Online Job Dispatching and Scheduling to Minimize Job Completion Time and to Meet Deadlines

In this paper, we study the problem of job dispatching and scheduling, where each job consists of a set of tasks. Each task is processed by a set of machines simultaneously. We consider two important performance metrics, the average job completion time (JCT), and the number of deadline-aware jobs that meet their deadlines. The goal is to minimize the former and maximize the latter. We first propose OneJ to minimize the job completion time (JCT) when there is exactly one single job in the system. Then, we propose an online algorithm called MultiJ, taking OneJ as a subroutine, to minimize the average JCT, and prove it has a good competitive ratio. We then derive another online algorithm QuickJ to maximize the number of jobs that can meet their deadlines. We show that QuickJ is competitive via a worst case analysis. We also conjecture that the competitive ratio of QuickJ is likely to be the best one that any deterministic algorithm can achieve. We also shed light on several important merits of MultiJ and QuickJ, such as no severe coordination overhead, scalability, work conservation, and no job starvation.

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Online peak-aware energy scheduling with untrusted advice

ACM SIGEnergy Energy Informatics Review ◽

10.1145/3508467.3508473 ◽

2021 ◽

Vol 1 (1) ◽

pp. 59-77

Author(s):

Russell Lee ◽

Jessica Maghakian ◽

Mohammad Hajiesmaili ◽

Jian Li ◽

Ramesh Sitaraman ◽

...

Keyword(s):

Competitive Ratio ◽

Energy Demand ◽

Large Scale ◽

Performance Metrics ◽

Randomized Algorithm ◽

Deterministic Algorithm ◽

Pareto Optimal ◽

Energy Prices ◽

Worst Case ◽

Cost Of Energy

This paper studies the online energy scheduling problem in a hybrid model where the cost of energy is proportional to both the volume and peak usage, and where energy can be either locally generated or drawn from the grid. Inspired by recent advances in online algorithms with Machine Learned (ML) advice, we develop parameterized deterministic and randomized algorithms for this problem such that the level of reliance on the advice can be adjusted by a trust parameter. We then analyze the performance of the proposed algorithms using two performance metrics: robustness that measures the competitive ratio as a function of the trust parameter when the advice is inaccurate, and consistency for competitive ratio when the advice is accurate. Since the competitive ratio is analyzed in two different regimes, we further investigate the Pareto optimality of the proposed algorithms. Our results show that the proposed deterministic algorithm is Pareto-optimal, in the sense that no other online deterministic algorithms can dominate the robustness and consistency of our algorithm. Furthermore, we show that the proposed randomized algorithm dominates the Pareto-optimal deterministic algorithm. Our large-scale empirical evaluations using real traces of energy demand, energy prices, and renewable energy generations highlight that the proposed algorithms outperform worst-case optimized algorithms and fully data-driven algorithms.

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Worst Case Analysis of a New Lower Bound for Flow Shop Weighted Completion Time Problem

Combinatorial Optimization and Applications - Lecture Notes in Computer Science ◽

10.1007/978-3-540-73556-4_22 ◽

2007 ◽

pp. 191-199 ◽

Cited By ~ 6

Author(s):

Danyu Bai ◽

Lixin Tang

Keyword(s):

Lower Bound ◽

Completion Time ◽

Flow Shop ◽

Case Analysis ◽

Worst Case Analysis ◽

Worst Case ◽

Time Problem ◽

Weighted Completion Time

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Worst case analysis for deterministic online algorithm in capacitated lot-sizing problem

10.1063/1.3663492 ◽

2011 ◽

Author(s):

Ekaterina Kaganova ◽

Ilias Kotsireas ◽

Roderick Melnik ◽

Brian West

Keyword(s):

Online Algorithm ◽

Lot Sizing ◽

Case Analysis ◽

Worst Case Analysis ◽

Worst Case ◽

Lot Sizing Problem ◽

Capacitated Lot Sizing

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Scheduling in the Random-Order Model

Algorithmica ◽

10.1007/s00453-021-00841-8 ◽

2021 ◽

Author(s):

Susanne Albers ◽

Maximilian Janke

Keyword(s):

Competitive Ratio ◽

High Probability ◽

Online Algorithm ◽

Fundamental Problem ◽

Random Order ◽

Random Permutation ◽

Worst Case Analysis ◽

Makespan Minimization ◽

Order Model ◽

Worst Case

AbstractMakespan minimization on identical machines is a fundamental problem in online scheduling. The goal is to assign a sequence of jobs to m identical parallel machines so as to minimize the maximum completion time of any job. Already in the 1960s, Graham showed that Greedy is $$(2-1/m)$$ ( 2 - 1 / m ) -competitive. The best deterministic online algorithm currently known achieves a competitive ratio of 1.9201. No deterministic online strategy can obtain a competitiveness smaller than 1.88. In this paper, we study online makespan minimization in the popular random-order model, where the jobs of a given input arrive as a random permutation. It is known that Greedy does not attain a competitive factor asymptotically smaller than 2 in this setting. We present the first improved performance guarantees. Specifically, we develop a deterministic online algorithm that achieves a competitive ratio of 1.8478. The result relies on a new analysis approach. We identify a set of properties that a random permutation of the input jobs satisfies with high probability. Then we conduct a worst-case analysis of our algorithm, for the respective class of permutations. The analysis implies that the stated competitiveness holds not only in expectation but with high probability. Moreover, it provides mathematical evidence that job sequences leading to higher performance ratios are extremely rare, pathological inputs. We complement the results by lower bounds, for the random-order model. We show that no deterministic online algorithm can achieve a competitive ratio smaller than 4/3. Moreover, no deterministic online algorithm can attain a competitiveness smaller than 3/2 with high probability.

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