Stability of non-Markovian polling systems

A stationary regime for polling systems with general ergodic (G/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. Our hypotheses cover the purely gated, the a-limited, the binomial-gated and other policies. As a by-product we obtain sufficient conditions for the stationary regime of a G/G/1/infinity queue with multiple server vacations (see Doshi [11]) to be ergodic.