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Online Single-Processor Scheduling with an Unexpected Breakdown

Sainan Guo

School of Mathematical Science and Institute of Mathematics, Nanjing Normal University, Nanjing, 210023, P. R. China

E-mail Address: athenagsn@163.com

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Yannan Chen

School of Mathematical Sciences, South China Normal University, Guangzhou 510631, P. R. China

E-mail Address: ynchen@scnu.edu.cn

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Yaping Mao

Department of Mathematics and Statistics, Qinghai Normal University, Xining 810008, Qinghai, P. R. China

Academy of Plateau Science and Sustainability, Xining 810008, Qinghai, P. R. China

E-mail Address: maoyaping@ymail.com

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, and

Xiaoyan Zhang

School of Mathematical Science and Institute of Mathematics, Nanjing Normal University, Nanjing, 210023, P. R. China

E-mail Address: zhangxiaoyan@njnu.edu.cn

Corresponding author.

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https://doi.org/10.1142/S0217595923500057Cited by:0 (Source: Crossref)

Abstract

In this paper, we consider two single-processor online scheduling problems with an unexpected breakdown. Speaking specifically, there is a group of nonresumable jobs being processed on the single processor. Note that the breakdown will emerge on the processor suddenly, which signifies that its beginning time and its length are unknown in advance. In this study, we are interested in scheduling the jobs so as to minimize the maximum weighted completion time. Most noticeably, when all jobs respect an agreeable condition, i.e., for each two jobs $J_{a}$ $J_{a}$ and $J_{b}$ $J_{b}$ , $w_{a} \geq w_{b}$ $w_{a} \geq w_{b}$ means that $p_{a} \geq p_{b}$ $p_{a} \geq p_{b}$ , we design an optimal online algorithm. In addition, for the general version, we propose an online algorithm with a competitive ratio of at most 2.

Keywords:

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