Scheduling Parallelizable Jobs Online to Maximize Throughput

Agrawal, Kunal; Li, Jing; Lu, Kefu; Moseley, Benjamin

doi:10.1007/978-3-319-77404-6_55

Cited by 9 publications

(7 citation statements)

References 26 publications

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“…The third principle is crucial to improve on existing results that only use the first two [22]. 1. A running job can be preempted only by significantly smaller jobs (parameter β).…”

Section: The Region Algorithmmentioning

confidence: 99%

“…We analyze the performance of algorithms using standard competitive analysis in which the performance of an algorithm is compared to that of an optimal offline algorithm with full knowledge of the future. More precisely, an online algorithm Alg is called c-competitive if it achieves for any input instance I a total value of Alg(I ) ≥ 1 c Opt(I ), where Opt is the value of an optimal offline algorithm.…”

Section: Introductionmentioning

confidence: 99%

“…Other results for scheduling with deadlines use speed scaling, which can be viewed as another way to add slack to the schedule, e.g. [1,3,16,23]. In this paper we quantify the impact that different job commitment requirements have on the performance of online algorithms.…”

Section: Introductionmentioning

confidence: 99%

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A general framework for handling commitment in online throughput maximization

et al. 2020

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We study a fundamental online job admission problem where jobs with deadlines arrive online over time at their release dates, and the task is to determine a preemptive single-server schedule which maximizes the number of jobs that complete on time. To circumvent known impossibility results, we make a standard slackness assumption by which the feasible time window for scheduling a job is at least 1+ε times its processing time, for some ε > 0. We quantify the impact that different provider commitment requirements have on the performance of online algorithms. Our main contribution is one universal algorithmic framework for online job admission both with and without commitments. Without commitment, our algorithm with a competitive ratio of O(1/ε) is the best possible (deterministic) for this problem. For commitment models, we give the first non-trivial performance bounds. If the commitment decisions must be made before a job's slack becomes less than a δ-fraction of its size, we prove a competitive ratio of O(ε/((ε − δ)δ 2)), for 0 < δ < ε. When a provider must commit upon starting a job, our bound is O(1/ε 2). Finally, we observe that for scheduling with commitment the restriction to the "unweighted" throughput model is essential; if jobs have individual weights, we rule out competitive deterministic algorithms.

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“…The third principle is crucial to improve on existing results that only use the first two [22]. 1. A running job can be preempted only by significantly smaller jobs (parameter β).…”

Section: The Region Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A general framework for handling commitment in online throughput maximization

et al. 2020

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“…Wave i has 2 i jobs. Each job from the i-th wave has release date i k · γ, deadline 1, and processing time 1 2 i · 1−γ 1+ε . Note that choosing p j ≤ 1−γ 1+ε for all jobs j makes sure that indeed ℓ j ≥ ε · p j , and observe that the total volume of jobs in wave i adds up to no more than 1 − γ.…”

Section: Theorem 7 No Randomized Online Algorithm Has a Bounded Compmentioning

confidence: 99%

“…Other results for scheduling with deadlines use speed scaling, which can be viewed as another way to add slack to the schedule, e.g. [1,3,15,22]. In this paper we quantify the impact that different job commitment requirements have on the performance of online algorithms.…”

Section: Introductionmentioning

confidence: 99%

A General Framework for Handling Commitment in Online Throughput Maximization

Chen¹,

Éberlé²,

Megow³

et al. 2019

Integer Programming and Combinatorial Optimization

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We study a fundamental online job admission problem where jobs with deadlines arrive online over time at their release dates, and the task is to determine a preemptive single-server schedule which maximizes the number of jobs that complete on time. To circumvent known impossibility results, we make a standard slackness assumption by which the feasible time window for scheduling a job is at least 1 + ε times its processing time, for some ε > 0. We quantify the impact that different provider commitment requirements have on the performance of online algorithms. Our main contribution is one universal algorithmic framework for online job admission both with and without commitments. Without commitment, our algorithm with a competitive ratio of O(1/ε) is the best possible (deterministic) for this problem. For commitment models, we give the first non-trivial performance bounds. If the commitment decisions must be made before a job's slack becomes less than a δ -fraction of its size, we prove a competitive ratio of O(ε/((ε − δ )δ 2 )), for 0 < δ < ε. When a provider must commit upon starting a job, our bound is O(1/ε 2 ). Finally, we observe that for scheduling with commitment the restriction to the "unweighted" throughput model is essential; if jobs have individual weights, we rule out competitive deterministic algorithms.

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Open problems in queueing theory inspired by datacenter computing

Harchol-Balter

2021

Queueing Syst

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Scheduling Parallelizable Jobs Online to Maximize Throughput

Cited by 9 publications

References 26 publications

A general framework for handling commitment in online throughput maximization

A general framework for handling commitment in online throughput maximization

A General Framework for Handling Commitment in Online Throughput Maximization

Open problems in queueing theory inspired by datacenter computing

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