Abstract
In this paper, we examine a problem which is an extension of the limited service in a queueing system with a cyclic server. In this service mechanism, each queue, after receiving service in cycle j, makes a reservation for its service requirement in cycle j + 1. In this paper, we consider symmetric case only, i.e., the arrival rates to all the queues are the same. The main contribution to queueing theory is that we propose an approximation for the queue length and sojourn-time distributions for this discipline. Most approximate studies on cyclic queues, which have been considered before, examine the means only. Our method is an iterative one, which we prove to be convergent by using stochastic dominance arguments. We examine the performance of our algorithm by comparing it to simulations and show that the results are very good.