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Techniques are presented for modeling and generating the univariate and multivariate probabilistic input processes that drive many simulation experiments. Among univariate input models, emphasis is given to the generalized beta distribution family, the Johnson translation system of distributions, and the Bezier distribution family. Among bivariate and higher dimensional input models, emphasis is given to computationally tractable extensions of univariate Johnson distributions. Also discussed are nonparametric techniques for modeling and simulating time dependent arrival streams using nonhomogeneous Poisson processes.