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SUMMARYIt has been reported in several studies that the probability distribution functions for interarrival times of tasks in multimedia systems cannot be represented by traditional probability distribution functions, such as exponential ones.In this paper we propose an approximation method, based on the Coxian distribution function, to calculate the probability distribution functions used in analyzing multimedia systems. Although the Coxian function can represent arbitrary distribution functions, it is difficult to determine their parameters directly from a given distribution function. In this work, this drawback is remedied by first approximating the given distribution function with a linear combination of Erlang function, and then converting it to a Coxian function. We also present examples of the approximation and evaluate its accuracy.

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When a group of parallel lines pass through an ellipse, the center point between two intersecting points of each straight line is on another straight line passing through the center of the ellipse. Furthermore, a graphical plot of the distance between the two intersecting points vs. a coordinate value (either x or y) of the center point will form an elliptical shape. These two characteristics of the ellipse are exploited by an algorithm for ellipse extraction. Given an input image of ellipses, a center point map is constructed. Then a Hough transform is used to detect the center line that represents the ellipse. Next, the center line so detected is used to estimate the parameters and to obtain sample pixels of the ellipse. This is followed by a least‐square fitting and high precision parameter value computation. Numerous experiments were conducted which demonstrated the effectiveness of our algorithm.

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