New PDF release: 14th IEEE International Conference on Embedded and Real-time

By Institute of Electrical and Electronics Engineers

ISBN-10: 0769533493

ISBN-13: 9780769533490

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Extra resources for 14th IEEE International Conference on Embedded and Real-time Computing Systems and Applications

Example text

Time Intervals Theorem 5 Let (ocdt : E(ocdt ), T (ocdt )) be a candidate task for the schedulability analysis and {∀i ∈ N, i ≤ n, (oi : E(oi ), T (oi ))} be a set of n tasks satisfying, for each two tasks (oa : E(oa ), T (oa )) and (ob : E(ob ), T (ob )), GCD(T (oa ), T (ob )) is equal to g and no T (oi ), ∀n divides T (ocdt . , Ωm } according to the GCD of each tasks subset, so we denote by BG (basic GCD) the GCD of all tasks of Ω. Let Ω1 be the set of tasks that satisfy the following property: for each two tasks (oa : E(oa ), T (oa )) and (ob : E(ob ), T (ob )) in Ω1 , GCD(T (oa ), T (ob )) is equal to BG, E(ok ) is de- GCD(g, T (ocdt )) − T (ocdt ) GCD(g, T (ocdt )) E(ocdt ) n i=0 noted by BE.

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? and (ii) given a number of processors, how does one determine the earliest completion time for the job on this many processors?

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 ?

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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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