Abstract: The traditional queuing theory is not applicable to the self-similar high-speed network traffic. A qualitative analysis of G/D/1 queue with FGN input by computer simulation was presented, and attention was focused on the average delay time and the tail behavior of infinite and finite queues. The effect of Hurst parameter was proven through these experiments that the average delay time rises evidently when Hurst parameter increases, while the input intensity and variance are almost equivalent and the utilization rate is above a certain threshold. Moreover, concerning the tail behavior under same conditions, the simulation results of the G/D/1 model with finite buffer are much more optimistic than the theoretical results of such model with infinite buffer.