A novel approach to queue stability analysis of polling models

Previous work in the stability analysis of polling models concentrated main ly on stability of the whole system. This system stability analysis, howeve r, fails to model many real-world systems for which some queues may continu e to operate under an unstable system. In this paper we address this proble m by considering queue stability problem that concerns stability of an indi vidual 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 sys tems, and Loynes' theorem. The polling model under consideration employs an m-limited service policy, with or without prior service reservation; moreo ver, it admits state-dependent set-up time and walk time. Our stability res ults generalize many previous results of system stability. Furthermore, we show that stabilities of any two queues in the system can be compared solel y based on their (lambda/m)'s, where lambda is the customer arrival rate to a queue. (C)2000 Elsevier Science B.V. All rights reserved.