Modern cloud computing workloads are composed of multiresource jobs that require a variety of computational resources in order to run, such as CPU cores, memory, disk space, or hardware accelerators. A single cloud server can typically run many multiresource jobs in parallel, but only if the server has sufficient resources to satisfy the demands of every job. A scheduling policy must therefore select sets of multiresource jobs to run in parallel in order to minimize the mean response time across jobs -- the average time from when a job arrives to the system until it is completed. Unfortunately, achieving low response times by selecting sets of jobs that fully utilize the available server resources has proven to be a difficult problem. In this paper, we develop and analyze a new class of policies for scheduling multiresource jobs, called Markovian Service Rate (MSR) policies. While prior scheduling policies for multiresource jobs are either highly complex to analyze or hard to implement, our MSR policies are simple to implement and are amenable to response time analysis. We show that the class of MSR policies is throughput-optimal in that we can use an MSR policy to stabilize the system whenever it is possible to do so. We also derive bounds on the mean response time under an MSR algorithm that are tight up to an additive constant. These bounds can be applied to systems with different preemption behaviors, such as fully preemptive systems, non-preemptive systems, and systems that allow preemption with setup times. We show how our theoretical results can be used to select a good MSR policy as a function of the system arrival rates, job service requirements, the server's resource capacities, and the resource demands of the jobs.

翻译：现代云计算工作负载由多资源作业构成，这些作业需要多种计算资源（如CPU核心、内存、磁盘空间或硬件加速器）才能运行。单个云服务器通常可以并行运行多个多资源作业，但前提是服务器拥有足够资源满足所有作业的需求。因此，调度策略必须选择能够并行运行的多资源作业集合，以最小化作业的平均响应时间——即从作业到达系统到完成所经历的平均时间。然而，通过选择能充分利用可用服务器资源的作业集合来实现低响应时间已被证明是一个难题。本文提出并分析了一类新的多资源作业调度策略，称为马尔可夫服务率（MSR）策略。以往的多资源作业调度策略要么分析复杂度极高，要么难以实现，而我们的MSR策略不仅易于实现，还适用于响应时间分析。我们证明MSR策略类具有吞吐量最优性：只要系统可稳定，就能通过MSR策略实现稳定。同时，我们推导出MSR算法下平均响应时间的紧界（误差仅为一个加性常数）。这些界限可适用于具有不同抢占行为的系统，包括完全抢占系统、非抢占系统以及允许带准备时间抢占的系统。最后，我们展示了如何根据系统到达率、作业服务需求、服务器资源容量及作业资源需求等参数，运用理论结果选择最优的MSR策略。