Polling systems in heavy traffic: A Bessel process limit

This paper studies the classical polling model under the exhaustive-service assumptions; such models continue to be very useful in performance studies of computer/communications systems. The analysis here extends earlier work of the authors to the general case of nonzero switchover times. It shows that, under the standard heavy-traffic scaling the total unfinished work in the system tends to a Bessel-type diffusion in the heavy-traffic limit. It verifies in addition that, with this change in the limiting unfinished-work process, the averaging principle established earlier by the authors carries over to the general model.