Determination Of Optimal Number Of Clusters In Wireless Sensor Networks

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.

💡 Research Summary

The paper addresses a fundamental inefficiency in many wireless sensor network (WSN) clustering protocols: the uniform probability election of cluster heads (CHs) regardless of a node’s distance from the base station (BS). In traditional schemes such as LEACH, every node has the same chance of becoming a CH, which leads to two major problems. First, nodes that are close to the BS become overloaded because they must forward traffic from many distant clusters, causing rapid energy depletion in the inner region. Second, nodes far from the BS expend excessive transmission energy because the radio model assumes that the energy required to send a packet grows with the square (or higher power) of the distance. The combination of these effects shortens the overall network lifetime and reduces scalability.

To overcome these drawbacks, the authors propose an analytical framework that models the sensor field as a series of concentric rings centered on a single, centrally located BS. The rings are of equal radial width, and each ring’s average distance to the BS increases with its index. Within this geometry, the probability that a node becomes a CH is made a function of its ring’s distance from the BS, yielding a non‑uniform probability election model (UEPEM). Specifically, a weight function w(d)=1/(d^α) (where α is the path‑loss exponent) is applied to each ring, and the probabilities are normalized so that the sum over all nodes equals one. Consequently, inner rings receive a lower CH election probability, while outer rings receive a higher probability, leading to smaller clusters near the BS and larger clusters farther away.

The authors derive the expected energy consumption for a given ring i as
E_i = N_i·P_CH(i)·E_CH + N_i·(1‑P_CH(i))·E_CM,
where N_i is the number of nodes in ring i, P_CH(i) is the election probability for that ring, E_CH is the energy a CH spends to aggregate and forward data, and E_CM is the energy a regular member spends to transmit its data to the CH. Summing E_i over all rings gives the total network energy consumption E_total. By differentiating E_total with respect to P_CH(i) and applying the constraint ΣP_CH(i)·N_i = 1, the authors obtain the optimal distance‑dependent probability distribution that minimizes overall energy usage. The resulting UEPEM distribution is shown analytically to be superior to the uniform model.

Simulation experiments were conducted with varying numbers of rings (3, 5, 7, etc.) to compare UEPEM against the uniform probability election model (EPEM). The results demonstrate that UEPEM reduces total energy consumption by approximately 21 % on average. Moreover, the energy savings increase as the number of rings grows, because finer granularity allows the probability function to better match the actual distance‑related energy costs. The paper also reports a significant extension of network lifetime, measured as the time until the first node dies, confirming that the non‑uniform election strategy balances load more effectively across the network.

Key contributions of the work include: (1) a mathematically rigorous derivation of a distance‑aware, non‑uniform CH election probability; (2) a concrete energy model for concentric‑ring WSNs that captures both intra‑cluster and inter‑cluster transmission costs; (3) quantitative evidence that the proposed UEPEM achieves roughly a 21 % reduction in energy consumption and a notable increase in network longevity compared with traditional uniform schemes. The authors suggest future research directions such as extending the model to non‑circular topologies, handling multiple base stations, incorporating node mobility, and dynamically adjusting ring boundaries as nodes die or are added. Real‑world hardware validation and comparative studies with other energy‑efficient protocols are also recommended to further establish the practicality of UEPEM.