We constructed mathematical models of cloud computing systems taking into account various mechanisms for increasing energy efficiency in terms of queuing theory, and analytical expressions for the main characteristics of energy consumption and server performance metrics were obtained. We investigated and compered three different energy efficiency improving mechanisms of cloud computing systems: the shutdown delay mechanism, the switch on delay mechanism and the threshold-based switch on mechanism. The general principle of functioning mechanisms for energy efficiency improving is that all mechanisms try to find a middle ground between continuous operation without shutdowns and with switching on as soon as it remains empty. We formulated the energy consumption optimization problem of the cloud computing system for each parameter used in this energy efficiency mechanisms. We conducted a numerical analysis of the formulas for solving the optimization problem of energy consumption in cloud computing system based on the initial data close to the real ones. Copyright © 2018 for the individual papers by the papers' authors.