A generic model for optimizing single-hop transmission policy of replenishable sensors

Energy harvesting from the working environment has received increasing attention in the research of wireless sensor networks. Recent developments in this area can be used to replenish the power supply of sensors. However, power management is still a crucial issue for such networks due to the uncertainty of stochastic replenishment. In this paper, we propose a generic mathematical framework to characterize the policy for single hop transmission over a replenishable sensor network. Firstly, we introduce a Markov chain model to describe different modes of energy renewal. Then, we derive the optimal transmission policy for sensors with different energy budgets. Depending on the energy status of a sensor and the reward for successfully transmitting a message, we prove the existence of optimal thresholds that maximize the average reward rate. Our results are quite general since the reward values can be made application-specific for different design objectives. Compared with the unconditional transmit-all policy, which transmits every message as long as the energy storage is positive, the proposed optimal transmission policy is shown to achieve significant gains in the average reward rate.