Energy Harvesting (EH) has emerged as a promising technique for Green Communications and it is a novel technique to prolong the lifetime of the wireless networks with replenishable nodes. In this paper, we consider the energy shortage analysis of fixed rate transmission in communication systems with energy harvesting nodes. First, we study the finite-horizon transmission and provide the general formula for the energy shortage probability. We also give some examples as benchmarks. Then, we continue to derive a closed-form expression for infinite-horizon transmission, which is a lower bound for the energy shortage probability of any finite-horizon transmission. These results are proposed for both Additive White Gaussian Noise (AWGN) and fading channels. Moreover, we show that even under \emph{random energy arrival}, one can transmit at a fixed rate equal to capacity in the AWGN channels with negligible aggregate shortage time. We achieve this result using our practical transmission schemes, proposed for finite-horizon. Also, comprehensive numerical simulations are performed in AWGN and fading channels with no Channel State Information (CSI) available at the transmitter, which corroborate our theoretical findings. Furthermore, we improve the performance of our transmission schemes in the fading channel with no CSI at the transmitter by optimizing the transmission initiation threshold.