A queueing system with constant repeated attempts and Bernoulli schedule

We consider a single-service queueing system with a waiting room of infinite capacity. Customers arrive according to a Poisson stream with rate L > 0. A customer who finds the server occupied at the time of arrival joins with probability p a retrial group, that will be called orbit, and with complementary probability q a waiting room in order to be served. Service times are general and retrial times are inversely proportional to the number of customers in the orbit. We derive the stationary distribution of the embedded Markov chain and also the joint generating function of the number of customers of both groups in the steady state regime. The results agree with known results for special cases.