Stability of non-Markovian polling systems
The paper considers polling systems where the arrivals at each station are stationary ergodic processes \((G/G)\), not necessarily mutually independent. The server switches from station to station in a Markovian fashion and each queue is attended according to a specific policy. Under certain conditions, a stationary regime is constructed in a recursive way, using a monotonicity property of the system. It is also shown that this stationary regime is the smallest in the stochastic ordering sense. The policies considered are of the gated type and satisfy a monotonicity condition. First deterministic policies are considered and later it is explained how the reasoning can be extended to random policies.
scientific article; zbMATH DE number 851505