Abstract In this paper, we study a variant of PS+PS multilevel scheduling, which we call the PS+IS queue. Specifically, we use Processor Sharing (PS) at both queues, but with linear frequency scaling on the second queue, so that the latter behaves like an Infinite Server (IS) queue. The goals of the system are low response times for small jobs in the first queue, and reduced power consumption for large jobs in the second queue. The novelty of our model includes the frequency scaling at the second queue, and the batch arrival process at the second queue induced by the busy period structure of the first queue which has strictly higher priority. We derive a numerical solution for the PS+IS queueing system in steady-state, and then study its properties under workloads obtained from fitting of TCP flow traces. The simulation results confirm the efficacy of the PS+IS model.

中文翻译：

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多级队列中的频率缩放

摘要 在本文中，我们研究了 PS+PS 多级调度的一种变体，我们称之为 PS+IS 队列。具体来说，我们在两个队列中使用处理器共享 (PS)，但在第二个队列上使用线性频率缩放，因此后者的行为类似于无限服务器 (IS) 队列。该系统的目标是缩短第一个队列中小作业的响应时间，并降低第二个队列中大作业的功耗。我们模型的新颖之处包括第二个队列的频率缩放，以及由具有严格更高优先级的第一个队列的繁忙时段结构引起的第二个队列的批量到达过程。我们推导出稳态下 PS+IS 排队系统的数值解，然后研究其在通过拟合 TCP 流迹获得的工作负载下的特性。