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The article proposes a new method for calculating occupancy distribution and blocking/loss probability in the limited availability group with bandwidth reservation. The proposed method makes it possible to model groups servicing multi-service BPP traffic streams (Binomial-Poisson-Pascal). The proposed method is based on the analysis of the service process occurring in the considered system on the basis of the one-dimensional Markov chain. Significant increase in the accuracy and precision of the proposed method, in relation to other methods known from the literature, was obtained as the result of a modification of service streams within the reservation space. The accuracy of the proposed method has been verified by simulation studies.