In a multi-user downlink system, the use of channel estimates in the scheduling process can significantly improve the spectral efficiency. Recent work has shown that from a sum rate capacity standpoint, and assuming infinite queue backlogs, the optimal transmission scheme is to select the user with the largest instantaneous channel gain. A more realistic scenario is considered in this work, in which the downlink scheduling problem with finite queue backlogs is analyzed. It is shown that although time division scheduling is optimal for infinite backlogs, this is not the case for finite buffer sizes. In fact, a simple broadcast scheduler is shown to be more power efficient than the maximum rate time division scheduler under such a scenario.