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Partitioned EDF scheduling: a closer look

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Abstract

The partitioned EDF scheduling of implicit-deadline sporadic task systems upon identical multiprocessor platforms is considered. The problem is known to be intractable, but many different polynomial-time algorithms have been proposed for solving it approximately. These different approximation algorithms have previously been compared using utilization bounds; they are compared here using a different metric—the speedup factor. It is shown that from the perspective of their speedup factors, the best partitioning algorithms are those that (i) assign the tasks in decreasing order of utilization; and (ii) are “reasonable” in the sense that they will assign a task if there is capacity available on some processor—such algorithms include the widely-used First-Fit Decreasing, Best-Fit Decreasing, and Worst-Fit Decreasing partitioning heuristics.

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Notes

  1. Actually, the result in Hochbaum and Shmoys (1987) was expressed in terms of minimizing the makespan of a given finite collection of non-preemptive jobs; however, the makespan minimization problem considered in Hochbaum and Shmoys (1987) is easily shown to essentially be equivalent to the partitioning problem we are interested in this paper. Details of this relationship are explicitly spelled out in Chattopadhyay and Baruah (2011).

  2. Indeed, there seems to be no reason why a system designer would ever consider using a non-RA partitioning algorithm.

  3. At the extreme, a partitioning algorithm with speedup factor one is optimal.

  4. To see that such a swap is permissible, we note that τ i is the task with largest utilization with index≥i. Hence the other task on P j in OPT, if present, will be of utilization ≤u i , and can therefore be accommodated in the capacity that OPT had assigned to τ i on P k . And, we conclude that τ i can be accommodated on P j by observing that RAD had made exactly this assignment.

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Acknowledgements

This research is supported in part by NSF grants CNS 0834270, CNS 0834132, and CNS 1016954; ARO grant W911NF-09-1-0535; AFOSR grant FA9550-09-1-0549; and AFRL grant FA8750-11-1-0033.

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  1. The University of North Carolina at Chapel Hill, Chapel Hill, NC, USA

    Sanjoy Baruah

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  1. Sanjoy Baruah
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Correspondence to Sanjoy Baruah.

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Baruah, S. Partitioned EDF scheduling: a closer look. Real-Time Syst 49, 715–729 (2013). https://doi.org/10.1007/s11241-013-9186-0

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