Dominant Resource Fairness (DRF) is an influential policy for sharing multiple resources among jobs with heterogeneous demands. It combines sharing incentive, strategy-proofness, envy-freeness, and Pareto efficiency, making it particularly attractive for shared computing systems. DRF has been implemented in major resource-management frameworks, including Apache Mesos and Hadoop YARN. DRF is also nonclairvoyant: it requires no advance knowledge of job sizes, making it practical when processing requirements are difficult to predict. This motivates understanding its completion-time performance relative to an optimal schedule that knows all job sizes. However, elementary arguments can only give an $Ω(\sqrt D)$ lower bound and an $O(D)$ upper bound for total completion time, where $D$ is the number of resource types. In this paper, we close this gap by proving that DRF is $Θ(\sqrt D)$-competitive. More generally, for every fixed real $q\geq1$, we show that DRF is $Θ(D^{1/(q+1)})$-competitive for the $\ell_q$ norm of completion times, with larger $q$ placing greater emphasis on late-finishing jobs. These bounds hold with arbitrary release times. We also give a refined analysis of total completion time for small $D$.

翻译：暂无翻译