A stationary regime for polling systems with general ergodic (GI/G) arrival processes at each station is constructed. Mutual independence of the arrival processes is not required. It is shown that the stationary workload so constructed is minimal in the stochastic ordering sense. In the model considered the server switches from station to station in a Markovian fashion, and a specific service policy is applied to each queue. The present hypotheses cover the purely gated, the a-limited, the binomial-gated and other policies. As a by-product the paper obtains sufficient conditions for the stationary regime of a GI/G/1 queue with multiple server vacations to be ergodic.
