State-dependent M/M/c/c + r retrial queues with Bernoulli abandonment

Abstract

This paper considers a state-dependent M/M/$c$/$c+r$ retrial queuewith Bernoulli abandonment, where the number of servers is equal to$c$, the capacity of the buffer is equal to $r$ and that of thevirtual waiting room (called orbit) for the retrial customers is infinite.We assume that the arrival,service and retrial rates depend on the number of customers in thesystem (the servers and buffer).In this paper, we first present the ergodic conditionfor our retrial queue. Then, by a continued fraction approach, wederive analytical solutions for the stationary joint distribution ofthe queue lengths in the system and in the orbit, assuming thatthe capacity of the system is less than or equal to 4. We further showthat our analytical solutions can be computed with any desired accuracy.Finally, we present some numerical results to show theimpact of the parameters on the performance of the system.