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The current state of information technology is to develop and implement new approaches to the computational process. Evaluating the effectiveness of cloud centers is an important challenge for research, but it is complicated by the dynamic of cloud environments and a variety of user requests. This evaluation is vital in cases where virtualization is used to provide well-defined computing resources for users. The proposed model for evaluating the effectiveness of cloud centers in a high degree of virtualization to solve this problem has been proposed. Compared to existing, it considers the ability to service requests for group requests and the distributed time of service requests. The model is based on a two-stage approximation technique. The main non-Markov process is first modeled as an embedded semi-Markov process, then modeled as an approximated Markov process but only when receiving group request flows. The technique of constructing Markov links to build the model has been used. This model provides a full probability distribution of request waiting time, response time to execute requests, and the number of requests in the system. The results show that the performance of cloud centers is highly dependent on the coefficient of variation (CoV), request service time, and the size of the group flow (i.e., the number of requests in the group flow of requests). The larger the flow rate and/or the value of the coefficient of variation of the service time of requests, the longer the response time. But this helps reduce the use of resources by cloud providers. As a result, the work shows that in the conditions of large group flow of requests and/or large value of CoV, it is possible to increase the efficiency of cloud centers by grouping requests using the criterion of homogeneity.