Energy harvesting (EH) has been developed to extend the lifetimes ofenergy-limited communication systems. In this letter, we consider a single-userEH communication system, in which both of the arrival data and the harvestedenergy curves are modeled as general functions. Unlike most of the works in thefield, we investigate the online algorithms which only acquire the causalinformation of the arrival data and the harvested energy processes. We studyhow well the optimal online algorithm works compared with the optimal offlinealgorithm, and thus our goal is to find the lower and upper bounds for theratio of the completion time in the optimal online algorithm to the optimaloffline algorithm. We propose two online algorithms which achieve the upperbound of 2 on this ratio. Also, we show that this ratio is 2 for the optimalonline algorithm.
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