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This paper traces the development/evolution of three of our previously proposed MPEG coded video traffic models, that can capture the statistical properties of MPEG video data. The basic ideas behind these models are to decompose an MPEG compressed video sequence into several parts according to motion/scene complexity or data structure. Each part is described by a self-similar process. These different self-similar processes are then combined to form the respective models. In addition, Beta distribution is used to characterize the marginal cumulative distribution (CDF) of the self-similar processes. Comparison among the three models shows that the latest model (called the simple IPB composite model) is the most practical one in terms of accuracy and complexity. Simulations based on many real MPEG compressed movie sequences, including StarWars, have demonstrated that the simple model can capture the autocorrelation function (ACF) and the marginal CDF very closely.