Optimal radius for connectivity in duty-cycled wireless sensor networks

We investigate the condition on transmission radius needed to achieve connectivity in duty-cycled wireless sensor networks (briefly, DC-WSN). First, we settle a conjecture of Das et. al. (2012) and prove that the connectivity condition on Random Geometric Graphs (RGG), given by Gupta and Kumar (1989), can be used to derive a weak sufficient condition to achieve connectivity in DC-WSN. We also present a stronger result which gives a necessary and sufficient condition for connectivity and is hence optimal. The optimality of such a radius is also tested via simulation for two specific duty-cycle schemes, called the contiguous and the random selection duty-cycle scheme.