Cloud computing paradigm proved itself to be a good approach for efficient high-performance computational infrastructure design. Besides performance, one of the most important measures for cloud service providers is energy efficiency of the system. For better energy efficiency, in light load case additional virtual machines are switched off, and switched on again when load increases. Dynamic scaling increases performance of the system, but leads to increase in service costs. To avoid ping-pong effect in dynamic scaling, hysteresis approach is applied. Considering number of virtual machines in modern cloud platforms, special attention should be paid to efficiency of computing algorithm. In this work, we describe behavior of cloud computing system in terms of queuing system with threshold-based hysteretic control of active servers number and noninstantaneous server activation. We use state elimination technique to develop efficient algorithm for stationary probabilities calculations and estimation of its performance measures. © Springer International Publishing Switzerland 2016.