In order to improve TCP performance, the use of a PEP (Performance Enhancing Proxy) has been 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 on behalf of the destination host, and stores a copy of the packet in a local buffer (PEP buffer) in case the packet needs to be retransmitted. In this paper, in accordance with a strategy that keeps the number of prematurely acknowledged packets in the PEP buffer below a fixed threshold (watermark) value, we investigate the relation between the watermark value and the average throughput. Extensive simulations show that the results can be roughly classified into two cases. In the first case, the average throughput becomes larger for larger watermark values and becomes a constant value when the watermark value is over a certain value. In the second case, although the average throughput becomes larger for lager watermark value in the same way, it decreases when the watermark value is over a certain value. We also show that the latter (former) case can occur more easily 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 also show that the latter (former) case can occur more easily as the transmission speed in the input side network becomes larger (smaller) and the transmission speed in the output side network becomes smaller (larger) while the PEP buffer capacity becomes smaller (larger).