## 3 System Model
### Subdivision Technique
```
Initial : Rectangular Network with dimension \(Len_{net}\) and \(Bred_{net}\) and \(n\) randomly distributed nodes Start Procedure
1 Set of Nodes \(N=\{1,2,3,.....n\}\)
2 BS divided the network into regions and sub-regions (Clusters) based on equation 1 to 7
3 Declare \(Region_{id}=\{Reg_{1},Reg_{2},Reg_{3},.....Reg_{h}\}\)
4 Declare \(Cluster_{id}=\{Clus_{1},Clus_{2},Clust_{3},.....Clus_{p}\}\)
5 Declare \(CH=\{\}\)  A set containing Id of nodes chosen as cluster heads
6 Assign \(Region_{id}\) and \(Cluster_{id}\) to each region and cluster, respectively. 7 for each region with \(Region_{id_{i}}\)
8 set \(Local-region=current-region_{id_{i}}\)
9 for each Cluster with \(cluster_{id_{i}}\) with in local-region
10 set \(local-cluster=current-cluster_{id_{j}}\)
11 Send the packets from local cluster ordinary node to local cluster \(CH\)
12 endfor
13\(CH_{a}\)= Cluster Head of nearest neighbor cluster in higher region, i.e. \(CH_{a}.Reg_{id}\)= \(local-cluster.Reg_{id}+1\)
14\(CH_{b}\)= Cluster Head of nearest neighbor cluster in higher region, i.e. \(CH_{b}.Reg_{id}\)= \(local-cluster.Reg_{id}+1\)
15 Compute distance of local cluster CH \((CH_{l})\) with \(CH_{a}\) and \(CH_{b}\) respectively
16\(Dis_{l,a}=\sqrt{(l_{x}-a_{x})^{2}+(l_{y}-a_{y})^{2}}\)
17\(Dis_{l,b}=\sqrt{(l_{x}-b_{x})^{2}+(l_{y}-b_{y})^{2}}\)
18 if\(\frac{CH_{a}.Energy>\frac{CH_{b}.Energy}{Dis_{l,b}}}\)
19 set \(CH_{dec}=CH_{a}\)
20 else
21 set \(CH_{dec}=CH_{b}\)
22 send the packet from \(CH_{l}\) to \(CH_{dec}\)
23 Finally sent the packets to BS. 24 endfor End Procedure
```  
**Algorithm 1**Region based Hierarchical Clustering for Efficient Routing (RHCER)  
```
Input: Local Region, Local Subregion (Cluster), S: Set of nodes within cluster Output: Local Cluster Head \((CH_{l})\) Start Procedure
1 Declare Base Station Position = \(\{BS_{x},BS_{y}\}\)
2 for each node \(s\in S\)
3 calculate distance of s from BS
4\(D_{BS,s}=\sqrt{(BS_{x}-s_{x})^{2}+(BS_{y}-s_{y})^{2}}\)
5\(Total-Distance=Total-Distance+D_{BS,s}\)
6 endfor
7\(Avg-Distance=\frac{Total-Distance}{|S|}\)
9 Calculate Energy Consumption (EC) of s for Transmission, sensing and Processing. 10\(EC_{s}=Energy_{trans}+G+D_{BS,s}\) Considering \(G\) is constant for sensing and processing
11\(Total-EC=Total-EC+EC_{s}\)
13\(Avg-EC=\frac{Total-EC}{|S|}\)
14\(Threshold_{energy}=\frac{Avg-EC}{Avg-Distance}\)
15 for each node \(s\in S\)
16 if\(s.residual_{energy}>Threshold_{energy}\)
17 s may participate in CH election process
18\(CH_{s}=s.residual_{energy}*\frac{1}{D_{BS,s}}*\frac{1}{SNR_{BS,s}}\)
19 else
20 s will act as normal node in cluster
21 endif
22 endfor
23 For all the nodes in set S where \(CH_{s}\) has been computed, arrange them in decreasing order of their \(CH_{s}\) values
24\(CH_{l}=\) first node of array End Procedure
```  
**Algorithm 2**Cluster Head Selection  
The selection of the most appropriate node as CH within the local cluster is crucial. The node with the highest residual energy within the local cluster can provide uniform energy depletion for the entire network. The energy of each node within a local cluster is mainly utilized for transmission. The energy consumed for sensing and processing is minimal and is therefore considered as constant G (Algorithm 2: Line 10). The distance between BS and node is also one of the factors impacting energy depletion. Satisfying the condition that residual energy is higher than chosen threshold, the Cluster Head election process in local cluster for eligible node determines its residual energy, distance from BS, and Signal to Noise (SNR) ratio from BS. The efficient cluster head selection through the multi-criteria decision-making function, which includes distance from BS(D), threshold energy (TE), and signal-to-noise ratio (SNR), would have a significant impact on packet drop ratio as the high number of requests would be satisfied by cluster heads first due to aggregation of data from nodes of the same cluster. The reduced packet drop ratio will ultimately enhance the packet delivery ratio.