On k −coverage in a mostly sleeping sensor network

Sensor networks are often desired to last many times longer than the active lifetime of individual sensors. This is usually achieved by putting sensors to sleep for most of their lifetime. On the other hand, event monitoring applications require guaranteed k -coverage of the protected region at all times. As a result, determining the appropriate number of sensors to deploy that achieves both goals simultaneously becomes a challenging problem. In this paper, we consider three kinds of deployments for a sensor network on a unit square—a √ n ×√ n grid, random uniform (for all n points), and Poisson (with density n ). In all three deployments, each sensor is active with probability p , independently from the others. Then, we claim that the critical value of the function np π r 2 /log ( np ) is 1 for the event of k -coverage of every point. We also provide an upper bound on the window of this phase transition. Although the conditions for the three deployments are similar, we obtain sharper bounds for the random deployments than the grid deployment, which occurs due to the boundary condition. In this paper, we also provide corrections to previously published results. Finally, we use simulation to show the usefulness of our analysis in real deployment scenarios.