Finite population multi-server retrial queueing system with an optional service and balking

In this paper, we study the retrial queueing system with an optional service and finite population subject to balking. If all the m servers are busy, a customer on arrival may decide to retry or balk from the system. On finding the free server, the arriving customers request for the essential service and then few of them may demand the optional service. All the random variables involved are exponentially distributed. The constructed model is examined as a quasi-birth and death process. The matrix-analytic approach is employed for the performance analysis of the concerned queueing model. Expressions for various performance measures are obtained in matrix form. For validation, the sensitivity analysis is also done by varying different system descriptors. © 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.