Cloud computing is promising technology to manage and improve utilization of computing center resources to deliver various computing and IT services. For the purpose of energy saving there is no need to unnecessarily operate many servers under light loads, and they are switched off. On the other hand, some servers should be switched on in heavy load cases to prevent very long delays. Thus, waiting times and system operating cost can be maintained on acceptable level by dynamically adding or removing servers. One more fact that should be taken into account is significant server setup costs and activation times. For better energy efficiency, cloud computing system should not react on instantaneous increase or instantaneous decrease of load. That is the main motivation for using queuing systems with hysteresis for cloud computing system modelling. In the paper, we provide a model of cloud computing system in terms of multiple server threshold-based infinite capacity queuing system with hysteresis and noninstantanuous server activation. For proposed model, we develop a method for computing steady-state probabilities that allow to estimate a number of performance measures. © 2015 AIP Publishing LLC.