A schedulable utilization bound for the multiprocessor $\mathsf{EPDF}$ Pfair algorithm

Devi, UmaMaheswari; Anderson, James H.

doi:10.1007/s11241-007-9045-y

Cited by 4 publications

(10 citation statements)

References 44 publications

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“…Therefore, the PF-window of T 2 overlaps T 3 's when Θ(T 3 ) = Θ(T 2 ) as in insets (a), (b), and (d). Further, as shown in [6], the following lemma holds.…”

Section: B-bit the B-bit Or Boundary Bit Is Associated With Each Submentioning

confidence: 79%

“…This lemma is proved in [6] Lemma 16. (from [6]) Let t < t d be a slot with holes. Let U j be a subtask that is scheduled at t and let the tardiness of U j be zero.…”

Section: Lemma 15 (Srinivasan and Andersonmentioning

confidence: 93%

“…To facilitate expressing A(ideal, T, 0, t) for GIS tasks, let A(ideal, T i , 0, t) and A(ideal, T i , t) denote the ideal allocations to subtask T i in [0, t) and slot t, respectively. In [2], Anderson and Srinivasan showed that A(ideal, T i , t) is given by (6) below. An example is given in Figure 3.…”

Section: B-bit the B-bit Or Boundary Bit Is Associated With Each Submentioning

confidence: 99%

“…As can be seen from (13) and (6), the lag of a task T at t depends on the allocations that subtasks of T receive in each time slot until t in the ideal schedule. Hence, a tight estimate of such allocations is essential to bounding the lag of T reasonably accurately.…”

Section: Categorization Of Subtasksmentioning

confidence: 99%

“…Hence, by (6), no subtask of T other than T i and T j receives any allocation in t h − 1 and/or t h . By (i) and (ii) above and because τ contains every subtask of T that is in τ except T i and T j , we have…”

Section: By (7) A(ideal T D(t I ) D(t I ) + S) ≤ S · Wt(t ) Hencmentioning

confidence: 99%

See 4 more Smart Citations

Improved conditions for bounded tardiness under EPDF fair multiprocessor scheduling

Maheswari

Devi

Anderson

18th International Parallel and Distributed Processing Symposium, 2004. Proceedings.

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The earliest-pseudo-deadline-first (EPDF) Pfair algorithm is more efficient than other known Pfair scheduling algorithms, but is not optimal for scheduling recurrent real-time task systems on more than two identical processors. Although not optimal, EPDF may be preferable for real-time systems instantiated on less-powerful platforms, those with soft timing constraints, or those whose task composition can change at run-time. In prior work, Srinivasan and Anderson established a sufficient per-task utilization restriction for ensuring a tardiness of at most q quanta, where q ≥ 1, under EPDF. They also conjectured that under this algorithm, a tardiness bound of one quantum applies to task systems that are not subject to any restriction other than the obvious restrictions, namely, that the total system utilization not exceed the available processing capacity and per-task utilizations not exceed 1.0. In this paper, we present counterexamples that show that their conjecture is false and present sufficient per-task utilization restrictions that are more liberal than theirs. For ensuring a tardiness bound of one quantum, our restriction presents an improvement of 50% over the previous one.

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“…Therefore, the PF-window of T 2 overlaps T 3 's when Θ(T 3 ) = Θ(T 2 ) as in insets (a), (b), and (d). Further, as shown in [6], the following lemma holds.…”

Section: B-bit the B-bit Or Boundary Bit Is Associated With Each Submentioning

confidence: 79%

“…This lemma is proved in [6] Lemma 16. (from [6]) Let t < t d be a slot with holes. Let U j be a subtask that is scheduled at t and let the tardiness of U j be zero.…”

Section: Lemma 15 (Srinivasan and Andersonmentioning

confidence: 93%

Section: B-bit the B-bit Or Boundary Bit Is Associated With Each Submentioning

confidence: 99%

Section: Categorization Of Subtasksmentioning

confidence: 99%

Section: By (7) A(ideal T D(t I ) D(t I ) + S) ≤ S · Wt(t ) Hencmentioning

confidence: 99%

See 3 more Smart Citations

Improved conditions for bounded tardiness under EPDF fair multiprocessor scheduling

Maheswari

Devi

Anderson

18th International Parallel and Distributed Processing Symposium, 2004. Proceedings.

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LRE-TL: an optimal multiprocessor algorithm for sporadic task sets with unconstrained deadlines

Funk

2010

Real-Time Syst

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This article presents a detailed discussion of LRE-TL (Local Remaining Execution-TL-plane), an algorithm that schedules hard real-time periodic and sporadic task sets with unconstrained deadlines on identical multiprocessors. The algorithm builds upon important concepts such as the TL-plane construct used in the development of the LLREF algorithm (Largest Local Remaining Execution First). This article identifies the fundamental TL-plane scheduling principles used in the construction of LLREF. These simple principles are examined, identifying methods of simplifying the algorithm and allowing it to handle a more general task model. For example, we identify the principle that total local utilization can never increase within any TL-plane as long as a minimal number of tasks are executing. This observation leads to a straightforward approach for scheduling task arrivals within a TL-plane. In this manner LRE-TL can schedule sporadic tasks and tasks with unconstrained deadlines. Like LLREF, the LRE-TL scheduling algorithm is optimal for task sets with implicit deadlines. In addition, LRE-TL can schedule task sets with unconstrained deadlines provided they satisfy the density test for multiprocessor systems. While LLREF has a O(n 2 ) runtime per TL-plane, LRE-TL's runtime is O(n log n) per TL-plane.

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Improved conditions for bounded tardiness under EPDF Pfair multiprocessor scheduling

Devi

Anderson

2009

Journal of Computer and System Sciences

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The earliest-pseudo-deadline-first (EPDF) Pfair algorithm is more efficient than other known Pfair scheduling algorithms, but is not optimal for scheduling recurrent real-time task systems on more than two identical processors. Although not optimal, EPDF may be preferable for real-time systems instantiated on less-powerful platforms, those with soft timing constraints, or those whose task composition can change at run-time. In prior work, Srinivasan and Anderson established a sufficient per-task utilization restriction for ensuring a tardiness of at most q quanta, where q 1, under EPDF. They also conjectured that under this algorithm, a tardiness bound of one quantum applies to task systems that are not subject to any restriction other than the obvious restrictions, namely, that the total system utilization not exceed the available processing capacity and per-task utilizations not exceed 1.0. In this paper, we present counterexamples that show that their conjecture is false and present sufficient per-task utilization restrictions that are more liberal than theirs. For ensuring a tardiness bound of one quantum, our restriction presents an improvement of 50% over the previous one.

show abstract

A schedulable utilization bound for the multiprocessor $\mathsf{EPDF}$ Pfair algorithm

Cited by 4 publications

References 44 publications

Improved conditions for bounded tardiness under EPDF fair multiprocessor scheduling

Improved conditions for bounded tardiness under EPDF fair multiprocessor scheduling

LRE-TL: an optimal multiprocessor algorithm for sporadic task sets with unconstrained deadlines

Improved conditions for bounded tardiness under EPDF Pfair multiprocessor scheduling

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