Online Starvation Mitigation to Balance Average Flow Time and Fairness
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In job scheduling, it is well known that Shortest Remaining Processing Time (SRPT) minimizes the average flow time. However, SRPT may cause starvation and unfairness. To balance fairness and average flow time, one common approach is to minimize the ℓ_2 norm of flow time. All non-trivial algorithms designed for this problem are offline algorithms based on linear programming rounding. For the online setting, all previous works consider standard scheduling algorithms under the assumptions of speed augmentation or certain input distributions. In their seminal paper, Bansal and Pruhs prove that under speed augmentation, fairness is not sacrificed much when SRPT is used [SICOMP 2010]. However, in practice, to achieve better fairness, it is not uncommon to complement SRPT with some starvation mitigation mechanism. Nonetheless, starvation mitigation inevitably destroys SRPT's optimality in minimizing the average flow time. Thus, it is not clear whether starvation mitigation can improve SRPT's performance on minimizing the ℓ_2 norm of flow time. In this paper, we answer this question in the affirmative. Let n be the number of jobs. We use an estimate of n to carefully mitigate the starvation caused by SRPT. Given a good estimate of n, our starvation mitigation mechanism reduces the competitive ratio of SRPT for the ℓ_2 norm of flow time from Ω(n^1/2) to O(n^1/3). Finally, we remark that all the online algorithms considered previously for this problem have competitive ratios Ω̃(n^1/2).
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