A Tandem Queue with Two Markovian Inputs and Retrial Customers

A tandem retrial queue consisting of two stations is studied. The first station has a single server. An input flow at the first station is described by the Markovian Arrival Process ( MAP ). If a customer from this flow meets the busy server, it goes to the orbit of infinite size and tries its luck later on in exponentially distributed random time. The service time distribution at the first station is assumed to be general. After service at this station the customer proceeds to the multi-server second station. If this customer meets a free server at the second station, it starts service immediately; else the customer leaves the system forever. Besides the customers proceeding from the first station, an additional MAP flow of customers arrives at the second station directly, not entering the first station. A customer from this flow is lost if there is no available server at the second station. The service time by a second station server is exponentially distributed. We derive the stationary distribution of the system states at embedded epochs and at an arbitrary time, calculate the main performance measures. Numerical results are presented.