Polling Systems with correlated arrivals

We study asymmetric cyclic polling models with general mixtures of gated and exhaustive service, with generally distributed service times and switch-over times, and in which batches of customers may arrive simultaneously at the different queues. We present closed-form expressions for the Laplace-Stieljties Transform of the steady-state delay incurred at each of the queues when the load tends to unity (under proper scalings), in a general parameter setting. The results are strikingly simple and show explicity how the distribution of the delay depends on the system parameters, and in particular, on the batch-size distributions and the simultaneity of the batch arrivals. In addition, the exact results lead to simple and fast approximations for the tail probabilities and the moments of the delay in stable polling systems, explicity capturing the impact of the correlation structure in the arrival processes on the delay incurred at each of the queues. Numerical experiments indicate that the approximations are highly accurate for medium and heavily loaded systems.