A two-queue model with exhaustive and limited service disciplines

In this paper, we analyze a single server model with two queues. The server serves customers in one queue according to an exhaustive discipline and serves the other queue according to a limited discipline. We study the embedded Markov chain at departure epochs and obtain the transforms of the queue length and sojourn time distributions. We also present a light traffic analysis and a heavy traffic limit analysis for this model. We show that when the system approaches saturation, the two queues become independent.