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.
Accepté le :
DOI : 10.1051/ro/2016037
Mots-clés : Queue, bulk service, multiple working vacations, server breakdown, supplementary variables
@article{RO_2017__51_2_485_0,
author = {Jeyakumar, S. and Senthilnathan, B.},
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},
volume = {51},
number = {2},
year = {2017},
doi = {10.1051/ro/2016037},
zbl = {1367.60114},
mrnumber = {3657436},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ro/2016037/}
}
TY - JOUR AU - Jeyakumar, S. AU - Senthilnathan, B. TI - Modelling and analysis of a bulk service queueing model with multiple working vacations and server breakdown JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2017 SP - 485 EP - 508 VL - 51 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2016037/ DO - 10.1051/ro/2016037 LA - en ID - RO_2017__51_2_485_0 ER -
%0 Journal Article %A Jeyakumar, S. %A Senthilnathan, B. %T Modelling and analysis of a bulk service queueing model with multiple working vacations and server breakdown %J RAIRO - Operations Research - Recherche Opérationnelle %D 2017 %P 485-508 %V 51 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2016037/ %R 10.1051/ro/2016037 %G en %F RO_2017__51_2_485_0
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. http://www.numdam.org/articles/10.1051/ro/2016037/
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