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Finite buffer GI/Geo/ 1 batch servicing queue with multiple working vacations

Published online by Cambridge University Press:  11 July 2014

P. Vijaya Laxmi  and
Kanithi Jyothsna
P. Vijaya Laxmi
Affiliation:
Department of Applied Mathematics, Andhra University, Visakhapatnam 530 003, India.. vijayaiit2003@yahoo.co.in; mail2jyothsnak@yahoo.co.in
Kanithi Jyothsna
Affiliation:
Department of Applied Mathematics, Andhra University, Visakhapatnam 530 003, India.. vijayaiit2003@yahoo.co.in; mail2jyothsnak@yahoo.co.in
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Abstract

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.

Keywords

Discrete-timefinite bufferbatch servicemultiple working vacationswaiting time
Type
Research Article
Information
RAIRO - Operations Research , Volume 48 , Issue 4 , October 2014 , pp. 521 - 543
Copyright
© EDP Sciences, ROADEF, SMAI 2014

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