2020
DOI: 10.1007/s10107-020-01469-2
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A general framework for handling commitment in online throughput maximization

Abstract: 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 requirement… Show more

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Cited by 8 publications
(12 citation statements)
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“…Constraint (5) guarantees each job is dispatched to one server. Constraint (6) guarantees each job is processed for at least p i, j .…”
Section: System Modelmentioning
confidence: 99%
See 1 more Smart Citation
“…Constraint (5) guarantees each job is dispatched to one server. Constraint (6) guarantees each job is processed for at least p i, j .…”
Section: System Modelmentioning
confidence: 99%
“…Gilad et al [19] and Bala et al [18] employed the power of randomization and derived the optimal randomized competitive ratio as Θ(min{log K, logψ }) where ψ is the ratio of the maximum to the minimum job size, which is still related to the input instance. Due to the hardness of approximation, some works [1,6,17,25] resorted the resource augmentation analysis, which means the servers running their algorithms can be (1 + ϵ ) faster than those running the optimal solution. In this line of work, Krik et al [25] constructed a (1 + ϵ )-speed O (1) competitive algorithm for any fixed constant ϵ > 0 in the identical severs setting.…”
Section: Related Workmentioning
confidence: 99%
“…Recently, unweighted throughput maximization has been solved on a single machine with a competitive ratio of O 1 ε [7], on identical machines with a O(1)-competitive algorithm [18], and on unrelated machines with a competitive ratio of O 1 ε [9]. For weighted throughput maximization it is known that O(1)-competitive algorithms are not possible, independent of the machine environment, even when allowing randomization [15].…”
Section: Introductionmentioning
confidence: 99%
“…For weighted throughput maximization it is known that O(1)-competitive algorithms are not possible, independent of the machine environment, even when allowing randomization [15]. Even on a single machine, there remained a gap between the performance bound O 1 ε 2 of the algorithm by [17] and the lower bound Ω 1 ε carried over from the unweighted setting [7]. In this work, we close this gap and give an (up to constant factors) best possible online algorithm for weighted throughput maximization on unrelated machines with competitive ratio O 1 ε .…”
Section: Introductionmentioning
confidence: 99%
“…Studies of scheduling and vehicle routing problems with time windows were initiated by Schrage [30] and Bodin et al [5]. Recent publications include Sarasola and Doerner [29], Gnegel and Fügenschuh [15], Mohammadi et al [25], Chen et al [8] and Lera‐Romero et al [23], among others.…”
Section: Introductionmentioning
confidence: 99%