  In this paper we consider a single-server, cyclic polling system with
switch-over times. A distinguishing feature of the model is that the rates of
the Poisson arrival processes at the various queues depend on the server
location. For this model we study the joint queue length distribution at
polling epochs and at server's departure epochs. We also study the marginal
queue length distribution at arrival epochs, as well as at arbitrary epochs
(which is not the same in general, since we cannot use the PASTA property). A
generalised version of the distributional form of Little's law is applied to
the joint queue length distribution at customer's departure epochs in order to
find the waiting time distribution for each customer type. We also provide an
alternative, more efficient way to determine the mean queue lengths and mean
waiting times, using Mean Value Analysis. Furthermore, we show that under
certain conditions a Pseudo-Conservation Law for the total amount of work in
the system holds. Finally, typical features of the model under consideration
are demonstrated in several numerical examples.
