The analysis of the method of balanced allocation of the frequency subchannels in a WiMAX downlink is carried out, which is based on the solution of the optimization problem of mixed integer linear programming related to maximizing the lower bound of satisfying the requirements for the allocated subscriber stations bandwidth based on their priority. The constraints were the conditions for allocating each subchannel to no more than one subscriber station and conditions for ensuring a balanced allocation of frequency subchannels to subscriber stations in accordance with their priorities. To evaluate the performance and the effectiveness of the considered method of channel resource allocation in WiMAX technology, the MATLAB Simulink package was used, which is represented by the block diagram of the downlink simulation model of the IEEE 802.16 Physical Layer. Using a downlink simulation model of the Physical Layer of the IEEE 802.16 standard, a comparative analysis of the proposed method and the previously known methods of Maximum Sum Rate (MSR), Maximum Fairness (MF), Proportional Fairness (PF), and Round Robin (RR) Scheduler was conducted. It is shown that the use of the proposed solutions allows increasing the level of Quality of Service of user requests for bandwidth on average from 12-16% compared with MF, The proposed method provided the highest efficiency with an increase in the number of subscriber stations, the number of frequency subchannels and an increase in heterogeneity in models and service priorities, as well as the requirements regarding the Quality of Service level.