ABSTRACT
Optimization of continuous-time, Markovian queueing systems is treated by optimal control theory with emphasis on the single server queue and variable service rate. The queueing problem, formulated as a time-varying continuous Markov chain, is described by a bilinear system of ordinary differential equations. Necessary and sufficient conditions for optimality are given. In particular, special monotonicity properties of the problem are used to obtain a characterization for switching and the relationship to Markovian dynamic programming approaches is discussed. Finally, we describe some properties of the unbounded horizon problem and a gradient method for solution.
