There is much experimental evidence that network traffic processes exhibit ubiquitous properties of self-similarity and long-range dependence, i.e., of correlations over a wide range of time scales. However, there is still considerable debate about how to model such processes and about their impact on network and application performance. In this paper, we argue that much recent modeling work has failed to consider the impact of two important parameters, namely the finite range of time scales of interest in performance evaluation and prediction problems, and the first-order statistics such as the marginal distribution of the process. We introduce and evaluate a model in which these parameters can be controlled. Specifically, our model is a modulated fluid traffic model in which the correlation function of the fluid rate matches that of an asymptotically second-order selfsimilar process with given Hurst parameter up to an arbitrary cutoff time lag, then drops to zero. We develop a very e...