Scheduling in polling systems in heavy traffic

We consider the classical cyclic polling model with Poisson arrivals and with gated service at all queues, but where the local scheduling policies are not necessarily First-Come- First-Served (FCFS). More precisely, we study the waitingtime performance of polling models where the local service order is Last-Come-First-Served (LCFS), Random-Orderof- Service (ROS) or Processor Sharing (PS). Under heavytraffic conditions the waiting times turn out to converge to products of generalized trapezoidal distributions and a gamma distribution.