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Asymptotic Evaluation of Delay in the SRPT Scheduler

机译：SRPT调度程序中延迟的渐近评估

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In this note, the shortest remaining processing time (SRPT) scheduler is considered. We focus on the SRPT scheduling policy for a discrete-time queueing system that is accessed by a large number of flows (a many flows regime). In such an asymptotic regime (large capacity and large number of flows), we derive the expression for the delay rate function, which describes the complete delay distribution, for batch arrival processes, and with bounded job sizes. Based on these results, we compare the delay rate function (i.e., for any finite delay, and asymptotic in the number of flows) of the SRPT scheduler with that of a first-in-first-out (FIFO) scheduler, when there is a mix of job sizes. Our analysis holds for any finite mix of job sizes and for truncated heavy-tailed arrival processes. We apply the result to a system accessed by jobs which are one of two sizes: 1 or M. We investigate the unfairness of SRPT by comparing the delay rate function of size M jobs for SRPT and FIFO. We show that the difference in the delay rate function between SRPT and FIFO for size M jobs decay as O(1/M gamma) for some gamma that satisfies 0
机译：在本说明中，考虑了最短的剩余处理时间（SRPT）调度程序。我们专注于由大量流（许多流机制）访问的离散时间排队系统的SRPT调度策略。在这样的渐近状态（大容量和大量流）中，我们导出了延迟率函数的表达式，该表达式描述了完整的延迟分布，批次到达过程以及有限的工作规模。基于这些结果，当存在以下情况时，我们将SRPT调度程序与先进先出（FIFO）调度程序的延迟率函数（即，对于任何有限的延迟和流的渐近性）进行比较。工作规模的混合。我们的分析适用于工作量的任何有限混合以及截尾的重尾到达过程。我们将结果应用于两个以下大小之一的作业访问的系统：我们通过比较大小为SRPT和FIFO的作业的延迟率函数来研究SRPT的不公平性。我们表明，对于满足0

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