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Online Preemptive Hierarchical Scheduling on Two Uniform Machines with Rejection

Author

Listed:
  • Xiao Min

    (College of Mathematics, Physics and Information Engineering, Jiaxing University, Jiaxing 314001, P. R. China)

  • Jing Liu

    (College of Mathematics, Physics and Information Engineering, Jiaxing University, Jiaxing 314001, P. R. China)

  • Yanxia Dong

    (College of Mathematics, Shanghai University, Shanghai 200444, P. R. China)

  • Ming Jiang

    (College of Computer Science, Hangzhou Dianzi University, Hangzhou 310018, P. R. China)

Abstract

This paper studies the online hierarchical scheduling problem on two uniform machines with rejection. Two uniform machines M1, M2 run at the speeds of s ∈ (0, +∞), 1 separately; and they are provided with different capabilities. Each machine has a certain GOS level 1 or 2 and every job is also associated with a hierarchy 1 or 2. The job can only be assigned to the machine whose GOS level does not exceed the job's hierarchy. Preemption is permitted but idle is not introduced. Jobs come one by one over list. When a job arrives, it can be accepted and scheduled on some machine or rejected by paying its penalty. The objective is to minimize the sum of makespan yielded by accepted jobs and total penalties of all rejected jobs. For this problem, we propose a family of several online algorithms according to the range of s and the related lower bound is also obtained. These algorithms achieve optimal competitive ratio when s ∈ (0, 1) ∪ [1.618, +∞), but have a small gap between upper bound and lower bound in interval [1, 1.618).

Suggested Citation

  • Xiao Min & Jing Liu & Yanxia Dong & Ming Jiang, 2015. "Online Preemptive Hierarchical Scheduling on Two Uniform Machines with Rejection," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(04), pages 1-15.
    • Handle: RePEc:wsi:apjorx:v:32:y:2015:i:04:n:s021759591550027x
    DOI: 10.1142/S021759591550027X
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    Citations

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    Cited by:

    1. Xianglai Qi & Jinjiang Yuan, 2019. "Semi-Online Hierarchical Scheduling on Two Machines for lp-Norm Load Balancing," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(01), pages 1-16, February.
    2. Ji Tian & Yan Zhou & Ruyan Fu, 2020. "An improved semi-online algorithm for scheduling on a single machine with unexpected breakdown," Journal of Combinatorial Optimization, Springer, vol. 40(1), pages 170-180, July.

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