We study the waiting-time distributions in cyclic polling models with renewal arrivals, general service and switch-over times, and exhaustive service at each of the queues. The assumption of renewal arrivals prohibits an exact analysis and reduces the available analytic results to heavy-traffic asymptotics, limiting results for large switch-over times and large numbers of queues, and some numerical algorithms. Motivated by this, the goal of this paper is to propose a new method for deriving simple closed-form approximations for the complete waiting-time distributions that work well for arbitrary load values. Extensive simulation results show that the approximations are highly accurate over a wide range of parameter settings. Copyright © Taylor & Francis Group, LLC.
Dorsman, J. L., van der Mei, R. D., & Winands, E. M. M. (2012). A new method for deriving waiting-time approximations for polling systems with renewal arrivals. Stochastic Models, 27(2), 318-332. https://doi.org/10.1080/15326349.2011.567933