Multiserver retrial queues with after-call work (Q428999)

The authors study a \(c\)-server retrial system with finite capacity \(K\); a blocked customer joins an infinite virtual capacity orbit and then retries to occupy the server again. Unlike classical retrial queues, an extra after-call work is done by server after a customer leaves the system. The case \(K<c\) is also discussed. A quasi-birth-death Markov process is constructed to obtain a stability condition for the system. Unfortunately, the authors do not mention that it is a very particular case of the well-known stability result for general multiserver retrial system. A truncation by means of a finite capacity system (with a limited orbit) is used to derive an approximation of stationary distribution. Some numerical results are also given.