Shared-buffer ATM switches can have severe cell loss under asymmetrical or heavy loading conditions, which makes buffer management essential. In this paper, we study the shared-buffer system under the class of all work-conserving pushout policies and derive the properties of the optimal policy, which gives the least-average expected total cell loss probability. In a 2/spl times/2 system with independent identically distributed Bernoulli arrivals, we show that the optimal policy can be characterized by a single threshold. In the case of correlated arrivals, modeled by a discrete batch Markovian arrival process, the optimal policy has multiple thresholds, one for each phase of the arrival process. For the N/spl times/N shared buffer ATM switch, we are unable to prove optimality of any policy, but we study the system via simulations. We provide a dynamic buffer management policy and compare its performance with that of static threshold-type policies.