Empirical formulation for estimation of optimum number of randomly deployed nodes in WSN

The most fundamental issue in any wireless sensor network (WSN) design and/or analysis is the node deployment strategy and the number of nodes to be deployed. In this regard, a critical quality of service (QoS) parameter is network coverage which defines how well an area of interest is being monitored by a deployed network. The percentage coverage achieved for a given number of nodes in a predetermined network area can be computed using various sensing models. However, a more practical computation must determine the optimum density of nodes to be deployed such that it satisfies the specific spatial and temporal sampling of the network area within a given economical budget. In this paper, investigation is carried out to estimate the optimum density of nodes to be randomly deployed in a given network area of any size in order to attain the desired network coverage using deterministic and probabilistic sensing models. Parametric analysis is carried out to study the effects of sensing device characteristics and environmental parameters on the optimum density of nodes. The results obtained are used to empirically derive a formula based on regression analysis using least square polynomial curve fitting technique. The formula includes the parameters that affect the optimum number of nodes and thus can be used to estimate the number of nodes to be randomly deployed in order to attain desired percentage coverage in a WSN system. To the best of our knowledge, ours is the first work that revisits the theoretical foundation of network coverage to result into a mathematical formulation that can be readily and accurately used to design any practical WSN system.