Consider an asymmetric cyclic polling system with general service-time and switch-over time distributions, and with general mixtures of exhaustive and gated service, in heavy traffic. We obtain explicit expressions for all moments of the steady-state delay at each of the queues, under heavy-traffic scalings. The expressions are strikingly simple: they depend on only a few system parameters, and moreover, can be expressed as finite products of simple known terms. The exact results provide new and useful insights into the behavior of polling systems in heavy traffic. In addition, the results suggest simple and fast approximations for the moments of the delay in stable polling systems. Numerical experiments demonstrate the usefulness of the approximations for moderately and heavily loaded systems.
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