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# Multiserver retrial queues with after-call work

• This paper considers a multiserver queueing system with finite capacity. Customers that find the service facility being fully occupied are blocked and enter a virtual waiting room (called orbit). Blocked customers stay in the orbit for an exponentially distributed time and retry to occupy an idle server again. After completing a service, the server starts an additional job that we call an after-call work. We formulate the queueing system using a continuous-time level-dependent quasi-birth-and-death process, for which a sufficient condition for the ergodicity is derived. We obtain an approximation to the stationary distribution by a direct truncation method whose truncation point is simply determined using an asymptotic analysis of a single server retrial queue. Some numerical examples are presented in order to show the influence of parameters on the performance of the system.
Mathematics Subject Classification: Primary: 60K25, 68M20; Secondary: 90B22.

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