A polynomial-time algorithm is presented for partitioning a collection of sporadic tasks among the processors of an identical multiprocessor platform with static-priority scheduling on each individual processor. Since the partitioning problem is easily seen to be NP-hard in the strong sense, this algorithm is not optimal. A quantitative characterization of its worst-case performance is provided in terms of sufficient conditions and resource augmentation approximation bounds. The partitioning algorithm is also evaluated over randomly generated task systems.
A polynomial-time algorithm is presented for partitioning a collection of sporadic tasks among the processors of an identical multiprocessor platform. Since the partitioning problem is NP-hard in the strong sense, this algorithm is unlikely to be optimal. A quantitative characterization of its worst-case performance is provided in terms of resource augmentation: it is shown that any set of sporadic tasks that can be partitioned among the processors of an m-processor identical multiprocessor platform will be partitioned by this algorithm on an m-processor platform in which each processor is (4 − 2/m) times as fast.
Current feasibility tests for the static-priority scheduling on uniprocessors of periodic task systems run in pseudo-polynomial time. We present a fully polynomial-time approximation scheme (FPTAS) for feasibility analysis in static-priority systems with arbitrary relative deadlines. This test is an approximation with respect to the amount of a processor's capacity that must be "sacrificed" for the test to become exact. We show that an arbitrary level of accuracy, , may be chosen for the approximation scheme, and present a runtime bound that is polynomial in terms of and the number of tasks, n.
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