Energy efficiency is always a concern in hosting servers. When any new development is added to a host server, the power consumption of the host server must be theoretically and empirically re-evaluated. Because of the ongoing development trends in computing systems at the hardware, software and middleware levels, deriving a direct mathematical model for quantifying the power consumption of a host server is difficult. Therefore, a system identification is used to construct the power consumption model for virtualized hosting servers. To date, three types of system identifications have been used in the literature for defining the power consumption model: the first-principles, the black-box and the gray-box identification approaches. To the best of our knowledge, the majority of these approaches are apparently used to model the power consumption in a single-input single-output (SISO) system model, in which a hardware component is reconfigured to meet the power budget target. In this paper, to accommodate the ongoing development trends in computing systems, we propose a multi-input single-output (MISO) model for modeling the power consumption of virtualized hosting servers. We use the black-box system identification method, and we utilize the Auto-Regressive eXogenous (ARX) mathematical model to construct the MISO power model. We compare our MISO power model with the SISO power model that is used in existing state-of-the-art works. Empirically, our MISO power model exhibits higher accuracy than the existing SISO power model in predicting power consumption. Using our model, we can achieve approximately 98 % accuracy in predicting the power consumption of virtualized hosting servers.