In this work we consider the allocation of buffer space to data streams sharing a common high-speed wireless transmitter. As an example, we focus on an OFDMA-based downlink system scenario. Scheduling for maximum throughput has been extensively studied in the literature. However, the practically interesting case of a finite buffer has not been sufficiently addressed before. Especially in the case of overloaded packet queues, the choice of buffer management policy substantially affects the throughput performance. We consider a physical-layer scheduling scheme that allocates users to subcarriers based on channel state, in order to make the most use of multiuser diversity. We then consider optimal buffer partitioning to accommodate the resulting rates. We study the system throughput by simulations. As a benchmark, we also simulate MaxWeight, a well-known cross-layer channel and queue-aware scheduling policy that is throughput-optimal in the absence of a finite buffer constraint. We observe that a suitable buffer management policy with a simple channel-aware queuing policy achieves cross-layer scheduling performance, and can exceed it.