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Summary form only given. We analyze the average-case performance of an online scheduling algorithm for independent parallel tasks. We develop a method to calculate an analytical asymptotic average-case performance bound for arbitrary probability distribution of task sizes. In particular, we show that when task sizes are uniformly distributed in the range [1..C], an asymptotic average-case performance bound of M-(3-(1+1/C)C+1)C-1 can be achieved, where M is the number of processors. We also present extensive numerical and simulation data to demonstrate the accuracy of our analytical bound.