Analysis of an M/{Dn}/1 retrial queue

We consider a single server retrial queueing system in which each customer (primary or retrial customer) has discrete service times taking on value Dj with probability pj, j=1,2,…, and ∑^∞j=1 pj = 1. An arriving primary customer who finds the server busy tries later. Moreover, each retrial customer has its own orbit, and the retrial customers try to enter the service independently of each other. We call this retrial queue an M/{Dn}/1 retrial queue. A necessary and sufficient condition for this system stability is given. In the steady state, we derive the joint distribution of the state of the server and the number of customers in the retrial orbits. The explicit expressions of some performance measures are given. In addition, the steady-state distribution of the waiting time is discussed.