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Today is an era where multiprocessor technology plays a major role in designs of modern computer architecture. While multiprocessor systems offer extra computing power, it also opens a new range of opportunities to improve fault-robustness. This paper focuses on a problem of achieving fault-tolerance using replications in real-time, multiprocessor systems. In the problem, multiple replicas, or copies, of a computing task are executed on distinct processors to resist potential processor failures and computing faults. Two greedy, approximation heuristics, named Worst Fit Increasing K-Replication and First Fit Increasing K-Replication, are studied to maximise the number of real-time tasks assigned on a system with identical processors, respecting to the tasks’ replicating and timely requirements. Worst case performance is analysed by using an approximation ratio between the algorithms and an optimal solution. We mathematically prove that the ratios of using both algorithms are infinitely close to 2. Simulations are performed on a large set of testing cases which can be used to bring to light the average performance of using the algorithms in practice. The results show that both heuristic algorithms provide simple but fast and effective solutions to solve the problem. Assigning real-time tasks to a multiprocessor system with replications. [ABSTRACT FROM PUBLISHER]

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]