We present an example of a single-server polling system with two queues and
an adaptive service policy where the stability region depends on the expected
values of all the primitives and also on a certain exponential moment of the
service-time distribution in one of the queues. The latter parameter can not be
determined, in general, in terms of any finite number of power moments. It
follows that the fluid approximation approach may not be an appropriate tool
for the stability study of this model.Comment: 6 page
