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We establish sufficient conditions for the existence of moments of thesteady-state queue in polling systems operating under the binomial-exhaustivepolicy (BEP). We assume that the server switches between the different buffersaccording to a pre-specified table, and that switchover times are incurredwhenever the server moves from one buffer to the next. We further assume thatcustomers arrive according to independent Poisson processes, and that theservice and switchover times are independent random variables with generaldistributions. We then propose a simple scheme to approximate the moments,which is shown to be asymptotically exact as the switchover times grow withoutbound, and whose computation complexity does not grow with the order of themoment. Finally, we demonstrate that the proposed asymptotic approximation forthe moments is related to the fluid limit under a large-switchover-timescaling; thus, similar approximations can be easily derived for otherserver-switching policies, by simply identifying the fluid limits under thosecontrols. Numerical examples demonstrate the effectiveness of ourapproximations for the moments under BEP and under other policies, and theirincreased accuracy as the switchover times increase.

Existence and Approximations of Moments for Polling Systems under the Binomial-Exhaustive Policy