Finite buffer GI/Geo/1 batch servicing queue with multiple working vacations
RAIRO - Operations Research - Recherche Opérationnelle, Tome 48 (2014) no. 4, pp. 521-543.

This paper analyzes a discrete-time finite buffer renewal input queue with multiple working vacations where services are performed in batches of maximum size “b”. The service times both during a regular service period and vacation period and vacation times are geometrically distributed. Employing the supplementary variable and imbedded Markov chain techniques, we derive the steady-state queue length distributions at pre-arrival, arbitrary and outside observer's observation epochs. Based on the queue length distributions, some performance measures and waiting time distribution in the queue have been discussed. Finally, numerical results showing the effect of model parameters on the key performance measures are presented.

DOI : 10.1051/ro/2014022
Classification : 60K25, 90B22
Mots-clés : discrete-time, finite buffer, batch service, multiple working vacations, waiting time 
@article{RO_2014__48_4_521_0,
     author = {Vijaya Laxmi, P. and Jyothsna, Kanithi},
     title = {Finite buffer $GI/Geo/ 1$ batch servicing queue with multiple working vacations},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {521--543},
     publisher = {EDP-Sciences},
     volume = {48},
     number = {4},
     year = {2014},
     doi = {10.1051/ro/2014022},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ro/2014022/}
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Vijaya Laxmi, P.; Jyothsna, Kanithi. Finite buffer $GI/Geo/ 1$ batch servicing queue with multiple working vacations. RAIRO - Operations Research - Recherche Opérationnelle, Tome 48 (2014) no. 4, pp. 521-543. doi : 10.1051/ro/2014022. http://www.numdam.org/articles/10.1051/ro/2014022/

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