A competitive analysis for the online and offline optimization problems for a slotted energy harvesting (EH) wireless communication system is studied. The objective is to design online strategies that minimize the competitive rate gap that is defined as the maximum gap between the optimal rates that can be achieved by the offline and online policies over all possible energy arrival profiles. It is shown that the competitive rate gap is upper-bounded by the logarithm of the number of slots, and

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... myopic online transmission policy is proposed that achieves a lower rate gap.