## On Non-Preemptive Scheduling of Recurring Tasks Using Inserted Idle Times (1995)

Venue: | Information and Computation |

Citations: | 19 - 0 self |

### BibTeX

@ARTICLE{Howell95onnon-preemptive,

author = {Rodney R. Howell and Muralidhar K. Venkatrao},

title = {On Non-Preemptive Scheduling of Recurring Tasks Using Inserted Idle Times},

journal = {Information and Computation},

year = {1995},

volume = {117},

pages = {117--50}

}

### OpenURL

### Abstract

We consider the problem of non-preemptively scheduling periodic and sporadic task systems on one processor using inserted idle times. For periodic task systems, we prove that the decision problem of determining whether a periodic task system is schedulable for all start times with respect to the class of algorithms using inserted idle times is NP-Hard in the strong sense, even when the deadlines are equal to the periods. We then show that if there exists a polynomial time scheduling algorithm which correctly schedules a periodic task system T whenever T is feasible for all start times, then P=NP. We also prove that with respect to the same class of algorithms, the problem of determining whether there exist start times for which a periodic task system is feasible is also NP-Hard in the strong sense even when the deadlines are equal to the periods. The second part of the paper concentrates on sporadic task systems and inserted idle times. It seems reasonable to suppose that to insert idl...

### Citations

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Citation Context ... all tasks in the system. Since pn represents the value of one of the inputs, the algorithm is not polynmial in the size of the input; so, technically, it is a pseudo-polynomial time algorithm (see [ =-=Garey and Johnson, 1979-=- ] ). The results of [ Jeffay, Stanat, and Martel, 1991 ] rely heavily on two restrictions. The first, as we have already noted, is that all deadlines are equal to their periods. The second restrictio... |

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Citation Context ...ling theory often models real world situations by considering a set of recurring tasks, called a Recurring Task System. Recurring task systems may be periodic or sporadic. In a periodic task system [ =-=Liu and Layland, 1973-=-; Leung and Merrill, 1980; Lawler and Martel, 1981; Leung and Whitehead, 1982; Mok, 1983; Baruah, Howell, and Rosier, 1990 ] , each task makes a request for processor time at regular periodic interval... |

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Citation Context ...curring tasks, called a Recurring Task System. Recurring task systems may be periodic or sporadic. In a periodic task system [ Liu and Layland, 1973; Leung and Merrill, 1980; Lawler and Martel, 1981; =-=Leung and Whitehead, 1982-=-; Mok, 1983; Baruah, Howell, and Rosier, 1990 ] , each task makes a request for processor time at regular periodic intervals. A sporadic task system [ Mok, 1983; Lehoczky, Sha, and Stronider, 1987; Ho... |

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Citation Context ...urring Task System. Recurring task systems may be periodic or sporadic. In a periodic task system [ Liu and Layland, 1973; Leung and Merrill, 1980; Lawler and Martel, 1981; Leung and Whitehead, 1982; =-=Mok, 1983-=-; Baruah, Howell, and Rosier, 1990 ] , each task makes a request for processor time at regular periodic intervals. A sporadic task system [ Mok, 1983; Lehoczky, Sha, and Stronider, 1987; Hong and Leun... |

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Citation Context ...artel, 1981; Leung and Whitehead, 1982; Mok, 1983; Baruah, Howell, and Rosier, 1990 ] , each task makes a request for processor time at regular periodic intervals. A sporadic task system [ Mok, 1983; =-=Lehoczky, Sha, and Stronider, 1987-=-; Hong and Leung, 1988; Sprunt, Lehoczky, and Sha, 1988; Jeffay, Stanat, and Martel, 1991; Sprunt, Sha, and Lehoczky, 1989; Baruah, Mok, and Rosier, 1990 ] is similar, except that the request times ca... |

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Citation Context ...is a well known result that the deadline algorithm constructs a valid preemptive uniprocessor schedule for a task system whenever it is feasible (see, e.g., [ Liu and Layland, 1973; Labetoulle, 1974; =-=Dertouzos, 1974-=- ] ). Such an algorithm is referred to as an optimal algorithm. Thus, the deadline algorithm forms a suitable online algorithm whenever one exists. The main problem, therefore, in preemptive schedulin... |

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Citation Context ... System. Recurring task systems may be periodic or sporadic. In a periodic task system [ Liu and Layland, 1973; Leung and Merrill, 1980; Lawler and Martel, 1981; Leung and Whitehead, 1982; Mok, 1983; =-=Baruah, Howell, and Rosier, 1990-=- ] , each task makes a request for processor time at regular periodic intervals. A sporadic task system [ Mok, 1983; Lehoczky, Sha, and Stronider, 1987; Hong and Leung, 1988; Sprunt, Lehoczky, and Sha... |

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Citation Context ...h task makes a request for processor time at regular periodic intervals. A sporadic task system [ Mok, 1983; Lehoczky, Sha, and Stronider, 1987; Hong and Leung, 1988; Sprunt, Lehoczky, and Sha, 1988; =-=Jeffay, Stanat, and Martel, 1991-=-; Sprunt, Sha, and Lehoczky, 1989; Baruah, Mok, and Rosier, 1990 ] is similar, except that the request times cannot be predicted; we do, however, require a minimum separation between successive reques... |

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Citation Context ...vals. A sporadic task system [ Mok, 1983; Lehoczky, Sha, and Stronider, 1987; Hong and Leung, 1988; Sprunt, Lehoczky, and Sha, 1988; Jeffay, Stanat, and Martel, 1991; Sprunt, Sha, and Lehoczky, 1989; =-=Baruah, Mok, and Rosier, 1990-=- ] is similar, except that the request times cannot be predicted; we do, however, require a minimum separation between successive requests of the same task. In a hard real time environment, none of th... |

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Citation Context ...s real world situations by considering a set of recurring tasks, called a Recurring Task System. Recurring task systems may be periodic or sporadic. In a periodic task system [ Liu and Layland, 1973; =-=Leung and Merrill, 1980-=-; Lawler and Martel, 1981; Leung and Whitehead, 1982; Mok, 1983; Baruah, Howell, and Rosier, 1990 ] , each task makes a request for processor time at regular periodic intervals. A sporadic task system... |

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Citation Context ...s are shared by various tasks (cf. [ Jeffay, 1989 ] ). The reason problems in non-preemptive scheduling are more complicated than those in preemptive scheduling is largely due to a result proved in [ =-=Garey and Johnson, 1977-=- ] . It is shown there that the non-preemptive feasibility problem for non-recurring task systems is NP-Complete in the strong sense. On the other hand, Jeffay, Stanat and Martel [ 1991 ] have recentl... |

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Citation Context ... Howell, and Rosier, 1990 ] , each task makes a request for processor time at regular periodic intervals. A sporadic task system [ Mok, 1983; Lehoczky, Sha, and Stronider, 1987; Hong and Leung, 1988; =-=Sprunt, Lehoczky, and Sha, 1988-=-; Jeffay, Stanat, and Martel, 1991; Sprunt, Sha, and Lehoczky, 1989; Baruah, Mok, and Rosier, 1990 ] is similar, except that the request times cannot be predicted; we do, however, require a minimum se... |

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Citation Context ...y considering a set of recurring tasks, called a Recurring Task System. Recurring task systems may be periodic or sporadic. In a periodic task system [ Liu and Layland, 1973; Leung and Merrill, 1980; =-=Lawler and Martel, 1981-=-; Leung and Whitehead, 1982; Mok, 1983; Baruah, Howell, and Rosier, 1990 ] , each task makes a request for processor time at regular periodic intervals. A sporadic task system [ Mok, 1983; Lehoczky, S... |

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Citation Context ...82; Mok, 1983; Baruah, Howell, and Rosier, 1990 ] , each task makes a request for processor time at regular periodic intervals. A sporadic task system [ Mok, 1983; Lehoczky, Sha, and Stronider, 1987; =-=Hong and Leung, 1988-=-; Sprunt, Lehoczky, and Sha, 1988; Jeffay, Stanat, and Martel, 1991; Sprunt, Sha, and Lehoczky, 1989; Baruah, Mok, and Rosier, 1990 ] is similar, except that the request times cannot be predicted; we ... |

44 | Feasibility problems for recurring tasks on one processor - Baruah, Howell, et al. - 1993 |

15 | Analysis of a Synchronization and Scheduling Discipline for Real-Time Tasks with Preemption Constraints - Jeffay - 1989 |

1 |
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Citation Context ...ve scheduling. It is a well known result that the deadline algorithm constructs a valid preemptive uniprocessor schedule for a task system whenever it is feasible (see, e.g., [ Liu and Layland, 1973; =-=Labetoulle, 1974-=-; Dertouzos, 1974 ] ). Such an algorithm is referred to as an optimal algorithm. Thus, the deadline algorithm forms a suitable online algorithm whenever one exists. The main problem, therefore, in pre... |