Polling systems with a patient server and state-dependent setup times

We analyze a class of cyclic service (polling) systems with multiple customer classes (stations) in which the server stops cycling upon finding the entire system empty and initiates a setup only when the polled station has at least one customer in the queue. Interest in such systems is fueled by applications in design and performance analysis of manufacturing as well as telecommunication systems. We develop a discrete Fourier transform (DFT)-based near-exact numerical technique and an approximate method for systems with any number of stations. The DFT-based algorithm is accurate but computationally demanding when either the number of stations is large or server utilization is high. In these cases, the approximate method appears to work well in a large number of numerical tests.