Polling systems with state-dependent setup times

We analyze a polling system with multiple stations (queues) attended by a cycling server, in which a setup occurs only when the queue that is polled by the server has one or more customers present. Although such systems are appropriate for modeling numerous manufacturing and telecommunication systems, their analysis is not well developed in the literature. We provide an exact analysis for the 2 station model and present two approximation schemes to determine the mean station waiting times for models with 3 or more stations. We show that some approximate models which have been proposed in the literature for providing upper bounds on the mean station waiting times do not always yield upper bounds. Extensive numerical tests indicate that a simple average of the two approximation schemes yields a close estimate of the true mean station waiting time. This average-of-approximations procedure appears to be robust for a large range of parameter values.