  In this paper we consider a single-server cyclic polling system. Between
visits to successive queues, the server is delayed by a random switch-over
time. The order in which customers are served in each queue is determined by a
priority level that is assigned to each customer at his arrival. For this
situation the following service disciplines are considered: gated, exhaustive,
and globally gated. We study the cycle time distribution, the waiting times for
each customer type, the joint queue length distribution of all priority classes
at all queues at polling epochs, and the steady-state marginal queue length
distributions for each customer type.
