A Two-queue Model with Alternating Limited Service and State-dependent Setups

We consider a two-queue model with state-dependent setups, in which a single server alternately serves the two queues. The high-priority queue is served exhaustively, whereas the low-priority queue is served according to the k-limited strategy. We obtain the transforms of the queue length and sojourn time distributions under the assumption of Poisson arrivals, generally distributed service times and generally distributed setup times. It is shown how the results of this analysis can be applied in the evaluation of a stochastic two-item single-capacity production system.