TY - JOUR

T1 - A theoretical and empirical study of job scheduling in cloud computing environments

T2 - the weighted completion time minimization problem with capacitated parallel machines

AU - Cohen, Ilan Reuven

AU - Cohen, Izack

AU - Zaks, Iyar

N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

KW - Approximation algorithms

KW - Capacitated machines

KW - Cloud computing

KW - Parallel machines

KW - Scheduling

UR - http://www.scopus.com/inward/record.url?scp=85174532998&partnerID=8YFLogxK

U2 - 10.1007/s10479-023-05613-x

DO - 10.1007/s10479-023-05613-x

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AN - SCOPUS:85174532998

SN - 0254-5330

JO - Annals of Operations Research

JF - Annals of Operations Research

ER -