This paper addresses the optimization of data transmission in wireless systems with energy harvesting nodes, focusing on maximizing throughput by a deadline and minimizing transmission completion time in fading wireless channels. The authors introduce a directional water-filling algorithm to optimize transmit power sequences, considering energy storage capacity and causality constraints. They demonstrate the optimality of this algorithm for throughput maximization and solve the transmission completion time minimization problem using its equivalence to throughput maximization. For online policies, they use stochastic dynamic programming to find the optimal policy that maximizes the average number of bits delivered by a deadline under stochastic fading and energy arrival processes. Additionally, they propose near-optimal policies with reduced complexity and evaluate their performance through numerical studies under various system configurations. The results show that the optimal offline and online policies perform well, while the sub-optimal policies have varying performance depending on the system parameters.This paper addresses the optimization of data transmission in wireless systems with energy harvesting nodes, focusing on maximizing throughput by a deadline and minimizing transmission completion time in fading wireless channels. The authors introduce a directional water-filling algorithm to optimize transmit power sequences, considering energy storage capacity and causality constraints. They demonstrate the optimality of this algorithm for throughput maximization and solve the transmission completion time minimization problem using its equivalence to throughput maximization. For online policies, they use stochastic dynamic programming to find the optimal policy that maximizes the average number of bits delivered by a deadline under stochastic fading and energy arrival processes. Additionally, they propose near-optimal policies with reduced complexity and evaluate their performance through numerical studies under various system configurations. The results show that the optimal offline and online policies perform well, while the sub-optimal policies have varying performance depending on the system parameters.