In data center networks, Quantized Congestion Notification (QCN) has been ratified as the standard congestion management mechanism in the link layer. Since QCN nonlinearly switches between the rate increase and decrease stages, it is very difficult to understand QCN in depth and provide theoretical guidelines on setting the buffer size of the QCN switch. This paper gives an explicit formula for the boundary of buffer occupancy of the QCN switch. Specifically, based on the fluid model of QCN, we first derive the uniformly asymptotic stability condition of the QCN system. Then, under the condition that QCN is uniformly asymptotically stable, we analyze the buffer occupancy of the QCN switch theoretically and show that the classic rule-of-thumb for buffer sizing is not suitable for QCN. Finally, simulations validate the accuracy of our theoretical results.