  We establish sufficient conditions for the existence of moments of the
steady-state queue in polling systems operating under the binomial-exhaustive
policy (BEP). We assume that the server switches between the different buffers
according to a pre-specified table, and that switchover times are incurred
whenever the server moves from one buffer to the next. We further assume that
customers arrive according to independent Poisson processes, and that the
service and switchover times are independent random variables with general
distributions. We then propose a simple scheme to approximate the moments,
which is shown to be asymptotically exact as the switchover times grow without
bound, and whose computation complexity does not grow with the order of the
moment. Finally, we demonstrate that the proposed asymptotic approximation for
the moments is related to the fluid limit under a large-switchover-time
scaling; thus, similar approximations can be easily derived for other
server-switching policies, by simply identifying the fluid limits under those
controls. Numerical examples demonstrate the effectiveness of our
approximations for the moments under BEP and under other policies, and their
increased accuracy as the switchover times increase.
