To Control or not to Control

Abstract

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.