In WSN, the energy consumed by each sensor node of the network influences the lifetime of the networks, more than the utilization of energy increases more than the lifetime of the networks decreases, this is why the enhance of the lifetime of the networks requires a strategy or protocol which reduces the power utilization of the transmission or reception of data by the nodes. In the recent years to a great extent research has been done to maximize a life time of network node. The hierarchical protocols (Cluster based-approach) have been developed in order to decrease the network traffic toward the BS (Base Station) and therefore extend the network lifetime. The number of clusters and also distribution of CH (Cluster Heads) are necessary for energy efficiency and adaptability of clustering approaches. EDCH (Effective Distance Cluster Head) is a novel energy-efficient clustering algorithm proposed recently for WSN (wireless sensor networks) to extend network lifetime by uniformly distributing of CHs (Cluster Heads) across the network. In this paper, we propose an mathematical method to model the energy utilization of the EDCH (Effective Distance Cluster Head) algorithm. The results of our extensive simulation study prove a reasonable accuracy of the proposed mathematical model to predict the energy utilization under different operational conditions. Here proposed mathematical model reveals a number of implications about the effects of different parameters on the energy utilization pattern of the EDCH (Effective Distance Cluster Head) clustering algorithm.

WSN, Clustering, Energy Efficiency, EDCH, Mathematical Model

[1] F. Akyildiz, S. Weilian, Y. Sankarasubramaniam, and E. Cayirci, “A Survey on Sensor Networks,” IEEE Communications Magazine, vol. 40, no. 8, pp. 102–114, 2002.
[2] W. R. Heinzelman, A. Chandrakasan, and H. Balakrishnan, “Energy-Efficient Communication Protocol for Wireless Microsensor Networks,” in 33rd Annual Hawaii International Conference on System Sciences, 2000.
[3] M. Mathew and N. Weng, “Quality of Information and Energy Efficiency Optimization for Sensor Networks via Adaptive Sensing and Transmit-ting,” IEEE Sensors Journal, vol. 14, pp. 341–348, February 2014.
[4] G. Anastasi, A. Falchi, A. Passarella, M. Conti, and E. Gregori, “Performance Measurements of Motes Sensor Networks,” in 7th ACM International Symposium on Modeling, Analysis and Simulation of Wireless and Mobile Systems (MSWiM), (Venice, Italy), pp. 174–181, ACM, 2004
[5] Karl, H., & Willig, A. (2005). Protocols and architectures for wireless sensor networks. Hoboken, NJ: Wiley.
[6] Rajkumar, Dr H G Chandrakanth, Dr D G Anand, and Dr T John Peter.” Research Challenges and Characteristic Features in Wireless Sensor Networks”, in Int. J. Advanced Networking and Applications, Volume: 09 Issue: 01 Pages: 3321-3328 (2017) ISSN: 0975-0290.
[7] M. M. Zanjireh, A. Shahrabi, and H. Larijani, “ANCH: A New Clus-tering Algorithm for Wireless Sensor Networks,” in 27th International Conference on Advanced Information Networking and Applications Workshops (WAINA), pp. 450–455, IEEE, 2013.
[8] Chan, H., & Perrig, A. (2004). ACE: An emergent algorithm for highly uniform cluster formation. In Wireless Sensor Networks. Lecture Notes in Computer Science, Vol. 2920, pp. 154–171.
[9] Low, C. P., Fang, C., Ng, J. M., & Ang, Y. H. (2008). Efficient load-balanced clustering algorithms for wireless sensor networks. Computer Communications, 31(4), 750–759.
[10] Manjeshwar, A., & Agrawal, D. P. (2002). APTEEN: A hybrid protocol for efficient routing and comprehensive information retrieval in wireless sensor networks. In Proceedings International Parallel and Distributed Processing Symposium, IPDPS 2002 (pp. 195–202).
[11] Gu, Y., Wu, Q., & Rao, N. S. V. (2010). Optimizing cluster heads for energy efficiency in large-scale heterogeneous wireless sensor networks. International Journal of Distributed Sensor Networks. doi:10.1155/2010/961591.3328 (2017) ISSN: 0975-0290.
[12] Tarannum, S., Srividya, S., Asha, D. S., Padmini, R., Nalini, L., Venugopal, K. R., et al. (2008). Dynamic hierarchical communication paradigm for Wireless Sensor Networks: A centralized, energy efficient approach. In 11th IEEE Singapore International Conference on Communication Systems, Singapore (pp. 959–963).
[13] Ci, S., Guizani, M., & Sharif, H. (2007). Adaptive clustering in wireless sensor networks by mining sensor energy data. Computer Communications, 30(14–15), 2968–2975.
[14] Huang, Y. F., Luo, W. H., Sum, J., Chang, L. H., Chang, C. W., & Chen, R. C. (2007). Lifetime Performance of an energy efficient clustering algorithm for cluster-based wireless sensor networks. In Frontiers of High Performance Computing and Networking ISPA 2007 Workshops. Lecture Notes in Computer Science, Vol. 4743, pp. 455–464.
[15] Zhang, M., Gong, C., & Lu, Y. (2008). An novel dynamic clustering algorithm based on geographical location for wireless sensor networks. In 2008 International Symposium on Information Science and Engineering (ISISE), Piscataway, NJ, USA (pp. 565–568).
[16] W. Heinzelman, A. Chandrakasan, H. Balakrishnan. "Energy-Efficient communication protocol for wireless microsensor network", Proc. of the Hawaii International Conference on System Sciences, IEEE Computer Society, Washington. DC USA,Jan 2000, pp.3005-3014
[17] Younis, O., & Fahmy, S. (2004). HEED: A hybrid, energy-efficient, distributed clustering approach for ad hoc sensor networks. IEEE Transactions on Mobile Computing, 3(4), 366–379.
[18] Manjeshwar, A., & Agrawal, D. P. (2001). TEEN: a routing protocol for enhanced efficiency in wireless sensor networks. In Proceedings of the 1st International Workshop on Parallel and Distributed Computing Issues in Wireless Networks and Mobile Computing, San Francisco, CA (pp. 2009-2015).
[19] Ye, M., Li, C., Chen, G., & Wu, J. (2005). EECS: An energy efficient clustering scheme in wireless sensor networks. In 24th IEEE International Performance, Computing, and Communications Conference, IPCCC 2005 (pp. 535–540).
[20] Kamimura, J., Wakamiya, N., & Murata, M. (2006). A distributed clustering method for energy-efficient data gathering in sensor networks. International Journal of Wireless and Mobile Computing, 1(2), 113–120.
[21] Suhas K. Pawar, Abhishek R. Tawde, ArchanaPokharkar, PriyaPanjwani, Prof.SuhasPatil “A Survey of Cluster formation Protocols in Wireless Sensor Networks”;2014 p. 40-49
[22] O. Younis and S. Fahmy. Heed: a hybrid, energy-efficient, distributed clustering approach for ad hoc sensor networks. Mobile Computing,
[23] C. Li, M. Ye, G. Chen, and J. Wu. An energy-efficient unequal clustering mechanism for wireless sensor networks. In Mobile Adhoc and Sensor Systems Conference, 2005. IEEE International Conference on, 2005.
[24] Q. Zhang, R. H. Jacobsen, and T. S. Toftegaard. Bio-inspired lowcomplexity clustering in large-scale dense wireless sensor networks. In Global Communications Conference (GLOBECOM), 2012 IEEE, pages
[25] A. Al Islam, C. S. Hyder, H. Kabir, and M. Naznin. Finding the optimal percentage of cluster heads from a new and complete mathematical model on leach. Wireless Sensor Network, 2(2):129–140, 2010.
[26] I. Beretta, F. Rincon, N. Khaled, P. R. Grassi, V. Rana, and D. Atienza. Design exploration of energy-performance trade-offs for wireless sensor networks. In Design Automation Conference (DAC), 2012 49th ACM/EDAC/IEEE, pages 1043–1048, 2012.
[27] J. Gupchup, A. Terzis, R. Burns, and A. Szalay. Model-based event detection in wireless sensor networks. In Workshop on Data Sharing and Interoperability on the World-Wide Sensor Web (DSI), 2008.
[28] S. Bandyopadhyay and E. J. Coyle. An energy efficient hierarchical clustering algorithm for wireless sensor networks. In INFOCOM 2003. Twenty-Second Annual Joint Conference of the IEEE Computer and Communications. IEEE Societies, volume 3, pages 1713–1723, 2003.
[29] J. C. Choi and C. W. Lee. Energy modeling for the cluster-based sensor networks. In Computer and Information Technology, 2006. CIT ’06. The Sixth IEEE International Conference on, pages 218–218, 2006.
[30] S. Foss and S. Zuyev. On a certain segment process with voronoi clustering. 1993