Is deterministic deployment worse than random deployment for wireless sensor networks?

Before a sensor network is deployed, it is important to determine how many sensors are required to achieve a certain level of coverage. The number of sensors required for maintaining k-coverage depends on the area of the monitored region, the probability that a node fails or powers off (to save energy), and the deployment strategy. In this paper, we derive the density required to maintain k-coverage under three deployment strategies: (i) nodes are deployed as a Poisson point process, (ii) nodes are uniformly randomly distributed, (iii) nodes are deployed on regular grids. Our results show that under most circumstances, grid deployment renders asymptotically lower node density than random deployment. These results override a previous conclusion that grid deployment may render higher node density than random node distributions. We also validate the above results via simulations.