Error Analysis and Kernel Density Approach of Scheduling Sleeping Nodes in Cluster-Based Wireless Sensor Networks

Energy consumption is an important research topic in wireless sensor networks. Putting sensor nodes to sleep is one of the most popular ways to save energy in battery-powered sensor nodes. Many existing research studies on sleeping techniques are based on preknowledge of deployment of sensor nodes, e. g., a known probability distribution of sensor nodes in a target-sensing field. Thus, whether a scheduling-sleeping scheme has good performance mostly depends on preknowledge of the deployment of sensor nodes. In this paper, we first show the discrepancy of system performance metrics, including energy consumption and network lifetime, based on inaccurate preknowledge of the deployment of sensor nodes in a cluster-based sensor network. Through analytical studies, we conclude that the discrepancy is very large and cannot be neglected. We hence propose a distribution-free approach to study energy consumption. In our approach, no assumption of the probability distribution of deployment of sensor nodes is needed. The proposed approach has yielded a good estimation of network energy consumption. Furthermore, previous studies normally assume that battery energy levels of sensor nodes are the same. However, in a real network, battery quality is different, and the energy in each sensor node is a random variable. We provide a mathematical approximation and a standard deviation study for energy consumption, as well as a more in-depth study for network lifetime under random batter energy.