The results of development a mathematical model for capacity allocation downlink technology WiMAX. The novelty of the proposed model is possible preventive limit transmission rate allocated to the service flows of the user stations in the downlink by using the WiMAX technology linear or linear-quadratic objective function. It is shown that the use of a linear-quadratic objective function in comparison with the linear, can produce a more equitable management of requests based on the relative priorities. The analysis of known methods for dividing the time-frequency resource WiMAX technology showed that they all focus on the distribution between the subscriber stations all bandwidth downlink. The model proposed is directed to the allocation of each user station a guaranteed bit rate in the absence of overload downlink as well as the preventive rate limiting allocated user stations under overload conditions. Using the mathematical model is directed to distribution between subscriber stations of a time-frequency re-source of the downlink, which in turn improves the conditions in the electromagnetic frequency range used. The influence of the priority request rate used in the model, the nature of the possible failures.