Statistical evidence suggests that the autocorrelation function of a compressed-video sequence is better captured by ρ(k) = e-β√k than by ρ(k) = k-β = e-βlog k (long-range dependence) or ρ(k) = e-βk (Markovian). A video model with such a correlation structure is introduced based on the so-called M/G/∞ input processes. Though not Markovian, the model exhibits short-range dependence. Using the queueing performance under 'real' video traffic as a reference, we study via simulations the queueing performance under two video models: the M/G/∞ model and the fractional ARIMA (F-ARIMA) model (which exhibits LRD). Our results indicate that the M/G/∞ model is much more accurate in predicting the actual queueing performance than the F-ARIMA model. Furthermore, only O(n) computations are required to generate an M/G/∞ trace of length n, compared to O(n2) for a F-ARIMA trace.