Online algorithms for scheduling unit length jobs on parallel-batch machines with lookahead

  • Authors:

  • Wenhua Li;Zhenkun Zhang;Sufang Yang

  • Affiliations:

  • Department of Mathematics, Zhengzhou University, Zhengzhou, Henan 450001, Peoples Republic of China;Department of Mathematics, Huanghuai University, Zhumadian, Henan 463000, Peoples Republic of China;Department of Mathematics, Zhengzhou University, Zhengzhou, Henan 450001, Peoples Republic of China

  • Venue:
  • Information Processing Letters
  • Year:
  • 2012

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Abstract

We consider online scheduling of unit length jobs on m parallel-batch machines with lookahead to minimize makespan. A parallel-batch machine can handle up to b jobs simultaneously as a batch with processing time equal to the maximum processing time of the jobs included in the batch. In the lookahead model, at a time instant t, an online algorithm can foresee all the jobs that will arrive in the time segment (t,t+@b]. In this paper, we deal with two variants: the unbounded model with b=~ and the bounded model with b=1/m, and provide a best possible online algorithm of competitive ratio 1+@a"m for 0=16, respectively, where @a^@? is the positive root of @a^2+(@b+1)@a+@b-1=0. The online algorithm is the best possible when 0=