## Skip-Over: Algorithms and Complexity for Overloaded Systems that Allow Skips (1996)

Venue: | In Proceedings of the 16th IEEE Real-Time Systems Symposium |

Citations: | 103 - 0 self |

### BibTeX

@INPROCEEDINGS{Koren96skip-over:algorithms,

author = {Gilad Koren and Dennis Shasha},

title = {Skip-Over: Algorithms and Complexity for Overloaded Systems that Allow Skips},

booktitle = {In Proceedings of the 16th IEEE Real-Time Systems Symposium},

year = {1996},

pages = {110--117},

publisher = {IEEE}

}

### Years of Citing Articles

### OpenURL

### Abstract

In applications ranging from video reception to telecommunications and packet communication to aircraft control, tasks enter periodically and have fixed response time constraints, but missing a deadline is acceptable, provided most deadlines are met. We call such tasks "occasionally skippable". We look at the problem of uniprocessor scheduling of occasionally skippable periodic tasks in an environment having periodic tasks. We show that making optimal use of skips is NP-hard. We then look at two algorithms called Skip-Over Algorithms (one a variant of earliest deadline first and one of rate monotonic scheduling) that exploit skips. We give schedulability bounds for both. 1 Introduction 1.1 Basic Assumptions and Definitions We consider a uni-processor system in which preemption is possible at any time and costs nothing. All tasks are periodic but they may enter the system at any time. A task is characterized by its computation requirements and period; the deadline of a task equals it...

### Citations

11366 |
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- Garey, Johnson
- 1979
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- Liu, Layland
- 1973
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- Sha, Lehoczky, et al.
- 1989
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- Lehoczky
- 1990
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- DERTOUZOS
- 1974
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- 1990
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- 1989
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A note on the preemptive scheduling of periodic, real-time tasks
- Leung, Merill
- 1980
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