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The Discrete Time Geo G/ /1 Queue with Negative Customers and Multiple Working Vacations

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Author(s): Yanheng Chen,Songfang Jia

Journal: International Journal of Engineering Research
ISSN 2319-6890

Volume: 2;
Issue: 6;
Start page: 393;
Date: 2013;
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Keywords: Keywords—Multiple vacation | Negative customers | Discrete time | PGF

ABSTRACT
—In this article, we study the discrete timeGeo G/ /1 queue with negative customers and multiple working vacations. Under the RCH disciple, the arrival of a negative customer does not receive service and removes the positive customer who is being served. Using embedded Markov chain and matrix analytic approach, we derive the probability generating function (PGF) and mean of the stationary queue length at the departure epoch. From the process of the proof and the results, we also obtain theprobabilities that the server is in idle, working vacation, and regular busy period, respectively. Finally, we discussnumerical results.
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