Phase 1 routing is activated by the source node when the source node detects an asset. The source node selects a random first level phantom node (\(P_{\textit{Nsf}}\)) using similar phantom node selection algorithm as in ProbR. After \(P_{\textit{Nsf}}\) is selected, it sends packet to the \(P_{\textit{Nsf}}\) using a directed random-walk routing strategy. The directed random-walk routing strategy involves a process of next-hop node selection at every packet forwarding instance. The forwarding node computes a set of neighboring nodes with a shorter hop distance to the destination node than the forwarding node itself. Then it randomly selects one neighboring node from the set as the next-hop node. The next-hop node becomes the forwarding node and forwards the packet. For easy of understanding, the group of neighboring nodes with shorter hop distance to the destination node is termed as \(SDR_{N}\), in Algorithms 1 and 2. Also, the selected next-hop node from the \(SDR_{N}\) is termed as \(DR_{N}\) and the destination nodes are termed as target node. At the source node, the destination node is the selected \(P_{\textit{Nsf}}\). 1.3. PHASE 2: Selection of \(P_{\textit{Nsf}}\) and Packet Routing from \(P_{\textit{Nsf}}\) to \(P_{\textit{Nsec}}\)  
After the \(P_{\textit{Nsf}}\) receives a packet from \(P_{\textit{Nsf}}\), it sets a bias threshold value, \(T_{P}\). Then it generates a random number, \(R_{N}\), between [0, 1]. The \(R_{N}\) and \(T_{P}\) values are compared. Depending on the comparison results, \(P_{\textit{Nsf}}\) selects a random \(P_{\textit{Nsec}}\) according to Table 4. The \(P_{\textit{Nsec}}\) selection process is highly dependent on the location of the \(P_{\textit{Nsf}}\) with respect to the sink node. The \(P_{\textit{Nsf}}\) may be located on the east or west side of the sink node according to the \(Y\)-axis. After the \(P_{\textit{Nsec}}\) is selected, \(P_{\textit{Nsf}}\) forwards the packet to the randomly selected \(P_{\textit{Nsec}}\) using the directed random-walk routing strategy. To guarantee high path diversity for successive packets, new \(P_{\textit{Nsf}}\) and \(P_{\textit{Nsec}}\) are selected for each packet transmission. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Location of \(P_{\textit{Nsf}}\)**} & \multicolumn{2}{c}{**Selection of \(P_{\textit{Nsec}}\)**} \\ \cline{2-3}  & \(R_{N}<T_{P}\) & \(R_{N}\geq T_{P}\) \\ \hline East of the sink node (\(X\)-coordinate \(<0\)) & \(P_{\textit{rNW}}\) & \(P_{\textit{rSE}}\) \\ West of the sink node (\(X\)-coordinate \(\geq 0\)) & \(P_{\textit{rNE}}\) & \(P_{\textit{rSW}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Selection of a second level phantom node (\(P_{\textit{Nsec}}\)) according to the first level phantom node (\(P_{\textit{Nsf}}\)) location and value of the random number (\(R_{N}\)). Figure 3: Computation of the inclination angle \(\theta\).