Energy harvesting wireless communication system (EH-WCS) has the capability of harvesting energy for system operations from the surrounding renewable energy sources. However, the randomness and instability of the harvested energy will result in the depletion of the energy consumption. To provide reliable communication services with the quality of service (QoS) guarantee, it is necessary for the EH-WCS to use a reliable energy backup (REB) for supplying energy to the system during the failure of its primary energy source. In this paper, a novel stochastic model, i.e., the extended Markov fluid ...