A theoretical and empirical study of job scheduling in cloud computing environments: the weighted completion time minimization problem with capacitated parallel machines

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Abstract

We consider the weighted completion time minimization problem for capacitated parallel machines, which is a fundamental problem in modern cloud computing environments. In our setting, the processed jobs may be of varying duration, require different resources, and be of unequal importance (weight). Each server (machine) can process multiple concurrent jobs up to its capacity. We study heuristic approaches with provable approximation guarantees and offer an algorithm that prioritizes the jobs with the smallest volume-by-weight ratio. We bound the algorithm’s approximation ratio using a decreasing function of the ratio between the highest resource demand of any job and the server’s capacity. Thereafter, we create a hybrid, constant approximation algorithm for two or more machines. We also develop a constant approximation algorithm for the case of a single machine. Via a numerical study and a mixed-integer linear program of the problem, we demonstrate the performance of the suggested algorithm with respect to the optimal solutions and alternative scheduling methods. We show that the suggested scheduling method can be applied to both offline and online problems that may arise in real-world settings. This research is the first, to the best of our knowledge, to propose a polynomial-time algorithm with a constant approximation ratio for minimizing the weighted sum of job completion times for capacitated parallel machines.

Original languageEnglish
JournalAnnals of Operations Research
DOIs
StateAccepted/In press - 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Keywords

  • Approximation algorithms
  • Capacitated machines
  • Cloud computing
  • Parallel machines
  • Scheduling

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