Stability of Polling Systems with State-Independent Routing

This paper deals with the stability study of polling systems with either finite or infinite (countable) number of stations (queues) and with a finite number of servers that poll (visit) the stations along some random (state-independent) routes. First, we formulate “global” and “local” stability theorems for systems with a single server and with a general stationary ergodic input. Their proofs are based on certain monotone properties of underlying stochastic processes (see [15-17]). Second, we give a stability criterion for systems with several servers, with a finite number of stations and with i.i.d. driving sequences. The proof of the latter criterion (see [18]) is based on the fluid approximation approach. Stability conditions for polling systems have undergone study rather recently (see, e.g., [1-12]) and all available papers deal with systems with finitely many stations and (except [2]) with either Poisson or renewal input.