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Executing computing tasks with replications is an essential choice to achieve fault-tolerance in designing real-time, embedded systems. A problem of maximizing the number of real-time tasks with replications running on a multiprocessor embedded system is discussed in this letter. The partitioning problem can be modeled as a variant of the bin-packing problem. In the original problem, it is known that the first-fit (FF) method has a good worst-case performance bound of 4/3. Whether or not the same bound is achievable in the variant problem remains an open question. This letter closes the question by proving that the worst-case performance bound of using the FF method approaches to 2 but it never reaches it. Then, a tight bound of asymptotic worst-case performance is shown. [ABSTRACT FROM PUBLISHER]