Geodesic
Modelling and analysis of a bulk service queueing model with multiple working vacations and server breakdown
Jeyakumar, S.1 ; Senthilnathan, B.2
1 Department of Mathematics, Government Arts College, Coimbatore, India.
2 Department of Mathematics, Jansons Institute of Technology, Coimbatore, India.
RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 2, pp. 485-508

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In this paper, a single server queue with variable batch size service, Poisson bulk arrival with multiple working vacations and server breakdown is considered. In working vacation, the server works with different rates rather than completely stoping the service during the vacation period. In this model, during the working vacation the server starts the service if it finds at least one customer in the queue with a maximum of ‘b’ customers, otherwise the server serves with variable batch size. Service time in working vacation and in regular period follows general distribution. The probability generating function of a queue size at an arbitrary time epoch as well as other completion epochs is derived. Expected queue length in a steady state is obtained. Also a numerical illustration is presented.

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DOI : 10.1051/ro/2016037
Classification : 60K20, 60K25, 68M20, 90B22
Keywords: Queue, bulk service, multiple working vacations, server breakdown, supplementary variables

Jeyakumar, S. 1 ; Senthilnathan, B. 2

1 Department of Mathematics, Government Arts College, Coimbatore, India.
2 Department of Mathematics, Jansons Institute of Technology, Coimbatore, India. 
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     title = {Modelling and analysis of a bulk service queueing model with multiple working vacations and server breakdown},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {485--508},
     publisher = {EDP-Sciences},
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Jeyakumar, S.; Senthilnathan, B. Modelling and analysis of a bulk service queueing model with multiple working vacations and server breakdown. RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 2, pp. 485-508. doi: 10.1051/ro/2016037

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