Optimal Cluster Number Determination for Clustered Wireless Sensor Networks

Abstract

A method to determine the optimal clusterhead number in a clustered wireless sensor network is proposed to improve the energy efficiency of clustering schemes. The wireless sensor network is modeled as points locating randomly on the plane according to a homogeneous spatial Poisson process. This leads to derive the means of some typical cluster parameters accordingly. After that, the total energy cost consumed in the system is calculated based on a practical radio model. As a result, the optimal probability of becoming a clusterhead for each node is deduced via minimizing the system energy cost. Ultimately, the total energy costs are compared in the scenarios that the networks employ the same clustering algorithm with a range of values for the probability of becoming a clusterhead. Simulation results show that the optimal probability we obtained has indeed minimized energy dissipation in the system and is applicable to other clustering algorithms directly.

Energy consumption and lifetime analysis in clustered multi-hop wireless sensor networks using the probabilistic cluster-head selection method

“…According to the Galois Theory [18], p* cannot be obtained by elementary algebra. However, we can use numerical methods to solve a general polynomial equation [9]. Since C(p) is a convex function, we use Newton's method to find a minimum of C(p).…”

“…Since the signaling overhead for clustering is not considered in the existing energy models, to compare the accuracy of the energy models under the same conditions, we evaluate the energy models ignoring the energy spent for signaling. Other multi-hop clustering algorithms such as OCND [9] and ECTC [10] adopt the same modeling approach as in EEHCA. Thus, their accuracies are almost identical to that of EEHCA.…”

“…For example, to give an better approximation to the energy consumption, in CRS [8] and OCND [9], energy models which consider data-receiving energy are extended. On the other hand, the energy model of ECTC [10] considers the energy consumed by a radio during an idle state which refers to the state when the radio is on but not transmitting nor receiving any data.…”

“…However, the shape of clusters and the number of members in each cluster are arbitrary in practice. Furthermore, clustering of distributed nodes generally results in a large signaling overhead but most of the studies neglect the signaling overhead in modeling [5][6][7][8][9][10]. Finally, most studies simply derive the number of hops between the nodes by dividing the distance between them into a radio range, thus the accuracies of their models are not satisfactory [5,[8][9][10].…”

“…To appropriately select the number of clusters, a number of studies have focused on derivation of energy models to estimate the energy consumed in the network with respect to the number of clusters [5][6][7][8][9][10]. However, accuracies of the existing models are not satisfactory because they make flawed assumptions.…”