AI 中文总结
该研究提出带控制假期的M/M/1排队模型，利用马尔可夫决策过程等方法构建降本策略，经仿真验证其可降低平均期望成本。
AI 中文摘要
我们引入了一种带有控制假期的模型，替代了具有永久控制的标准排队控制系统。所研究的模型是M/M/1排队系统，具有两个可用服务速率的临时服务速率控制周期。在一段服从指数分布长度的控制周期结束后，将启动控制假期，此期间使用固定服务速率μ。下一个控制周期的开始需要直接安排，并产生一定成本。我们将使用Kanavetas等人arXiv:2605.31573中的马尔可夫决策过程，找到一个充分条件，确保与仅使用固定服务速率的模型相比，平均期望成本可以降低。在该条件下，我们将利用此相关过程的性质构建一种降低成本的策略。在特定策略下，带有控制假期的过程会诱导出更新奖励过程。我们使用Tauberian定理将此更新奖励过程的平均期望成本与消失折扣方法关联起来，并解析确定平均期望成本降低的下界。最后，我们通过仿真研究这些策略实际实现的平均成本降低。
英文摘要
We introduce a model with control vacations instead of standard queueing control systems with permanent control. The researched model is an M/M/1 queue with temporary periods of service rate control with two available service rates. After a control period of exponentially distributed length, a control vacation is initiated during which a fixed service rate $μ$ is used. The start of the next control period needs to be scheduled directly at a certain cost. We will use the Markov Decision Process from Kanavetas et al. arXiv:2605.31573 to find a sufficient condition that ensures that the average expected cost can be reduced w.r.t. the model that only uses the fixed service rate. Under this condition we will use properties of this related process to construct a cost reducing policy. The process with control vacations under specific policies induces a renewal reward process. We use a Tauberian theorem to relate the average expected cost of this renewal reward process to a vanishing discount method and analytically determine a lower bound of the average expected cost reduction. Finally, we study the actual attained average cost reduction for these policies through simulation.
