Online Hierarchical Scheduling on Two Uniform Machines with Bounded Job Sizes

Abstract

This paper studies the online hierarchical scheduling problem on two uniform machines with bounded job sizes, where the first machine M1 receives both low and high hierarchy jobs, while the second machine M2 only receives high hierarchy jobs. The machines have a speed ratio of s(s ≥ 1), and M2 runs faster. Jobs are revealed one by one, and before the current job is scheduled, we have no information about next jobs except that the size of any job is in the interval [1, t]. The objective is to minimize the makespan. We present optimal algorithms for all (s, t) pairs.