Polling systems with periodic server routing in heavy traffic: renewal arrivals

This paper considers heavy-traffic limit theorems for polling models with periodic server routing with general renewal arrivals and with mixtures of gated and exhaustive service policies, in a general parameter setting. We provide a strong conjecture for the limiting waiting-time distribution in a general parameter setting when the load tends to 1, under proper heavy-traffic scalings. The results in this paper, which generalize those in [14] for the special case of Poisson arrivals, are obtained by following the non-Poisson transient systems approach developed in [6]. Numerical results with simulations support the correctness our results, and moreover, show that the expressions for the waiting-time distributions in the limiting case lead to sharp approximations for the waiting-time distributions for stable polling systems with medium and heavy load.