A finite buffer shared by multiple packet queues is considered. Partitioning the buffer to maximize total throughput is formulated as a resource allocation problem, the solution is shown to be achieved by a greedy incremental algorithm in polynomial time. The optimal buffer allocation strategy is applied to different models for a wireless downlink. First, a set of parallel M/M/1/m_i queues, corresponding to a downlink with orthogonal channels is considered. It is verified that at high load, optimal buffer partitioning can boost the throughput significantly with respect to complete sharing of the buffer. Next, the problem of optimal combined buffer allocation and channel assignment problems are shown to be separable in an outage scenario. Motivated by this observation, buffer allocation is considered in a system where users need to be multiplexed and scheduled based on channel state. It is observed that under finite buffers in the high load regime, scheduling simply with respect to channel state with a simply partitioned buffer achieves comparable throughput to combined channel and queue-aware scheduling.