Some Fundamental Results on Complex Network Problem for Large-Scale Wireless Sensor Networks

Wireless sensor networks (WSNs) are typically constituted by a large number of connected wireless sensors (nodes), generally distributed at random on a given surface area. In such large-scale networks, the desired global system performance is achieved by gathering local information and decisions collected from each individual node. There exist two fundamental global issues on WSNs that we consider here, i.e. full network connectivity and network lifetime. Full connectivity can be obtained either by increasing transmission range, at the expense of consuming higher transmission power, or by increasing the number of sensors, i.e. by increasing network costs. Both of them are closely related to global network lifetime, in the sense that the higher the power consumption or the more sensors deployed the shorter the network lifetime [31]. So the main question is, how can one design large-scale random networks in order to have both global connectivity and maximum network lifetime? Although these questions have been addressed often in the past, a definite, simple predicting algorithm for achieving these goals does not exist so far. In this paper, we aim to discuss such a scheme and confront it with extensive simulations of random networks generated numerically. Specifically, we study the minimum number of nodes required to achieve full network connectivity, and present an analytical formula for estimating it. The results are in very good agreement with the numerical simulations as a function of transmission range. In addition, we study in detail several other statistical properties of large-scale WSNs, such as average path distance, clustering coefficient, degree distribution, etc., also as a function of the transmission range, both qualitatively and quantitatively. We discuss results on how to further improve network energy consumption from the original networks considered by switching off (deleting) some nodes at random but keeping whole network connectivity. The present results are expected to be useful for the design of more efficient large-scale WSNs.