Traditionally, the size of router buffers is determined by the bandwidth-delay product discipline (normal discipline), which is the product of the link bandwidth and average round-trip time (RTT) of flows passing through the router. However, recent research results have revealed that when the number of flows is sufficiently large, the buffer size can be decreased to the bandwidth-delay product divided by the square-root of the number of flows (sqrtN discipline), without introducing underutilization of the link bandwidth. This assertion has been verified mainly for long-lived flows; in contrast, there has not been a thorough verification of short-lived flows, which are the majority of Internet flows. Furthermore, the effects of network parameters, such as the link bandwidth and propagation delay, have not been investigated. In this paper, we compare the performance of the above two disciplines, normal and sqrtN, for sizing the router buffer. We focus on the performance of both long-lived and short-lived TCP connections traversing the router under various network environments. Through extensive simulations, we show that the sqrtN discipline would degrade the TCP performance in terms of the packet loss ratio and file transmission delay, and it may be useful only when the transferring file size is about 50-100 Kbytes or when the propagation delay between the sender and the receiver hosts is significantly small.