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In this paper, we evaluate the performance of cloud centers with high degree of virtualization and Poisson batch task arrivals. To this end, we develop an analytical model and validate it with an independent simulation model. Task service times are modeled with a general probability distribution, but the model also accounts for the deterioration of performance due to the workload at each node. The model allows for calculation of important performance indicators such as mean response time, waiting time in the queue, queue length, blocking probability, probability of immediate service, and probability distribution of the number of tasks in the system. Furthermore, we show that the performance of a cloud center may be improved if incoming requests are partitioned on the basis of the coefficient of variation of service time and batch size.