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Accurate performance evaluation of cloud computing resources is a necessary prerequisite for ensuring that quality of service parameters remain within agreed limits. In this paper, we employ both the analytical and simulation modeling to addresses the complexity of cloud computing systems. Analytical model is comprised of distinct functional submodels, the results of which are combined in an iterative manner to obtain the solution with required accuracy. Our models incorporate the important features of cloud centers such as batch arrival of user requests, resource virtualization, and realistic servicing steps, to obtain important performance metrics such as task blocking probability and total waiting time incurred on user requests. Also, our results reveal important insights for capacity planning to control delay of servicing users requests.