Analysis of Residual Energy Thresholds and Their Effect on Cluster Head Rotation Frequency and Network Lifetime in Wireless Sensor Networks

Wireless Sensor Networks (WSNs) are battery-constrained distributed systems where energy efficiency directly determines network operational lifetime. Clustering protocols, most prominently LEACH (Low-Energy Adaptive Clustering Hierarchy), rely on a threshold function T(n) to probabilistically elect cluster heads (CHs) in each operational round. While this threshold incorporates parameters such as the desired CH probability (p) and round number (r), its interaction with residual node energy remains insufficiently analyzed in the existing literature. This paper presents a comprehensive analytical study of how different residual energy threshold formulations — namely fixed-threshold (LEACH), average-energy threshold (LEACHC), and residual-energy-weighted threshold (RELEACH variants) — affect the cluster head rotation frequency, energy distribution fairness, and overall network lifetime. Through mathematical modeling and comparative protocol analysis, we demonstrate that the choice of threshold value and its sensitivity to residual energy significantly governs how rapidly nodes deplete and when the first and last node deaths occur. We identify critical research gaps in current threshold design, particularly the absence of adaptive threshold mechanisms that respond to real-time network energy states. This analysis serves as a foundation for proposing dynamic, energyaware threshold adaptation in future simulation-based work.