The performance of random beamforming (RBF) with partial channel state information (CSI) feedback is investigated here for millimeter wave (mmWave) multiuser multiple-input single-output (MU-MISO) downlink systems using the uniform random multipath (UR-MP) channel model. In particular, the required number of users in the cell for RBF to yield linear sum rate scaling with respect to the number of transmit antennas is identified under the UR-MP channel model for different levels of channel sparsity. Then, the problem of user scheduling inMU-MISO downlink is considered when the number of users in the cell is not sufficiently large (sparse user regime) for the system to operate in the identified sufficient user regime. By exploiting the sparsity of mmWave radio channels, several user scheduling algorithms based on beam aggregation with reasonable amount of feedback are proposed for the sparse user regime. Our numerical results show that the proposed algorithms yield very good sum-rate performance in sparse mmWave channels.