Optimal power allocation on discrete energy harvesting model

This paper studies the power allocation problem in energy harvesting systems with finite battery. We adopt the discretized energy arrival and power allocation model. Hence, the service process can be modeled as a finite state Markov chain. Based on the discretized model, we analyze the stationary distribution of the Markov chain and formulate the utility maximization problem, which is then reformed as a linear programming problem. By analyzing the linear programming problem, we provide some intuition on the structure of the optimal power allocation policy and find the condition in which the greedy power allocation is optimal. Numerical simulations show the influence of the energy arrival process on the optimal power allocation policy, and the results are consistent with our analysis.