Optimal monotone hysteretic Markov policies in anM/M/1 queueing model with switching costs and finite time horizon

In anM/M/1 queueing model, a decision maker can choosem pairs of arrival- and service rates. He can change his action at any time epoch, a switch of action costs an amount depending on the size of the switch. Besides that there are continuously incurring costs. Over a finite time horizon, there exists an optimal monotone hysteretic Markov policy. This is shown essentially by the technique of time discretization.The work producing this article was done during a half year stay at the University of Leiden, The Netherlands, with Prof. Arie Hordijk. A technical report (a more detailled version of this article) was written there 6]. The opportunity for this stay was given by the University of Bonn, Germany, where the author, at that time, worked as scientific assistant of Prof. M. Schäl.