In fast long-distance networks (FLDN), TCP Reno was proved to have poor throughput performance and several variations were proposed to improve it by faster increasing of congestion window (cwnd). However, too fast increasing of cwnd will cause buffer overflow and the effect of TCP configurations on the queue buffer (qbuf) is a very important issue. In this paper, we study the relationships among the throughput, cwnd, and qbuf in FLDN. Some theorems are created from established mathematical models to characterize the behaviors of TCP in FLDN. We find that the qbuf not only relates to cwnd, but also to network configuration such as link bandwidth. Furthermore, we also simulate a bottlenecked topology to confirm the derived mathematic theorems. The proven theorems will bestead TCP configurations to improve TCP throughput in FLDN.