Queue length performance of some non-exhaustive polling models with Bernoulli feedback

We study the queue length performance in non-exhaustive asymmetric polling systems with Bernoulli feedback. We obtain the PGF (probability generating functions) and the mean values of the queue lengths. For the gated polling model we define two new service policies: departure-gated policy and service-gated policy, and we demonstrate their difference in queueing performance. In an asymmetric system, the departure-gated policy is better than the service-gated policy. In a symmetric system however, these two non-exhaustive policies are not as good as an exhaustive policy. We also observe that the performance of 1-limited system degrading faster as the load increases.