Online deadline scheduling with preemption penalties

  • Authors:

  • Feifeng Zheng;Yinfeng Xu;Chung Keung Poon;E. Zhang;Xiaoping Wu

  • Affiliations:

  • School of Management, Xi'an JiaoTong University, Xi'an 710049, China and The State Key Lab for Manufacturing Systems Engineering, Xi'an 710049, China;School of Management, Xi'an JiaoTong University, Xi'an 710049, China and The State Key Lab for Manufacturing Systems Engineering, Xi'an 710049, China;Department of Computer Science, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong, China;Shanghai University of Finance and Economics, Shanghai 200433, China;Xi'an University of Posts and Telecommunications, Xi'an 710049, China

  • Venue:
  • Computers and Industrial Engineering
  • Year:
  • 2011

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Abstract

This paper presents a study of the problem of online deadline scheduling under the preemption penalty model of Zheng, Xu, and Zhang (2007). In that model, each preemption incurs a penalty of @r times the weight of the preempted job, where @r=0 is the preemption penalty parameter. The objective is to maximise the total weight of jobs completed on time minus the total penalty. When the scheduler knows the ratio of longest to shortest job length, @D, we show that the WAL algorithm of Zheng et al. (2007) is ((1+@r)@D+o(@D))-competitive for sufficiently large @D. This improves the bound shown in Zheng et al. (2007). When the scheduler only knows that @D=(k(1+@r))^3 for some k1, we propose a ((k(1+@r)@D/(k-1))+o(@D))-competitive algorithm. When @r=0, we give an optimal, O(@D/log @D)-competitive algorithm that, unlike previous algorithms, does not require knowledge of @D. This settles an open problem mentioned in Ting (2008).