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arXiv 2602.01411cs.DC
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均场最优可变作业核心分配

Mean field optimal Core Allocation across Malleable jobs

Carnegie Mellon University(卡内基梅隆大学);UNC Chapel Hill(北卡罗来纳大学教堂山分校)

Zhouzi Li, Mor Harchol-Balter, Benjamin Berg

AI总结:

本文提出两种均场最优策略FW-CAM和WHAM,用于在可变作业环境下优化核心分配,以最小化平均响应时间。

摘要:

现代数据中心和云计算集群越来越多地运行由可变作业组成的负载。可变作业可以在任意数量的核心上并行化,但通常每个额外的核心会带来递减的边际收益。这可以通过作业速度提升函数的凹性来体现,该函数描述了作业处理速度随运行核心数的变化。鉴于可变作业的普遍性,已有理论工作探讨了如何将固定数量的核心分配到到来的可变作业流中,以最小化作业的平均响应时间。我们称此问题为可变作业核心分配(CAM)问题。我们在一个高度通用的设置下解决了CAM问题,允许多个作业类别,每个类别具有任意凹的速度提升函数和持有成本(权重)。此外,我们还允许一般分布的到达间隔时间和作业大小。我们分析了CAM问题在均场渐近 regime 中,并推导出两种不同的均场最优策略,FW-CAM和WHAM。FW-CAM之所以有趣,是因为它展示了一个新的直觉:在均场 regime 中,作业大小在寻找最优策略时并不相关。WHAM(可变作业的Whittle分配)之所以有趣,是因为它在渐近意义上最优,而且即使在非渐近 regime 中也表现良好。值得注意的是,之前文献中提出的任何策略在作业可能具有不同速度提升函数时都不是均场最优的。

英文摘要:

Modern data centers and cloud computing clusters are increasingly running workloads composed of malleable jobs. A malleable job can be parallelized across any number of cores, yet the job typically exhibits diminishing marginal returns for each additional core on which it runs. This can be seen in the concavity of a job's speedup function, which describes the job's processing speed as a function of the number of cores on which it runs. Given the prevalence of malleable jobs, several theoretical works have posed the problem of how to allocate a fixed number of cores across a stream of arriving malleable jobs so as to minimize the mean response time across jobs. We refer to this as the Core Allocation to Malleable jobs (CAM) problem. We solve the CAM problem under a highly general setting, allowing for multiple job classes, each with an arbitrary concave speedup function and holding costs (weight). Furthermore, we allow for generally distributed inter-arrival times and job sizes. We analyze the CAM problem in the mean field asymptotic regime and derive two distinct mean field optimal policies, FW-CAM and WHAM. FW-CAM is interesting because it demonstrates a new intuition: in the mean field regime, job sizes are not relevant in finding an optimal policy. WHAM (Whittle Allocation for Malleable jobs) is interesting because it is asymptotically optimal and also serves as a good heuristic even outside of the asymptotic regime. Notably, none of the policies previously proposed in the literature are mean field optimal when jobs may follow different speedup functions.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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