Online scheduling to minimize maximum weighted flow-time on a bounded parallel-batch machine

Abstract

An online scheduling problem on a bounded parallel-batch machine to minimize the maximum weighted flow-time is considered in this paper. Jobs arrive over time with the identical processing time. The maximum ratio between the weights of any two jobs is w. The parallel-batch machine can process at most b jobs simultaneously as a batch, and the jobs in a batch have the same starting time and the same completion time. For this problem, a deterministic online algorithm is presented. The algorithm is showed to be the best possible with a competitive ratio of $$\\frac{\\sqrt{4w+1}+1}{2}$$\n when $$w\\in [1,2]$$\n , and to have a competitive ratio not greater than w when $$w\\in (2,+\\infty )$$\n .