A discrete-time Geo/G/1 retrial queue with \(J\)-vacation policy and general retrial times.

*(English)*Zbl 1292.90094Summary: The authors discuss a discrete-time Geo/G/1 retrial queue with \(J\)-vacation policy and general retrial times. As soon as the orbit is empty, the server takes a vacation. However, the server is allowed to take a maximum number \(J\) of vacations, if the system remains empty after the end of a vacation. If there is at least one customer in the orbit at the end of a vacation, the server begins to serve the new arrivals or the arriving customers from the orbit. For this model, the authors focus on the steady-state analysis for the considered queueing system. Firstly, the authors obtain the generating functions of the number of customers in the orbit and in the system. Then, the authors obtain the closed-form expressions of some performance measures of the system and also give a stochastic decomposition result for the system size. Besides, the relationship between this discrete-time model and the corresponding continuous-time model is also investigated. Finally, some numerical results are provided.

##### MSC:

90B22 | Queues and service in operations research |

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\textit{D. Yue} and \textit{F. Zhang}, J. Syst. Sci. Complex. 26, No. 4, 556--571 (2013; Zbl 1292.90094)

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