Considering a cloud system, we propose in this paper to apply bounding aggregations for mathematical analysis of a data center. Modeled as a hysteresis queueing system, a data center is characterized by a forward and backward threshold which allow to represent its dynamic behavior. The client requests (or jobs) are represented by bulk arrivals which arrive into the buffers and are executed by Virtual Machines (VMs). According to the occupation of the queue and the thresholds, the VMs are activated and deactivated. The system is represented by a complex Markov chain which is difficult to analyze when the size of the system is huge. We propose to use in this case bounding aggregations on the batch arrivals, in order to compute performance measure bounds. We present some numerical results for the performance measures in order to compare the bounding values with the exact ones according to the different input parameters. The relevance of this paper is to propose a tradeoff between computational complexity and accuracy of the results, which provides very interesting solutions in networking dimensioning