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Equivalence between Schedule Representations: Theory and Applications
 In Proceedings of the 2008 IEEE RealTime and Embedded Technology and Applications Symposium  Volume 00 (April 22  24, 2008). RTAS. IEEE Computer Society
"... Multiprocessor scheduling problems are hard because of the numerous constraints on valid schedules to take into account. This paper presents new schedule representations in order to overcome these difficulties, by allowing processors to be fractionally allocated. We prove that these representation ..."
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Multiprocessor scheduling problems are hard because of the numerous constraints on valid schedules to take into account. This paper presents new schedule representations in order to overcome these difficulties, by allowing processors to be fractionally allocated. We prove that these representations are equivalent to the standard representations when preemptive scheduling is allowed. This allows the creation of scheduling algorithms and the study of feasibility in the simpler representations. We apply this method throughout the paper. Then, we use it to provide new simple solutions to the previously solved implicitdeadline periodic scheduling problem. We also tackle the more general problem of scheduling arbitrary timetriggered tasks, and thus in particular solve the open multiprocessor general periodic tasks scheduling problem. Contrary to previous solutions like the PFair class of algorithms, the proposed solution also works when processors have different speeds. We complete the method by providing an online schedule transformation algorithm, that allows the efficient handling of both timetriggered and eventtriggered tasks, as well as the creation of online ratebased scheduling algorithms on multiprocessors. 1.
Generalized Feasibility Analysis on Uniform Multiprocessors
"... This paper presents feasibility tests for scheduling instances of realtime jobs on uniform multiprocessor platforms. In a uniform multiprocessor, each processor has an associated speed – a job executing on a processor of speed s for t time units performs s × t units of work. Two feasibility tests a ..."
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This paper presents feasibility tests for scheduling instances of realtime jobs on uniform multiprocessor platforms. In a uniform multiprocessor, each processor has an associated speed – a job executing on a processor of speed s for t time units performs s × t units of work. Two feasibility tests are presented. First, a sufficient condition is presented – whenever this condition holds the jobs are known to be feasible on the multiprocessor. Then, a necessary condition is presented – whenever the jobs are feasible on the multiprocessor, this condition must hold. 1