  In the present paper we address two open problems concerning polling systems,
viz., queueing systems consisting of multiple queues attended by a single
server that visits the queues one at a time. The first open problem deals with
a system consisting of two queues, one of which has gated service, while the
other receives 1-limited service. The second open problem concerns polling
systems with general (renewal) arrivals and deterministic switch-over times
that become infinitely large. We discuss related, known results for both
problems, and the difficulties encountered when trying to solve them.
