On the Relevance of Node Isolation to the K-Connectivity of Wireless Optical Sensor Networks

In designing wireless multihop sensor networks, determining system parameters that guarantee a reasonably connected network is crucial. In this paper, we investigate node isolation in wireless optical sensor networks (WOSNs) as a topology attribute for network connectivity. Our results pertain to WOSNs modeled as random-scaled sector graphs that employ directional broad-beamed free space optics for point-to-point communication. We derive a generalized analytical expression relating the probability that no node is isolated to the physical layer parameters of node density, transmitter radius, and angular beam width. Through simulations, we demonstrate that for probability values close to 1, dense networks, and increasing beam width, the probability that the WOSN is connected is tightly upper bounded by the probability that no isolated node exists. In addition, our study demonstrates conditions for probabilistic K-connectivity guarantees and provides empirical insights on the impact of clustering on connectivity by employing simulations to validate analytical derivations. Our analysis provides a methodology of practical importance to choosing physical layer parameter values for effective network level design.