A novel approach to queue stability analysis of polling models

Previous work in the stability analysis of polling models concentrated mainly on stability of the whole system. This system stability analysis, however, fails to model many real-world systems for which some queues may continue to operate under an unstable system. In this paper we address this problem by considering queue stability problem that concerns stability of an individual queue in a polling model. We present a novel approach to the problem which is based on a new concept of queue stability orderings, dominant systems, and Loynes’ theorem. The polling model under consideration employs an m-limited service policy, with or without prior service reservation; moreover, it admits state-dependent set-up time and walk time. Our stability results generalize many previous results of system stability. Furthermore, we show that stabilities of any two queues in the system can be compared solely based on their (λ/m)’s, where λ is the customer arrival rate to a queue.