In order to improve TCP performance, a method using a PEP (Performance Enhancing Proxy) is proposed. The PEP operates on a router along a TCP connection. When a data packet arrives at the PEP, it forwards the packet to the destination host, transmits the corresponding ACK (premature ACK) to the source host in behalf of the destination host and stores the copy of the packet into its own buffer (PEP buffer) in case of the retransmission of the packet. In this paper, under the strategy which keeps the number of packets in the PEP buffer for which premature ACKs have been returned being less than or equal to a fixed threshold value (watermark value), we investigate the relation between the watermark value and the maximum throughput. Extensive simulation runs show that the simulation results are roughly classified into two cases. One case is that the maximum throughput becomes larger for larger watermark value and becomes a constant value when the watermark value is over a value. The other case is that though the maximum throughput becomes larger for lager watermark value in the same way, it reversely decreases when the watermark value is over a value. We also show that the latter (former) case is easier to occur as the propagation delay in the input side network of the PEP becomes smaller (larger) and the propagation delay in the output side network of the PEP becomes larger (smaller) and the PEP buffer capacity becomes smaller (larger).