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| Discrete time Geom/Geom/1 queue with negative customers and multiple working vacations |
| Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, China |
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Abstract Concerning that the server works at a lower rate rather than completely stop service during the exhaustive service and multiple working vacations, where the negative customer only removes the positive customer one by one at the end, and by introducing the negative customers and multiple working vacations into discrete-time queue, the method of embed Markov chains is used. The transition probability of diagonal matrix and the solution of rate matrix R are obtained by the formula of extracting roots on cubic equation. After that the system equilibrium conditions and distributions and the stochastic decomposition of the queue length under the steady-state distributions in the system are reached. Finally the multiple working vacations in discrete-time queuing models are further extended
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2010, Vol. 31 
