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This paper presents a single hysteresis model for limited-availability group that are offered Erlang, Engset and Pascal traffic streams. The occupancy distribution in the system is approximated by a weighted sum of occupancy distributions in multi-threshold systems. Distribution weights are obtained on the basis of a specially constructed Markovian switching process. The results of the calculations of radio interfaces in which the single hysteresis mechanism has been implemented are compared with the results of the simulation experiments. The study demonstrates high accuracy of the proposed model.