## 3 Proposed Model
### Proposed Mobile-Aware Cluster Head-Election Scored (MACHES) Algorithm
#### 3.3.2 Mobility-Aware Cluster-Head Election Scored (MACHES) Procedure  
The selection of a CH within each cluster is determined through a triple scoring mechanism based on the integration of \(S_{M}\) (mobility score), \(S_{BS}\) (BS score), and \(S_{CC}\) (CCscore). This scored mechanism guarantees the selection of a CH that not only has high residual energy but is also optimally positioned in relation to both the BS and the cluster's centroid. This strategic positioning aids in conservative energy usage and extends the network's operational lifespan. Nodes transmit data to their designated CHs. The energy expended in these transmissions is computed based on the distance to the CH and predefined transmission energy parameters, adjusting for the distance relative to a preset distance threshold (\(d_{th}\)). CHs then aggregate the received data and forward it to the BS, a process that incurs additional energy consumption based on the distance to the BS and the volume of data transmitted. The residual energy level of each node is recalculated to reflect consumption, and the system progresses to the next round unless a termination condition is met. The protocol restricts reconfiguration to only the initial setup round and subsequent rounds where additional nodes exhaust their energy reserves. This adjustment ensures that cluster reconfigurations are not excessively frequent, which can be a significant time sink. The protocol enhances decision-making during CH elections by considering not just the residual energy of the nodes but also their proximity to the CH and BS. This holistic view prevents suboptimal cluster head selections that could lead to quicker energy depletion, especially in nodes that are distant from the base station. * CH-Election Scoring (CHES) Mechanism. Each node \(i\) within a cluster computes three scores: (i) BS score based on its distance to the base station (\(S_{BS}\)), (ii) CC score based on its distance to the CC's point (\(S_{CC}\)), and (iii) mobility score based on node's normalized displacement and direction change (\(S_{M}\)), as specified by the following equations:  
\[S_{(i)BS}=\frac{E_{(i)res}}{E_{init}}-\frac{d_{(i)toBS}}{max(d_{toBS})} \tag{10}\]  
\[S_{(i)CC}=\frac{E_{(i)res}}{E_{init}}-\frac{d_{(i)toCC}}{max(d_{toCC})} \tag{11}\]  
where \(E_{(i)res}\) represents the residual energy of node \(i\), \(E_{init}\) is the initial energy, \(d_{(i)toBS}\) is the distance from node \(i\) to the BS, \(d_{(i)toCC}\) is the distance from node \(i\) to the CC point, and the maximum distances are taken over all nodes to normalize the impact of geographical dispersion. \(S_{BS}\) assesses the node's energy efficiency relative to its distance from the BS, while \(S_{CC}\) focuses on the node's location in relation to the cluster's centroid. The ratio of residual energy to the initial energy, the first term of Equations (10) and (11), means the relative size (normalization value) of the residual energy. Since this ratio presents a decrease over time and the distance metric inversely relates to score, a node's score values are normalized between 0 and 1. The closer proximity yields the higher scores. If the scores derived from Equations (10) and (11) are substantial, the corresponding nodes are nominated as CHs. This scoring system ensures that the selected node not only possesses high residual energy but also occupies a strategic location relative to both the BS and the cluster's centroid. Upon calculating these scores, the node with the highest combined score is designated as the CH. The mobility score \(S_{M}\) for each mode is weighted combination of two key factors, such as displacement and direction change. This score, normalized between 0 and 1, is designed to prioritize nodes that are relatively stable (exhibiting low displacement and minimal direction change) as CHs since high mobility can result in instability during cluster formation.