An M/G/1 retrial queue with a threshold in the retrial group (Q2782744)

The paper deals with an M/G/1 retrial queueing system under the following threshold control policy: an arriving customer who finds the server idle receives service immediately, otherwise he joins the retrial group, consisting of an orbiting group of finite capacity \(D\) and a feedback queue of infinite capacity. Blocked customers go into the orbiting group if there is a place free, otherwise they go into the feedback queue. The customers in the orbiting group wait an exponentially time for retrial. As soon as there is a waiting place free in the orbiting group a customer from the feedback queue joins the orbiting group. For this model first the embedded Markov chain (EMC) of the number of customers in the system at the service completion epochs is derived. Then by applying Pakes' lemma the stability condition for the system is given. Then the probability generating function of the stationary distribution of the EMC is derived, which requires to solve a linear system of equations. For \(D=1\), \(D=2\) the results are specialized. Finally, some numerical results are presented.