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In this paper, we study the problem of scheduling arbitrary-deadline real-time sporadic task sets on a multiprocessor system under global fixed-priority scheduling. Two contributions are made in this paper. First, it has been shown that the existing response time analysis in arbitrary-deadline systems is flawed: the response time may be larger than the derived bound. This paper provides a revised analysis resolving the problems with the original approach, and then propose a corresponding schedulability test. Secondly, we derive a linear-time upper bound on the response time of arbitrary-deadline tasks in multiprocessor systems. To the best of our knowledge, this is the first work presenting a linear-time response time upper bound for arbitrary-deadline sporadic tasks in multiprocessor systems. Empirically, this linear-time response time bound is shown to be highly effective in terms of the number of task sets that are deemed schedulable.

Response time bounds for sporadic arbitrary-deadline tasks under global fixed-priority scheduling on multiprocessors