For the Energy harvesting (EH) transmitter equipped with a Reliable Energy Backup (REB), the following problem is challenging and important: how to minimize the amount of energy supplied by the REB, such that the harvested energy is efficiently utilized for transmitting a given amount of data within a fixed delay constraint. In this paper, we first develop a stochastic model for this problem. We then discuss the optimization issue of delay-constrained data transmission over a fading wireless channel. We transform the delay constraint into the penalty function, and then the energy constrained c...