Virtually all practical settings where preemptive scheduling is employed are susceptible to preemption overhead, and accounting for these overheads is necessary to make informed scheduling design decisions. However, preemption overhead is almost never accounted for in queueing-theoretic analyses of preemptive scheduling policies. This is true even for simple preemptive policies in simple queueing models: even the stability region, let alone the response time distribution, is difficult to analyze under overhead. In this work, we give the first response time distribution analysis of an M/G/1 under a preemptive scheduling policy with preemption overhead. Specifically, we consider class-based preemptive priority, where a stochastic overhead is incurred when pausing or resuming a job. We derive a recursive formula for the Laplace transform of response time for jobs of any given class, from which all response time moments can be extracted. Beyond the specific policy and model we analyze, our broader aim is to provide a first step towards a general framework for analyzing queues with preemption overhead. To that end, we perform much of our analysis in a way that applies to a wide variety of overhead models by introducing a new theoretical tool called the job joint transform.

翻译：几乎所有采用抢占式调度的实际场景都可能受到抢占开销的影响，而考虑这些开销对于做出明智的调度设计决策是必要的。然而，在排队论对抢占式调度策略的分析中，抢占开销几乎从未被考虑。即使对于简单排队模型中的简单抢占策略也是如此：在存在开销的情况下，不仅响应时间分布，甚至连稳定区域都难以分析。在这项工作中，我们首次给出了在具有抢占开销的抢占式调度策略下M/G/1队列的响应时间分布分析。具体而言，我们考虑基于类别的抢占优先级，其中暂停或恢复作业时会 incur 随机开销。我们推导了任意给定类别作业的响应时间拉普拉斯变换的递归公式，从中可以提取所有响应时间矩。除了我们分析的具体策略和模型外，我们的更广泛目标是提供迈向分析具有抢占开销队列的通用框架的第一步。为此，我们通过引入一种称为作业联合变换的新理论工具，以适用于多种开销模型的方式进行了大部分分析。