## 3 System Model
### Subdivision Technique  
To increase the network lifetime by evenly distributing the load across all network nodes, the network is divided into regions and sub-regions. Assuming \(r\) as the radius of sensor node, the diameter of the node sensing area was \(D_{n}\). The maximum size rectangle  
Figure 1: Proposed multi-tier clustering framework for WSN-IoT applications. that could be formed within the node sensing area has a diagonal \(D_{rec}\) and side length as \(s_{l}en\). The breadth of the entire network area is presented as \(Bred_{net}\). Therefore, the number of regions that could be formed are calculated as:  
\[Number_{reg}=\frac{Bred_{net}}{r}+1 \tag{1}\]  
From mathematics we know,  
\[D_{n}=2*r\quad and\quad D_{rec}=s_{len}*\sqrt{2}\]  
Here, the length of both \(D_{n}\) and \(D_{rec}\) are the same and therefore:  
\[D_{n}=D_{rec}\]  
This implies  
\[2*r=s_{len}*\sqrt{2}\]  
\[s_{len}=\frac{2*r}{sqrt2}\]  
The area covered by the rectangle is  
\[s_{len}*s_{len} \tag{2}\]  
\[\frac{2*r}{sqrt2}*\frac{2*r}{sqrt2}\]  
\[2*r^{2}\]  
Assuming \(m*n\) as the dimension of the bottom region (region 1), respectively, the number of sub-regions (clusters) that could be formed in this area are:  
\[N_{clust_{k}}=\frac{m*n}{2*r^{2}} \tag{3}\]  
Keeping in mind that the number of clusters at bottom regions (region 1) are minimal, the number of clusters in the next regions would be:  
\[Number_{reg}=\frac{Bred_{net}}{r}+1 \tag{1}\]0  
The breadth of the regions are:  
\[Number_{reg}=\frac{Bred_{net}}{r}+1 \tag{1}\]1  
\[Number_{reg}=\frac{Bred_{net}}{r}+1 \tag{1}\]2  
\[Number_{reg}=\frac{Bred_{net}}{r}+1 \tag{1}\]3  
Here, \( breadth_{reg_{app}}\) denotes the topmost region which is nearest to BS, \( breadth_{reg_{low}}\) represents the lowest region, and \( breadth_{reg_{mid}}\) represents the middle region. Any region beyond these mentioned can be formed and area can be calculated based on the above calculations. Proposed Energy Efficient Data Communication Scheme: Region Based Hierarchical Clustering for Efficient Routing (RHCER)  
The RHCER is a multi-tier clustering protocol for improving the network lifetime by achieving efficient balance between load and energy depletion across all network nodes. The Base Station (BS) is presented at the top of the network. Each node in the network sends their data to BS in multihop way. BS is aware of the entire network location and divides the whole network into various regions and sub-regions, as mentioned in Algorithm 1: Line 1-6. The proposed RHCER protocol deploys the multi-tier network for an agriculture scenario. The selection of CH in each cluster is done via BS using Algorithm 2: Cluster Head Selection. Immediately after the selection of CH in each cluster, the local cluster nodes send Join-Req to CH. Upon the reception of the Join-Req message from the sensor nodes, CH sends a reply via an acknowledgment message. Once connection between sensor nodes and CH within a local cluster is established, sensor nodes start sending their sensed data to CH. CH aggregates the data received from the nodes and transmits the data to the nearest neighbor CH present in its upper region. The selection of nearest neighbor CH in the upper region (One region above the current region towards BS) is done through Algorithm 1: Line 13-22. In this process, CH is chosen based on the ratio of residual energy of CH of the upper region to the distance between CHs of local region and the upper region. The process repeats itself until the packets finally reach BS. The energy of selected CH periodically gets checked and compared with the energy threshold. If at any point in time the CH energy is found to be lower than the threshold, the CH selection process gets started in that cluster. The time required for the evaluation of Algorithm 1 depends on the number of regions and the number of clusters in each region, and was therefore computed as \(N_{regions}*N_{clusters}\).