关于具有凹加速比的可塑作业的最优服务器分配
On Optimal Server Allocation for Moldable Jobs with Concave Speed-Up
AI总结：
针对可并行、凹加速比作业在多服务器系统中的分配问题，提出一种简单方案，使被接受作业平均执行时间最优，并在大规模及异构负载下保证阻塞概率趋零。
摘要：
提交到现代计算集群和数据中心的作业中，有很大一部分是可并行化的，并且能够在数量灵活的计算核心或服务器上运行。尽管为此类作业分配更多服务器会提高作业执行的加速比，但这会减少其他作业可用的服务器数量，在最坏情况下，可能导致一个到达的作业在到达时找不到任何可用服务器来立即运行。因此，需要解决的一个关键问题是：如何最优地为作业分配服务器，使得（i）各作业的平均执行时间最小化，并且（ii）几乎所有作业在到达时都能立即找到至少一台服务器。为解决这一问题，我们考虑一个具有 $n$ 台服务器的系统，其中作业最多可并行到 $d^{(n)}$ 台服务器，并且作业的加速比函数是凹的且递增的。进入时找不到任何可用服务器的作业将被阻塞并丢失。我们提出了一种简单的服务器分配方案，该方案实现了被接受作业的最小平均执行时间，同时确保随着系统规模变大（$n \to \infty$），作业的阻塞概率趋于零。该结果在多种流量条件以及异构工作负载下均成立。为证明我们的结果，我们采用 Stein 方法，该方法还给出了关于阻塞概率和平均执行时间的非渐近界。此外，我们的仿真表明，该方案的性能对作业执行时间的分布不敏感。
英文摘要：
A large proportion of jobs submitted to modern computing clusters and data centers are parallelizable and capable of running on a flexible number of computing cores or servers. Although allocating more servers to such a job results in a higher speed-up in the job's execution, it reduces the number of servers available to other jobs, which in the worst case, can result in an incoming job not finding any available server to run immediately upon arrival. Hence, a key question to address is: how to optimally allocate servers to jobs such that (i) the average execution time across jobs is minimized and (ii) almost all jobs find at least one server immediately upon arrival. To address this question, we consider a system with $n$ servers, where jobs are parallelizable up to $d^{(n)}$ servers and the speed-up function of jobs is concave and increasing. Jobs not finding any available servers upon entry are blocked and lost. We propose a simple server allocation scheme that achieves the minimum average execution time of accepted jobs while ensuring that the blocking probability of jobs vanishes as the system becomes large ($n \to \infty$). This result is established for various traffic conditions as well as for heterogeneous workloads. To prove our result, we employ Stein's method which also yields non-asymptotic bounds on the blocking probability and the mean execution time. Furthermore, our simulations show that the performance of the scheme is insensitive to the distribution of job execution times.
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。
