A discrete-time retrial queueing system with recurrent customers

We consider a discrete-time single-server retrial queue with general service times and two classes of customers: transit and a fixed number of recurrent customers. After service completion, recurrent customers always return to the orbit and transit customers leave the systems forever. In this work we study the influence of recurrent customers. This structure appears in many applications on computer and communication networks, but also has theoretical interest. The explicit expressions of generating functions of the stationary distribution of the Markov chain are given. We also provide the main reliability indexes and numerical examples with the use of discrete Fourier transform inversion.