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In the sporadic task model, a task is characterized by three parameters 驴 an execution requirement, a relative deadline, and a period parameter 驴 and has the interpretation that it generates an infinite sequence of jobs, such that (i) the arrival-times of any two successive jobs are separated by a time-interval at least as long as the period parameter; (ii) each job has a deadline that is separated from its arrival-time by a time-interval exactly equal to the relative deadline parameter of the task; and (iii) each job must execute for an amount equal to its execution requirement by its deadline. Most previous research concerning the scheduling of collections of sporadic tasks upon multiprocessor platforms has added the additional constraint that all tasks have their relative deadline parameters equal to their period parameters. In this research, we consider the scheduling of systems of sporadic tasks that do not necessarily satisfy this additional constraint, upon preemptive multiprocessor platforms. We propose, and evaluate, an algorithm for partitioning a given collection of arbitrary sporadic tasks upon a specified number of preemptive processors such that all deadlines are guaranteed to always be met.