  In this paper we consider a single-server cyclic polling system consisting of
two queues. Between visits to successive queues, the server is delayed by a
random switch-over time. Two types of customers arrive at the first queue: high
and low priority customers. For this situation the following service
disciplines are considered: gated, globally gated, and exhaustive. We study the
cycle time distribution, the waiting times for each customer type, the joint
queue length distribution at polling epochs, and the steady-state marginal
queue length distributions for each customer type.
