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Resource allocations represent a major challenge and an important step in the design of cellular network. The constraint of channel conditions can induce unequal spectral efficiency typically for users, which suffer path losses. However, for such a constraint, an inequality in terms of throughput fairness and delay are observed. In order to solve this problem, we propose in this paper to use the Schedulers algorithm based on Proportional Fair (PF), which introduces compensation with the Signal Interference Noise Ratio (SINR). The results obtained show by the approach proposed in this case achieved us to provide an optimal solution for the allocation of resources in the OFDM multi-carrier system. This distribution of resources leads to a compromise between throughput and fairness in relation to schedulers and jointly provides a high throughput.