In order to improve TCP performance, a method using a PEP (Performance Enhancing Proxy) is proposed. In the method, the PEP is located in a intermediate router along a TCP connection. When a data packet arrives at the PEP, it forwards the packet, stores the copy of the packet into its own buffer (PEP buffer), and returns the corresponding ACK (premature ACK) in behalf of the destination host. In this paper, under the strategy which keeps the number of the 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. Simulation results show that (i) when there exist the upper and lower bounds of the watermark value at which the maximum throughput becomes maximum, the both bounds increase for the increase of the propagation delay in the input side network of the PEP, and the upper bound increases and the lower bound decreases for the increase of the propagation delay in the output side network of the PEP, (ii) when there exists the lower bound only, the bound increases (decreases) for the increase of the propagation delay in the input (output) side network. We also show that when the watermark value is greater than the upper bound, the larger the PEP buffer capacity is, the smaller the decreasing ratio of the maximum throughput is.