Developments in micro electro mechanical systems and wireless communications have led to the development of low power, low cost, multi functional, wireless sensing devices. Distributed communication network formed with the help of these sensing devices is called Wireless Sensor Network (WSN). WSN forms the fundamental infrastructure for future unique network for variety of potential and powerful applications such as defense, environmental monitoring, facilities management, manufacturing and agriculture. Many fundamental operations of WSN such as Time Synchronization among nodes and sink, routing of data, clustering of nodes, localization schemes, data aggregation and dissemination consume excess part of the energy utilized. To optimize energy consumption, this paper focuses on the time synchronization between nodes and the cluster head within the cluster, to reduce the relative drift of clocks between two different nodes at two different times thus reducing the synchronization error. We prove the minimization of the relative drift of clocks through a mathematical model with few assumptions on applications. The output of the mathematical model, based on the assumptions, clearly prove that the relative drift of clocks between two different nodes drops to an infinitesimally small value, which is better than many of the existing time synchronization schemes for WSNs.

Wireless Sensor Network Energy Efficiency Time Synchronization Relative Clock Drift Synchronization error