Competitive analysis of fundamental scheduling algorithms on a fault-prone machine and the impact of resource augmentation

Anta, Antonio Fernández; Georgiou, Chryssis; Kowalski, Dariusz R.; Zavou, Elli

doi:10.1016/j.future.2016.05.042

Cited by 6 publications

(6 citation statements)

References 21 publications

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“…In another work, Anta et al (2018) consider popular scheduling algorithms and analyze their performance under speed augmentation with respect to three efficiency measures, which they call completed load, pending load, and latency. The first is precisely the objective that we aim to maximize, the second is the total size of the available but not yet completed packets (which we minimize in turn), and finally, the last one is the maximum time elapsed from a packet's arrival till the end of its successful transmission.…”

Section: Previous and Related Resultsmentioning

confidence: 99%

On packet scheduling with adversarial jamming and speedup

Böhm

Jeż

Sgall³

et al. 2019

Ann Oper Res

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In Packet Scheduling with Adversarial Jamming, packets of arbitrary sizes arrive over time to be transmitted over a channel in which instantaneous jamming errors occur at times chosen by the adversary and not known to the algorithm. The transmission taking place at the time of jamming is corrupt, and the algorithm learns this fact immediately. An online algorithm maximizes the total size of packets it successfully transmits and the goal is to develop an algorithm with the lowest possible asymptotic competitive ratio, where the additive constant may depend on packet sizes. Our main contribution is a universal algorithm that works for any speedup and packet sizes and, unlike previous algorithms for the problem, it does not need to know these parameters in advance. We show that this algorithm guarantees 1-competitiveness with speedup 4, making it the first known algorithm to maintain 1-competitiveness with a moderate speedup in the general setting of arbitrary packet sizes. We also prove a lower bound of φ + 1 ≈ 2.618 on the speedup of any 1-competitive deterministic algorithm, showing that our algorithm is close to the optimum. Additionally, we formulate a general framework for analyzing our algorithm locally and use it to show upper bounds on its competitive ratio for speedups in [1, 4) and for several special cases, recovering some previously known results, each of which had a dedicated proof. In particular, our algorithm is 3-competitive without speedup, matching both the (worst-case) performance of the algorithm by Jurdzinski et al.

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Section: Previous and Related Resultsmentioning

confidence: 99%

On packet scheduling with adversarial jamming and speedup

Böhm

Jeż

Sgall³

et al. 2019

Ann Oper Res

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“…The model was introduced by Anta et al [1], who resolved it for two packet sizes: If γ > 1 denotes the ratio of the two sizes, then the optimum competitive ratio for deterministic algorithms is (γ + γ )/ γ , which is always in the range [2,3). This result was extended by Jurdzinski et al [10], who proved that the optimum ratio for the case of multiple (though fixed) packet sizes is given by the same formula for the two packet sizes which maximize it.…”

Section: Previous and Related Resultsmentioning

confidence: 99%

“…In another work, Anta et al [3] consider popular scheduling algorithms and analyze their performance under speed augmentation with respect to three efficiency measures, which they call completed load, pending load, and latency. The first is precisely the objective that we aim to maximize, the second is the total size of the available but not yet completed packets (which we minimize in turn), and finally, the last one is the maximum time elapsed from a packet's arrival till the end of its successful transmission.…”

Section: Previous and Related Resultsmentioning

confidence: 99%

On Packet Scheduling with Adversarial Jamming and Speedup

Böhm

Jeż

Sgall

et al. 2018

Approximation and Online Algorithms

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In Packet Scheduling with Adversarial Jamming packets of arbitrary sizes arrive over time to be transmitted over a channel in which instantaneous jamming errors occur at times chosen by the adversary and not known to the algorithm. The transmission taking place at the time of jamming is corrupt, and the algorithm learns this fact immediately. An online algorithm maximizes the total size of packets it successfully transmits and the goal is to develop an algorithm with the lowest possible asymptotic competitive ratio, where the additive constant may depend on packet sizes.Our main contribution is a universal algorithm that works for any speedup and packet sizes and, unlike previous algorithms for the problem, it does not need to know these parameters in advance. We show that this algorithm guarantees 1-competitiveness with speedup 4, making it the first known algorithm to maintain 1-competitiveness with a moderate speedup in the general setting of arbitrary packet sizes. We also prove a lower bound of φ + 1 ≈ 2.618 on the speedup of any 1-competitive deterministic algorithm, showing that our algorithm is close to the optimum.Additionally, we formulate a general framework for analyzing our algorithm locally and use it to show upper bounds on its competitive ratio for speedups in [1,4) and for several special cases, recovering some previously known results, each of which had a dedicated proof. In particular, our algorithm is 3-competitive without speedup, matching both the (worst-case) performance of the algorithm by Jurdzinski et al. [10] and the lower bound by Anta et al. [1].deviates from previous work, which focused on the case with no speedup or on the speedup sufficient for ratio 1, ignoring intermediate cases. Competitive Analysis and its ExtensionsCompetitive analysis focuses on determining the competitive ratio of an online algorithm. The competitive ratio coincides with the approximation ratio, i.e., the supremum over all valid instances I of OPT(I)/ALG(I), which is the ratio of the optimum profit to the profit of an algorithm ALG on instance I. 1 This name, as opposed to approximation ratio, is used for historical reasons, and stresses that the nature of the hardness at hand is not due to computational complexity, but rather the online mode of computation, i.e., processing an unpredictable sequence of requests, completing each without knowing the future. Note that the optimum solution is to the whole instance, so it can be thought of as being determined by an algorithm that knows the whole instance in advance and has unlimited computational power; for this reason, the optimum solution is sometimes called "offline optimum". Competitive analysis, not yet called this way, was first applied by Sleator and Tarjan to analyze list update and paging problems [19]. Since then, it was employed to the study of many online optimization problems, as evidenced by (now somewhat dated) textbook by Borodin and El-Yaniv [6]. A nice overview of competitive analysis and its many extensions in the scheduling context, including...

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“…This opens up the future possibility of the use of artificial intelligence both for pure scheduling design and for new resilience strategies. Approaches using simulation [42] and forecasting methodologies can also be considered here [43].…”

Section: Discussionmentioning

confidence: 99%

Job migration in HPC clusters by means of checkpoint/restart

et al. 2019

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Until now, jobs running on HPC clusters were tied to the node where their execution started. We have removed that limitation by integrating a user level Checkpoint/Restart library into a Resource Manager, fully transparent to both the user and running application. This opens the door to a whole new set of tools and scheduling possibilities based on the fact that jobs can be migrated, checkpointed and restarted on a different place or in a different moment, while providing fault-tolerance for every job running on the cluster. This is of utmost importance in the future generation of exascale HPC clusters, where an increasing degree and complexities of efficient scheduling make it challenging to obtain the required degree of parallelism demanded by the applications.

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Competitive analysis of fundamental scheduling algorithms on a fault-prone machine and the impact of resource augmentation

Cited by 6 publications

References 21 publications

On packet scheduling with adversarial jamming and speedup

On packet scheduling with adversarial jamming and speedup

On Packet Scheduling with Adversarial Jamming and Speedup

Job migration in HPC clusters by means of checkpoint/restart

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