## Mixed Pfair/ERfair Scheduling of Asynchronous Periodic Tasks (2001)

Citations: | 109 - 46 self |

### BibTeX

@MISC{Anderson01mixedpfair/erfair,

author = {James H. Anderson and Anand Srinivasan},

title = {Mixed Pfair/ERfair Scheduling of Asynchronous Periodic Tasks},

year = {2001}

}

### Years of Citing Articles

### OpenURL

### Abstract

Pfair Scheduling was proposed by... In this paper, we introduce a work-conserving variant of Pfair scheduling called "early-release" fair (ERfair) scheduling. We also present a new scheduling algorithm called PD² and show that it is optimal for scheduling any mix of early-release and non-early-release asynchronous, periodic tasks. In contrast, almost all prior work on Pfair scheduling has been limited to synchronous systems. PD²is an optimization of an earlier deadline-based algorithm of Baruah, Gehrke, and Plaxton called PD; PD² uses a simpler tie-breaking scheme than PD to disambiguate equal deadlines. We present a series of counterexamples that suggest that, in general, the PD² tie-breaking mechanism cannot be simplified. In contrast to this, we show that no tie-breaking information is needed on two-processor systems.

### Citations

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(Show Context)
Citation Context .... A flow is called integral if and only if flow across each edge is integral. We use the following theorem about integral flows in graphs with integral edge capacities. Theorem 25 (Ford and Fulkerson =-=[8]-=-) A graph in which all edge capacities are integral has a integral maximal flow. Feasibility proof. The existence of a schedule for an asynchronous task system τ that satisfies Expression (B.1) follow... |

328 | Fundamental Design Problems of Distributed Systems for the Hard Real-Time Environment - Mok - 1983 |

279 | Proportionate progress: a notion of fairness in resource allocation
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Citation Context ...mes.) In addition, nonwork-conserving algorithms often entail higher runtime overheads because of extra bookkeeping required to keep track of when a job is and is not eligible. In two separate papers =-=[6,7]-=-, Baruah et al. presented two optimal Pfair scheduling algorithms, called PF and PD. In both algorithms, subtasks are prioritized by their deadlines. The two algorithms differ in the way in which ties... |

113 | Fast scheduling of periodic tasks on multiple resources
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- 1995
(Show Context)
Citation Context ...sk released by T is T1 and ∆(T ) reduces to r. 3 The PD 2 Algorithm For synchronous, periodic task systems, the most efficient Pfair scheduling algorithm previously proposed is an algorithm called PD =-=[7]-=-. PD prioritizes 9subtasks by pseudo-deadline (hence its name). It is related to an earlier algorithm called PF [6] in which ties among subtasks with the same deadline are broken by comparing vectors... |

96 | Early-release fair scheduling
- Anderson, Srinivasan
- 2000
(Show Context)
Citation Context ...NSF grants CCR 9732916, CCR 9972211, CCR 9988327, and ITR 0082866. Some of the results in this paper were presented in preliminary form at the 12th and 13th Euromicro Conferences on Real-time Systems =-=[1,3]-=-. Preprint submitted to Elsevier Science 31 July 2003in the periodic task model, each task T executes at a rate given by T.e/T.p, where T.e is the execution cost of each job (i.e., invocation) of T ,... |

84 | Optimal rate-based scheduling on multiprocessors
- Srinivasan, Anderson
- 2002
(Show Context)
Citation Context ... bounds on the amount by which a deadline is missed if no tie-breaking information is used [12]. We have also shown that PD 2 can be used to optimally schedule intra-sporadic tasks on multiprocessors =-=[11]-=-. The swapping proof technique used in this paper reveals many fundamental properties of Pfair- and ERfairscheduled systems that were essential in showing the optimality of PD 2 for intra-sporadic tas... |

72 | Pfair scheduling: Beyond periodic task systems
- Anderson, Srinivasan
- 2000
(Show Context)
Citation Context ...ous task systems is given [10]. Such static-priority algorithms are not optimal. In other recent work, we proposed a task model called the intra-sporadic model that generalizes the asynchronous model =-=[2]-=-. However, the algorithms given by us for that model are applicable only to two-processor systems. (In the time since the research in this paper was conducted, we have extended work on Pfair schedulin... |

55 | Pfair scheduling of fixed and migrating periodic tasks on multiple resources
- Moir, Ramamurthy
- 1999
(Show Context)
Citation Context ...no tie-breaking information is required. • Fifth, all of our results apply to asynchronous task systems. In contrast, almost all prior work on Pfair scheduling has focused only on synchronous systems =-=[4,6,7,9]-=-. One exception is a recent paper by Moir and Ramamurthy in which a static-priority Pfair scheduling algorithm for asynchronous task systems is given [10]. Such static-priority algorithms are not opti... |

46 | Efficient scheduling of soft real-time applications on multiprocessors
- Srinivasan, Anderson
- 2005
(Show Context)
Citation Context ...per was conducted, we have extended work on Pfair scheduling in several ways. In particular, we have obtained bounds on the amount by which a deadline is missed if no tie-breaking information is used =-=[12]-=-. We have also shown that PD 2 can be used to optimally schedule intra-sporadic tasks on multiprocessors [11]. The swapping proof technique used in this paper reveals many fundamental properties of Pf... |

27 | Fairness in periodic real-time scheduling
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- 1995
(Show Context)
Citation Context ...no tie-breaking information is required. • Fifth, all of our results apply to asynchronous task systems. In contrast, almost all prior work on Pfair scheduling has focused only on synchronous systems =-=[4,6,7,9]-=-. One exception is a recent paper by Moir and Ramamurthy in which a static-priority Pfair scheduling algorithm for asynchronous task systems is given [10]. Such static-priority algorithms are not opti... |

15 | A new look at Pfair priorities - Anderson, Srinivasan - 2000 |

11 | Static-priority periodic scheduling on multiprocessors
- Ramamurthy, Moir
- 2000
(Show Context)
Citation Context ... has focused only on synchronous systems [4,6,7,9]. One exception is a recent paper by Moir and Ramamurthy in which a static-priority Pfair scheduling algorithm for asynchronous task systems is given =-=[10]-=-. Such static-priority algorithms are not optimal. In other recent work, we proposed a task model called the intra-sporadic model that generalizes the asynchronous model [2]. However, the algorithms g... |

2 |
private communication
- Baruah
(Show Context)
Citation Context ...roved correct by means of a simulation argument that shows that PD “closely” tracks the behavior of PF. This proof is quite “brittle” and is difficult to extend beyond the synchronous, periodic model =-=[5]-=-. In contrast, we prove that PD 2 is correct by means of an inductive “swapping” argument in which an arbitrary schedule is converted into one in accordance with the PD 2 priority definition by system... |