We consider a single-server retrial queueing system with K(K ≥ 1) Poisson input flows. The service times have a common arbitrary distribution function Bi(x) for customer of type i. An arriving customer of type i, i = 1,K, who finds the server free begins to get service immediately and leaves the system after completion. Otherwise, if the server is busy, the customer with probability 1 − Hi leaves the system without service and with probability Hi > 0 joins an orbit of repeated customer but conserves its own type. The intervals separating two successive repeated attempts of each customer from the orbit are exponentially distributed with rate γ. The orbit is finite or infinite. In case of a finite orbit an arriving customer who finds the server busy and the orbit completely full is lost. We derive the steady state probabilities of the multidimensional Markov process underlying the considered queueing system.
