  Prolonged network lifetime, scalability and efficient load balancing are
essential for optimal performance of a wireless sensor network. Clustering
provides an effective way of extending the lifetime of a sensor network.
Clustering is the process that divides sensor networks into smaller localized
group (called clusters) of members with a cluster head. Clustering protocols
need to elect optimal number of clusters in hierarchically structured wireless
sensor networks. Any clustering scheme that elects clusters uniformly
(irrespective of the distance from Base Station) incurs excessive energy usage
on clusters proximal and distant to Base Station. In single hop networks a
gradual increment in the energy depletion rate is observed as the distance from
the cluster head increases. This work focuses on the analysis of wasteful
energy consumption within a uniform cluster head election model (EPEM) and
provides an analytic solution to reduce the overall consumption of energy usage
amongst the clusters elected in a wireless sensor network. A circular model of
sensor network is considered, where the sensor nodes are deployed around a
centrally located Base Station. The sensor network is divided into several
concentric rings centred at the Base Station. A model, Unequal Probability
Election Model (UEPEM), which elects cluster heads non-uniformly is proposed.
The probability of cluster head election depends on the distance from the Base
Station. UEPEM reduces the overall energy usage by about 21% over EPEM. The
performance of UEPEM improves as the number of rings is increased.
