In this paper, we consider a polling system consisting of two-parallel queues and a single server under an (M,N)-threshold nonpreemptive priority service schedule. Two thresholds M and N(0 ≤ M < N) are set up in one of two queues, say, the second queue. At each epoch of service completion, the server decides which queue is to be served next according to the control level reached by the number of customers in the second queue. For the queueing model, we vary out the performance analysis by using the transform method and propose an algorithm to compute the generating functions of the stationary joint queue length distributions at service completion instants. We also determine the Laplace–Stieltjes transforms of the waiting time distributions for both queues, and obtain their mean waiting times.
