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A scheduling problem that maximizes the system throughput under a constraint on the time-slot allocation ratio of users is considered in the systems having Gaussian-distributed performance metrics, which include multiple-input-multiple-output (MIMO) systems. Two schedulers, which are denoted by the control variance (CV) scheduler and the control mean (CM) scheduler, are proposed in this paper. The proposed schedulers have a beneficial characteristic wherein parameters of the schedulers are independent of channel statistics. Due to this characteristic, the parameters can be precalculated and then applied in the systems where only a limited number of desired ratios exist. For the systems that include an infinitely or extremely large number of desired ratios, parameter computation for the CV scheduler is greatly simplified by eliminating integral calculations. An approximation of the complementary error function is applied for simplification. Simulation results show that the proposed schedulers achieve nearly the maximum system throughput, and the Gaussian assumption and the approximation of the complementary error function cause a negligible error on the time-slot allocation ratio, even in MIMO systems equipped with a small number of antennas.