Asymptotic connectivity of low duty-cycled wireless sensor networks

In this paper we study the asymptotic connectivity of a low duty-cycled wireless sensor network, where all sensors are randomly duty-cycled such that they are on/active at any time with a fixed probability. A wireless network is often said to be asymptotically connected if there exists a path from every node to every other node in the network with high probability as the network density approaches infinity. Within the context of a low duty-cycled wireless sensor network, the network is said to be asymptotically connected if for all realizations of the random duty-cycling (i.e., the combination of on and off nodes) there exists a path of active nodes from every node to every other node in the network with high probability as the network density approaches infinity. With this definition, we derive conditions under which a low duty-cycled sensor network is asymptotically connected. These conditions essentially specify how the nodes' communication range and the duty-cycling probability should scale as the network grows in order to maintain connectivity.