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This paper proposes the use of a "Drop from Front" scheme for improving TCP performance in high bandwidth-delay product networks. In particular, for "TCP over ATM" we compare the performance when drop from front is used at the output port of ATM switches with the performance under tail drop, its variations, and with variations of Random Early Detection (RED). In drop from front, when a cell arrives at a full buffer, the cell closest to being transmitted is dropped, thus creating space for the arriving cell. This policy causes duplicate acknowledgements to be sent one whole buffer drain time earlier than is the case under tail drop. These quicker duplicate acknowledgements cause TCP with Fast Retransmit to recognize losses faster and invoke congestion control actions earlier than would be the case under tail drop. This earlier reaction translates into considerable performance improvement. Hence, drop from front successfully utilizes the ability of TCP wath Fast Retransmit to quickly recognize and react to congestion information (at the third repeat acknowledgement, as opposed to time-out). Roughly, the earlier action by the sources causes the congestion not to grow quite as severe, which prevents later over-reaction by the sources, and thus increases throughput. Our simulations show that, for the same buffer size, drop from front results in considerably higher TCP throughput than tail drop, and for all but very small buffers even higher than tail drop combined with partial frame drop. Without partial frame drop, drop from front performs better than RED and with partial frame drop its performance is very close to that of RED with complete frame drop. Drop from front is also fairer than tail drop because it partially counteracts TCP's bias against connections with larger round trip times.