Dominance Theorems and Ergodic Properties of Polling Systems

We consider a class of polling systems with stationary ergodic input flow such that the control in a system obeys a certain regeneration property. For this class, necessary and sufficient conditions for the queue-length process to be bounded in probability are found. Under these conditions, we prove that a stationary regime exists and the queue-length process for a system that starts from the zero initial state converges to this regime. In the proof, we use some monotonicity properties of the models considered and some dominance theorems based on these properties.