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Multiuser Multi-Packet Transmission (MPT) from an Access Point (AP) equipped with multiple antennas to multiple single-antenna nodes can be achieved by exploiting the spatial dimension of the channel. In this paper we present a queueing model to analytically study such systems from the link-layer perspective, in presence of random packet arrivals, heterogeneous channel conditions and packet errors. The analysis relies on a blind estimation of the number of different destinations among the packets waiting in the queue, which allows for building a simple, but general model for MPT systems with per-node First-In First-Out (FIFO) packet scheduling. Simulation results validate the accuracy of the analytical model and provide further insights on the cross-relations between the channel state, the number of antennas, and the number of active users, as well as how they affect the system performance. The simplicity and accuracy of the model makes it suitable for the evaluation of Medium Access Control (MAC) protocols for Ad Hoc or Wireless Local Area Networks supporting Multiuser MPT in non-saturation conditions, where the queueing dynamics play an important role on the achieved performance, and simple user selection algorithms are required.