## 4 System Model and Description of the Proposed Protocols
### Proposed Protocol 1 (EP-VIR-Three)
#### 4.1.2 Detailed Theoretical Analysis of Propagation and Data Transmission Model  
In this routing protocol, every node broadcasts a message to find its neighbor nodes and a number of hops. These two parameters are computed through beacon from the sink. Furthermore, the reactive beaconing mechanism is adapted to synchronize the routing table of the sensor nodes. This information is shared with neighbors by using hello packet (see Table 2). When a sensor node receives a hello packet, it upgrades its routing table (see Table 3). When a sender sends DP, it includes a hello packet. Upon data reception, the receiver node upgrades its table again, if its depth is higher than sender node [7].  
EP-VIR-Three selects the next forwarder node by checking the 3-hop neighbor's availability of the next forwarder node to avoid the void hole occurrence and data loss. For example, in Figure 2, the current source node \(C\) checks its neighbor nodes and select the current forwarder node by checking the 3-hop neighbor's availability of the next forwarder nodes (i.e., node \(A\) and node \(B\)). Therefore, node \(C\) will select the node \(B\) as its current forwarder node because node \(B\) has neighbors until its \(3^{rd}\) hop. Furthermore, we exploited the 2D mobility model and piggybacking mechanism to lower neighbors' request.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline Node ID & Number of Neighbour Nodes & Distance from Sink & Number of Hops from Sink \\ \hline \hline \end{tabular}
\end{table}
Table 2: Format of Hello packet.  
Figure 9: System Model of EP-VIR-Three.  
The source node selects the next forwarder node on the bases of Cost Function (CF) value, which is calculated using the Equation (1) as in [7]:  
\[CF(k)=\frac{Dis(j,k)}{Hop(k)\times Neighbor(k)}, \tag{1}\]  
where \(Hop(k)\) is the \(k\)th forwarder node of the source node, \(Neighbor(k)\) is used to represent the neighbors of the \(k\)th node and \(Dis(j,k)\) is used to represent the distance between the \(k\)th forwarder node and the source node \(j\). This equation shows that \(CF\) has the maximum value until the forwarder node has the minimum number of neighbors, minimum hops from the sink and the maximum distance from the sender node (source node). The node having maximum \(CF\) value and 3-hop neighbors is selected as next forwarder for the current source node. Then, the source node broadcasts this information to its neighbors using beacon message. When the neighbors receive this beacon message, they perform a comparative analysis of their nodes ID. If this ID matches the ID of the DP, then this node is selected as a forwarder. In addition, all other nodes discard that DP. This process continues until data reaches the destined sink. Then, the sink forwards the data to a respective control station.  
How to ensure minimum neighbors? Protocol EP-VIR-Three selects the next potential node using 3-hop neighbor's information, its distance and its hop count from destined sink node. Therefore, the potential forwarder node is elected on the base closeness from the destined sink. The reason behind this selection criteria is maximum EC during communication between the nodes. Therefore, protocol chooses the path with the minimum participating nodes in the communication range. In the current scenario, this selection criteria affirms minimum neighbor nodes. The current source node elects the next potential forwarder node using these parameters, i.e., \(Hop(k)\), \(Neighbor(k)\) and \(Dis(j,k)\).  
How \(3^{rd}\) hop neighbors availability acquired? In Figure 2, forwarder node selection criteria for both proposed protocols is pictorially described. In this figure, the current source node \(C\) checks its neighbor nodes and selects the current forwarder node by checking the 3-hop neighbor's availability of the next forwarder nodes (i.e., node \(A\) and node \(B\)). Therefore, node \(C\) will select the node \(B\) as its current forwarder node because node \(B\) has neighbors until its \(3^{rd}\) hop.