Trade-offs between mobility and density for coverage in wireless sensor networks

In this paper, we study the coverage problem for hybrid networks which comprise both static and mobile sensors. We consider mobile sensors with limited mobility, i.e., they can move only once over a short distance. Such mobiles are simple and cheap compared to sophisticated mobile robots. In conventional static sensor networks, for a random deployment, the sensor density should increase as O(log L + k log log L) to provide k-coverage in a network with a size of L. As an alternative, an all mobile sensor network can provide k-coverage over the field with a constant density of O(k), independent of network size L. We show that the maximum distance that any mobile sensor will have to move is O(1 over √k log ^{3 over 4} (kL)). We then propose a hybrid network structure, comprising static sensors and a small fraction of O(1 over √(k)) of mobile sensors. For this network structure, we prove that k-coverage is achievable with a constant sensor density of O(k), independent of network size L. Furthermore, for this hybrid structure, we prove that the maximum distance which any mobile sensor has to move is bounded as O(log^{3 over 4} L). We then propose a distributed relocation algorithm, where each mobile sensor only requires local information in order to optimally relocate itself and characterize the algorithm's computational complexity and message overhead. Finally, we verify our analysis via extensive numerical evaluations.