14th IEEE International Conference on Embedded and Real-time - download pdf or read online

By Institute of Electrical and Electronics Engineers

ISBN-10: 0769533493

ISBN-13: 9780769533490

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Scheduling Time Intervals ([S(on−1 ) + ln−1 g, S(on−1 ) + ln−1 g + E(on−1 ) − 1]∩ [S(on ), S(on ) + E(on ) − 1]) = ∅ Clearly, this must be the case since free intervals between the intervals ([S(o0 ) + l0 g, S(o0 ) + l0 g + E(o0 ) − 1] ∪ ... ∪ [S(on−1 ) + ln−1 g, S(on−1 ) + ln−1 g + E(on−1 ) − n−1 1]) are of length (g − i=0 E(oi )), while the intervals [S(on ), S(on ) + E(on ) − 1] are of length E(on ). ∪[S(on−1 )+ln−1 g, S(on−1 )+ln−1 g+E(on−1 )−1]) and [S(on ), S(on ) + E(on ) − 1] overlap. This completes the proof by induction and at the same time it completes the proof of the theorem At first, we wanted to know, once a task oa is scheduled, by taking into account all the time intervals occupied by the instances of this task, how many time intervals can be used to execute another task ob ?

From this, if the sum of execution times of these tasks is larger than g then it means that these tasks cannot be scheduled on the interval I whereas the periods impose it. Therefore, the sum of tasks execution times must be less or equal to g, which proves the sufficiency of 3. We prove the necessity of 3 by showing that, if g < n i=0 E(oi ), then tasks of the set {∀i ∈ N, i ≤ n, oi } cannot be scheduled. To do that we use a proof by induction. The base case: for a set with two task {o0 , o1 } the necessity was proved in theorem 1.

Deogun, and S. Goddard. Real-time divisible load scheduling for cluster computing. In Proceedings of the IEEE Real-Time Technology and Applications Symposium (RTAS). IEEE, 2007. , has the potential to provide a solid theoretical foundation for the provision of real-time performance guarantees whilst executing arbitrarily divisible workloads on parallel computing clusters. In this work, we have studied two scheduling problems in RT-DLT when applied to clusters in which different processors become available at different time-instants: (i) how does one compute the minimum number of processors needed to meet a job’s deadline?

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14th IEEE International Conference on Embedded and Real-time Computing Systems and Applications by Institute of Electrical and Electronics Engineers

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