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

Abstract

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 (LEACH-C), 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.

Introduction

Wireless Sensor Networks (WSNs) consist of spatially distributed, energy-constrained nodes that sense, process, and transmit data to a base station. Energy efficiency is critical, as data transmission consumes the most power. Cluster-based protocols, like LEACH, reduce energy use by grouping nodes into clusters with a Cluster Head (CH) responsible for aggregating and forwarding data. LEACH elects CHs probabilistically using a threshold function but ignores residual energy, often leading to premature node deaths and energy imbalance.

Subsequent protocols—LEACH-C, SEP, RE-LEACH, and AvgRLEACH—incorporate residual energy or statistical metrics into CH election, improving network lifetime, energy fairness, and CH survival. Threshold formulation directly affects CH rotation frequency, energy distribution, and network lifetime metrics: First Node Death (FND), Half Node Death (HND), and Last Node Death (LND). Residual-energy-aware thresholds (Type-III and IV) provide self-correcting load balancing, reduce energy variance, and prolong network operation, especially under low CH fractions.

The study highlights key trade-offs: higher rotation frequency balances energy but increases overhead, while static or energy-agnostic thresholds risk hotspots. Limitations include fixed CH fraction assumptions, neglect of node spatial distribution, single-hop CH-to-BS reliance, and homogeneous network assumptions. Future research should explore adaptive, energy- and distance-aware thresholds, multi-hop clustering, and heterogeneous networks to optimize lifetime and efficiency.

Conclusion

This paper has presented a systematic analytical study of residual energy thresholds and their effect on cluster head rotation frequency and network lifetime in Wireless Sensor Networks. Four categories of threshold formulations were analyzed — fixed probabilistic (LEACH), average energy-based (LEACH-C), residual energy-weighted (RE-LEACH), and statistical energy-based (AvgRLEACH) — and evaluated against key metrics including First Node Death, Half Node Death, Last Node Death, Energy Variance, CH Survival Rate, and Rotation Fairness Index. The analysis demonstrates that the degree to which residual energy is incorporated into the threshold function is the primary determinant of energy balance and network lifetime. Residual energy-weighted thresholds (Type-III) achieve up to 35% improvement in FND and 30% improvement in LND compared to the original LEACH threshold, while maintaining high scalability and requiring only moderate control overhead. Statistical energy thresholds (Type-IV) provide the best overall performance but require more network-level energy information. A critical finding is that the sensitivity of network lifetime to threshold formulation is highest at low values of p, precisely the regime where most real deployments operate, underscoring the urgency of adopting energy-aware threshold designs in practical WSN deployments. The self-correcting load-balancing property of energy-proportional thresholds represents a theoretically elegant and practically implementable mechanism for extending network lifetime without centralized coordination.

References

[1] A. 1. W. R. Heinzelman, A. Chandrakasan, and H. Balakrishnan, \"Energy-Efficient Communication Protocol for Wireless Microsensor Networks,\" Proc. 33rd Annual Hawaii International Conference on System Sciences (HICSS), 2000. [2] S. Lindsey and C. S. Raghavendra, \"PEGASIS: Power-Efficient Gathering in Sensor Information Systems,\" Proc. IEEE Aerospace Conference, vol. 3, pp. 3-1125, 2002. [3] S. K. Panda, P. K. Jana, \"Modified threshold for cluster head selection in WSN using first and second order statistics,\" IET Wireless Sensor Systems, vol. 11, no. 1, pp. 12-22, 2020. [4] S. E. Pour and R. Javidan, \"A New Energy Aware Cluster Head Selection for LEACH in Wireless Sensor Networks,\" IET Wireless Sensor Systems, vol. 11, no. 1, pp. 45-53, 2021. [5] P. Kale, A. Ikhar, and M. Hassan, \"Optimization Network Lifetime Through Residual EnergyBased Cluster Head Selection in IoT-Enabled WSNs,\" International Journal of Scientific Research in Science and Technology, vol. 10, no. 2, pp. 763-767, 2023. [6] S. Lekhi and S. Singh, \"Energy Efficient Clustering Mechanism and Cluster Head Election in Wireless Sensor Network,\" Journal of Electrical Systems, vol. 20, no. 2s, pp. 81-91, 2024. [7] A. Zabielski, et al., \"A Cluster Head Selection Algorithm for Extending Last Node Lifetime in Wireless Sensor Networks,\" PMC / Sensors, 2024. [8] B. Negash et al., \"Improving Wireless Sensor Network Lifespan with Optimized Clustering Probabilities, Improved Residual Energy LEACH and Energy Efficient LEACH for CornerPositioned Base Stations,\" Heliyon, vol. 10, no. 14, e34382, 2024. [9] H. El-Sayed et al., \"An Efficient Neural Network LEACH Protocol to Extended Lifetime of Wireless Sensor Networks,\" Scientific Reports, vol. 14, no. 1, 2024. [10] W. R. Heinzelman, A. P. Chandrakasan, and H. Balakrishnan, \"An Application-Specific Protocol Architecture for Wireless Microsensor Networks,\" IEEE Transactions on Wireless Communications, vol. 1, no. 4, pp. 660-670, 2002. [11] G. Smaragdakis, I. Matta, and A. Bestavros, \"SEP: A Stable Election Protocol for Clustered Heterogeneous Wireless Sensor Networks,\" Proc. 2nd International Workshop on Sensor and Actor Network Protocols and Applications (SANPA), 2004. [12] L. Qing, Q. Zhu, and M. Wang, \"Design of a Distributed Energy-Efficient Clustering Algorithm for Heterogeneous Wireless Sensor Networks,\" Computer Communications, vol. 29, no. 12, pp. 2230-2237, 2006.

Copyright

Copyright © 2026 Shri Ram Mansore, Amrita Soni, Kapil Malviya. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.