Randomized selection algorithm for online stochastic unrelated machines scheduling

We consider an online stochastic unrelated machines scheduling problem. Specifically, a set of jobs arriving online over time must be randomly scheduled on the unrelated machines, which implies that the information of each job, including the release date and the weight, is not known until it is released. Furthermore, the actual processing time of each job is disclosed upon completion of this job. In addition, we focus on unrelated machines, which means that each job has a processing speed on every machine. Our goal is to minimize the expected total weighted completion time of all jobs. In this paper, we present a randomized selection algorithm for this problem and prove that the competitive ratio is a constant. Moreover, we show that it is asymptotic optimal for the online stochastic uniform machines scheduling problem when some parameters are bounded. Moreover, our proof does not require any probabilistic assumption on the job parameters.