## Optimal Rate-based Scheduling on Multiprocessors (2001)

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Venue: | In Proceedings of the 34th ACM Symposium on Theory of Computing |

Citations: | 84 - 41 self |

### BibTeX

@INPROCEEDINGS{Srinivasan01optimalrate-based,

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

title = {Optimal Rate-based Scheduling on Multiprocessors},

booktitle = {In Proceedings of the 34th ACM Symposium on Theory of Computing},

year = {2001},

pages = {189--198},

publisher = {ACM}

}

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### Abstract

We consider the intra-sporadic task model, which is a generalization of the sporadic task model motivated by recent work on Pfair scheduling. The intra-sporadic model is essentially a quantum-based, multiprocessor variant of the uniprocessor rate-based execution model of Jeffay and Goddard. In the intra-sporadic model, a task is specified by an average rate of execution, and there is no restriction on instantaneous execution rates. Such exibility is useful in applications in which some processing steps may be highly jittered. In previous work, we showed that an intra-sporadic task system is feasible on M processors i its total utilization is at most M . We also gave an optimal algorithm for scheduling intra-sporadic tasks on two processors. In this paper, we show that the PD² Pfair algorithm can be used to schedule any intra-sporadic task system that is feasible on M processors. Because the sporadic model is a special case of the intrasporadic model, our work shows that PD² is also optimal for scheduling sporadic tasks on a multiprocessor. This paper is the first to show that sporadic or intra-sporadic tasks can be optimally scheduled on systems of more than two processors.

### Citations

3268 | Scheduling algorithms for multiprogramming in a hard-real-time environment
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(Show Context)
Citation Context ... generalizes the widely-studied sporadic task model. Key words: Fairness, multiprocessors, optimality, Pfair, real time, scheduling 1 Introduction In the real-time scheduling literature, the periodic =-=[15]-=- and sporadic [16] task models have received the most attention. In the periodic model, each task is invoked repeatedly, with consecutive invocations, or jobs, being spaced apart by a fixed amount; in... |

328 |
Fundamental Design Problems of Distributed Systems for the Hard Real-Time Environment
- Mok
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(Show Context)
Citation Context ...idely-studied sporadic task model. Key words: Fairness, multiprocessors, optimality, Pfair, real time, scheduling 1 Introduction In the real-time scheduling literature, the periodic [15] and sporadic =-=[16]-=- task models have received the most attention. In the periodic model, each task is invoked repeatedly, with consecutive invocations, or jobs, being spaced apart by a fixed amount; in the sporadic mode... |

279 | Proportionate progress: a notion of fairness in resource allocation
- Baruah, Cohen, et al.
- 1996
(Show Context)
Citation Context ...ways be less than one quantum. The lag bounds above have the effect of breaking each task T into an infinite sequence of unit-time subtasks. Wedenotetheith subtask of task T as Ti, where i ≥ 1. As in =-=[6]-=-, we associate a pseudo-release r(Ti) andpseudo-deadline d(Ti) with each subtask Ti, as follows. (For brevity, we often drop the prefix “pseudo-.”) r(Ti) = ⌊ ⌋ i − 1 wt(T ) ⌈ ⌉ d(Ti) = i wt(T ) (2) (3... |

267 | Integrating Multimedia Applications in Hard Real-Time Systems - Abeni, Buttazzo - 1998 |

207 | C.: A proportional share resource allocation algorithm for real-time, time-shared systems - Stoica, Abdel-Wahab, et al. - 1996 |

113 | Fast scheduling of periodic tasks on multiple resources - Baruah, Gehrke, et al. - 1995 |

109 | Mixed Pfair/ERfair scheduling of asynchronous periodic tasks
- Anderson, Srinivasan
(Show Context)
Citation Context ... open the problem of optimally scheduling IS tasks on systems of more than two processors. 2Contributions of this paper. In this paper, we close this problem by showing that the PD 2 Pfair algorithm =-=[3,5]-=- correctly schedules any feasible IS task system on M processors. Because the IS model is a generalization of the sporadic model, our work also shows that PD 2 is optimal for scheduling sporadic tasks... |

96 | Early-release fair scheduling
- Anderson, Srinivasan
- 2000
(Show Context)
Citation Context ...ltiprocessors. Since the presentation of this work as a conference paper [18], this approach has been used as a basis for proving a number of other results about fair-scheduled multiprocessor systems =-=[2,8,11,13,12,19,20]-=-. In addition to presenting a fundamentally new proof approach, this paper breaks new ground by being the first to show that sporadic or IS tasks can be optimally scheduled on systems of more than two... |

72 | Pfair scheduling: Beyond periodic task systems
- Anderson, Srinivasan
- 2000
(Show Context)
Citation Context ...air (ERfair) scheduling. Under ERfair scheduling, subtasks may be released “early,” i.e., such a subtask may become eligible for execution before its Pfair window. This is illustrated in Figure 2. In =-=[4,18]-=-, we proposed a further extension of the Pfair task model called the intra-sporadic (IS) model. The sporadic model generalizes the periodic model by allowing jobs to be released “late,” i.e., the sepa... |

71 | Surplus fair scheduling: A Proportional-Share CPU scheduling algorithm for symmetric multiprocessors
- Chandra, Adler, et al.
- 2000
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Citation Context ...y). This observation led researchers at the University of Massachusetts and Ensim Corp. to investigate the use of fair scheduling algorithms on multiprocessor servers for commercial web-hosting sites =-=[9,10]-=-. 33However, this prior investigation was entirely empirical in nature. In this paper, we have given the first ever general optimality proof for a multiprocessor rate-based scheduling algorithm that ... |

62 | Deadline fair scheduling: Bridging the theory and practice of proportionate-fair scheduling in multiprocessor servers
- Chandra, Adler, et al.
- 2001
(Show Context)
Citation Context ...y). This observation led researchers at the University of Massachusetts and Ensim Corp. to investigate the use of fair scheduling algorithms on multiprocessor servers for commercial web-hosting sites =-=[9,10]-=-. 33However, this prior investigation was entirely empirical in nature. In this paper, we have given the first ever general optimality proof for a multiprocessor rate-based scheduling algorithm that ... |

62 | A theory of rate-based execution
- Jeffay, Goddard
- 1999
(Show Context)
Citation Context ...trated in Figure 3. Early-release behavior is also allowed. As explained later, the IS notion of a rate is quite similar to that found in the recently-proposed uniprocessor rate-based execution model =-=[14]-=-. In [4], we presented an algorithm that optimally schedules IS tasks on two processors. However, we left open the problem of optimally scheduling IS tasks on systems of more than two processors. 2Co... |

46 | Efficient scheduling of soft real-time applications on multiprocessors
- Srinivasan, Anderson
- 2005
(Show Context)
Citation Context ...ltiprocessors. Since the presentation of this work as a conference paper [18], this approach has been used as a basis for proving a number of other results about fair-scheduled multiprocessor systems =-=[2,8,11,13,12,19,20]-=-. In addition to presenting a fundamentally new proof approach, this paper breaks new ground by being the first to show that sporadic or IS tasks can be optimally scheduled on systems of more than two... |

32 | Fair Scheduling of Dynamic Task Systems on Multiprocessors
- Srinivasan, Anderson
- 2005
(Show Context)
Citation Context ...ltiprocessors. Since the presentation of this work as a conference paper [18], this approach has been used as a basis for proving a number of other results about fair-scheduled multiprocessor systems =-=[2,8,11,13,12,19,20]-=-. In addition to presenting a fundamentally new proof approach, this paper breaks new ground by being the first to show that sporadic or IS tasks can be optimally scheduled on systems of more than two... |

16 | Multiprocessor scheduling in processor-based router platforms: Issues and ideas
- Srinivasan, Holman, et al.
- 2003
(Show Context)
Citation Context ...veral applications in networking. Examples include web servers that provide quality-of-service guarantees, packet scheduling in networks, and the scheduling of packet-processing activities in routers =-=[21]-=-. Due to network congestion and other factors, packets may arrive late or in bursts. The IS model treats these possibilities as first-class 7concepts and handles them more seamlessly. In particular, ... |

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

15 | Fine-grained task reweighting on multiprocessors
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- 2005
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14 | Improved conditions for bounded tardiness under EPDF fair multiprocessor scheduling
- Devi, Anderson
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10 | Parallel switching in connection-oriented networks
- Anderson, Baruah, et al.
- 1999
(Show Context)
Citation Context ..., optical multiplexing techniques are used to send multiple packets over the same link in parallel. In a similar vein, PD 2 canbeusedtosolvethe parallel switching problem in ATM networks mentioned in =-=[1]-=-. Also, as noted earlier, PD 2 might be useful in multiprocessor real-time applications that have processing steps that are triggered by messages sent over a network. The fairness properties of PD 2 a... |

4 | The Rate-Based Execution Model - Jeay, Goddard - 1999 |

3 | Fair integrated scheduling of soft real-time tardiness classes on multiprocessors (full paper). Available at http://www.cs.unc.edu/˜anderson/papers.html
- Devi, Anderson
- 2004
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3 | Schedulable utilization bounds for EPDF fair multiprocessor scheduling (full paper). Available at http://www.cs.unc.edu/˜anderson/papers.html
- Devi, Anderson
(Show Context)
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