Work-Conserving Disciplines Are Asymptotic Optimal in Completion Time Minimization

Abstract

In this paper, we prove that in a stable multi-server system, where different machines are allowed to have different speeds, all work-conserving disciplines are asymptotic optimal for minimizing total completion time, if job size and interarrival time distributions have finite moments. As a byproduct of our analysis, we obtain tight upper bound on the competitive ratios of work-conserving disciplines on minimizing the metric of flow time.