Gated polling with stationary ergodic walking times, Markovian routing and random feedback

We investigate a gated polling system with semi-linear feedback and Markovian routing. We thereby relax the classical independence assumption on the walking times; the walking times constitute a sequence of stationary ergodic random variables. It is shown that the dynamics of this polling system can be described by semi-linear stochastic recursive equations in a Markovian environment. We obtain expressions for the first and second order moments of the workload and queue content at polling instants and for the mean queue content and workload at random instants