While throughput declines gradually as self-similarity increases, queuing delay increases more drastically. When traffic is self-similar, we find that queuing delay grows proportionally to the buffer capacity present in the system. Taken together, these two observations have potentially dire implications for QoS provisions in networks. To achieve a constant level of throughput or packet loss as self-similarity is increased, extremely large buffer capacity is needed. However, increased buffering leads to large queuing delays and thus self-similarity significantly steepens the trade-off curve between throughput/ packet loss and delay.