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In this paper, the well known proportional fairness scheduling is investigated when we joint transmit beamforming and packet level scheduling taking into consideration the traffic arrival process with different packet lengths for the downlink of multiple-input multiple-output (MIMO) multi-user systems. The new scheduler called the proportional fairness zero-forcing beamforming (PF-ZB) can perform at the packet level and provide low average packet transmission delay as well as fairness to users. The scheduler is work conserving. We compare the performance of our scheduler with another well known MIMO scheduler when it is performing in the packet level with transmit beamforming. Simulations that consider the traffic characteristics show the low average packet transmission delay and demonstrate the fairness capabilities of PF-ZB.