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Abstract: In this paper we use a small amount of video files to design a video-on-demand server. We use the available video information to overcome uncertainties such as future user preference, type of video file (movie, cartoon, documentary), video compression technique, etc. Using principal component analysis we overcome such uncertainties by reducing the dimensionality of the video data, creating a new video trace that captures statistical characteristics of most video files; we call this the characteristic video trace. Using the Pareto probability distribution for the size of the video frames (of the characteristic video trace) and self-similarity we develop a non-asymptotic model which predicts memory buffer size for a required quality of service. By obtaining the necessary parameters for the mathematical model from the characteristic video trace we could design the server without more information. [Copyright &y& Elsevier]