List scheduling for jobs with arbitrary release times and similar lengths

Abstract This paper considers the problem of on-line scheduling a list of independent jobs in which each job has an arbitrary release time and length in [1,r] with r≥1 on m parallel identical machines. For the list scheduling algorithm, we give an upper bound of the competitive ratio for any m≥1 and show that the upper bound is tight when m=1. When m=2, we present a tight bound for r≥4. For r<4, we give a lower bound and show that 2 provides an upper bound.