Paper depicts that one of the main challenges in wireless networks WiMAX is the task of ensuring the required service quality, which involves the separation of user stations network of guaranteed rate in the downlink. Providing guaranteed transmission rate in the WiMAX technology can be achieved by solving bandwidth allocation downlink. Therefore, existing approaches to analyze the distribution of bandwidth downlink wireless WiMAX technology whereby determined that they use the principle of Best Effort. The quality of service is not guaranteed, and between user stations distributed all of the available bandwidth. The result is a mathematical model, the novelty of which is the possibility of pre-emptive rate limiting, a dedicated service flows user stations in the downlink WiMAX technology by using a linear-quadratic objective function that organizes the fair management of requests based on the relative priorities. In the course of solving the problem of scheduling data packets for transmission service flows of all user stations in the downlink of the proposed model it is necessary to perform a number of important constraint equations: the condition securing a sub-channel for the transmission of one slot for no more than one user station, the condition of adopting a one user station the number of slots, providing the required transmission rate used by the system modulation and coding, the condition of formation of a single packet of data for each user station, the condition of the formation of the packages "rectangular", terms and conditions for the required number of slots for the transmission of official information. The model proposed is directed to the allocation of each user station guaranteed bit rate in the absence of overload downlink as well as the preventive rate limiting allocated for user station overload conditions. Furthermore the proposed mathematical model addresses the problem of distribution slots between data packets as problems balancing the available bandwidth of WiMAX downlink channel for transmitting payload towards subscriber stations, taking account of the form of modulation and coding. As a result, decision analysis found that the service requests from the service flows user stations is realized on the basis of so-called absolute priority. Thus, in the case where the programming service flow requests from subscriber stations exceed bandwidth downlink preventive restriction mostly experienced service request from a low priority flow. Request transmission rate of the service stream with a higher priority on preventive ogrnaichenie rate experienced in a lesser degree. When using a linear objective function restriction preventive tests first service request from a low priority flow until the complete denial of access. When using a linear-quadratic objective function in the case of overload failures relate to maintain all service flows with high priority to a lesser extent, and in higher concentrations - low priority.