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Cloud computing provides a new paradigm for industries to meet the emerging business needs by accessing distributed computing resources such as infrastructure, hardware and software applications on-demand over the internet as services. As the technology and the need is growing very fast, in future there may be multiple vendors offering different services with different Quality of Services (QoS) and at various prices. This would lead to development of new methods and tools for the performance evaluation of the system to meet the offerings and requirements. In this paper, we present an analytical finite population model for performance evaluation of a private cloud computing system. Various performance measures of the cloud system for finite population environment indicate that the proposed provisioning technique helps the cloud operators in tuning the resources accordingly to improve the QoS targets.