Impact of mobility on energy provisioning in wireless rechargeable sensor networks

One fundamental question in Wireless Rechargeable Sensor Networks (WRSNs) is the energy provisioning problem, i.e., how to deploy energy sources in a network to ensure that the nodes can harvest sufficient energy for continuous operation. Though the potential mobility of nodes has been exploited to reduce the number of sources necessary in energy provisioning problem in existing literature, the non-negligible impacts of the constraints of node speed and battery capacity on energy provisioning are completely overlooked, in order to simplify the analysis. In this paper, we propose a new metric - Quality of Energy Provisioning (QoEP) - to characterize the expected portion of time that a mobile node can sustain normal operation in WRSNs, which factors in the constraints of node speed and battery capacity. To avoid confining the analysis to a specific mobility model, we study spatial distribution instead. We investigate the upper and lower bounds of QoEP in one-dimensional case with one single source and multiple sources respectively. For single source case, we prove the tight lower bound and upper bound of QoEP. Extending the results to multiple sources, we obtain tight lower bound and relaxed upper bound in normal cases, together with tight upper bound for one special case. Moreover, we give the tight lower bounds in both 2D and 3D cases. Finally, we perform extensive simulations to verify our findings. Simulation results show that our bounds perfectly hold, and outperform the former works.