| Issue |
RAIRO-Oper. Res.
Volume 51, Number 2, April-June 2017
|
|
|---|---|---|
| Page(s) | 485 - 508 | |
| DOI | https://doi.org/10.1051/ro/2016037 | |
| Published online | 07 April 2017 | |
Modelling and analysis of a bulk service queueing model with multiple working vacations and server breakdown
1 Department of Mathematics, Government Arts College, Coimbatore, India.
jeyakumar19@yahoo.co.in
2 Department of Mathematics, Jansons Institute of Technology, Coimbatore, India.
svbsn2@yahoo.com
Received: 17 July 2014
Accepted: 26 April 2016
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.
Mathematics Subject Classification: 60K20 / 60K25 / 68M20 / 90B22
Key words: Queue / bulk service / multiple working vacations / server breakdown / supplementary variables
© EDP Sciences, ROADEF, SMAI 2017
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