Energy Harvesting is a promising feature for supplying energy to a wireless device. However, due to the mobility of wireless device and the stochastic nature of the energy arrivals, innovative management strategies should be adopted to maximize the energy efficiency. In this paper, we consider the utility maximization problem of a wireless transmitter with delay limited communications and energy harvesting capability. The throughput maximization problem is formulated as a Constrained Markov Decision Process (CMDP). To deal with the curse of the dimensionality, we introduce a new technique named Lyapunov Optimization. Based on Lyapunov Optimization theory, we propose an online expected transmission utility maximization algorithm (ETUMA) which is adaptive to the wireless channel state information as well as the data and the energy queue state information. Derived ETUMA has an advantage of low complexity and requires no prior knowledge of the system. Finally, simulations are provided to illustrate the effectiveness and potential of the proposed algorithm.
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