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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 multipleworking vacations where services are performed in batches of maximum size “b”. The service times bothduring a regular service period and vacation period and vacation times are geometricallydistributed. Employing the supplementary variable and imbedded Markov chain techniques, wederive the steady-state queue length distributions at pre-arrival, arbitrary and outsideobserver’s observation epochs. Based on the queue length distributions, some performancemeasures and waiting time distribution in the queue have been discussed. Finally,numerical results showing the effect of model parameters on the key performance measuresare 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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References

H. Bruneel and B.G. Kim, Discrete-time models for communication systems including ATM. Kluwer Academic Publishers, Boston (1983).
M.L. Chaudhry and J.G.C. Templeton, A first course in bulk queues. Wiley, New York (1983).
Goswami, V. and Mund, G.B., Analysis of discrete-time GI / Geo /1 / N queue with multiple working vacations. J. Sys. Sci. Sys. Eng. 19 (2011) 367–384. Google Scholar
Goswami, V. and Vijaya Laxmi, P., Analysis of finite-buffer discrete-time batch-service queue with multiple vacations. Int. J. Inform. Manage. Sci. 22 (2011) 291–310. Google Scholar
Gravey, A. and Hébuterne, G., Simultaneity in discrete-time single server queues with Bernoulli inputs. Perform. Eval. 14 (1992) 123–131. Google Scholar
Gupta, U.C. and Goswami, V., Performance analysis of finite buffer discrete-time queue with bulk service. Comput. Oper. Res. 29 (2002) 1331–1341. Google Scholar
Hajek, B., The proof of a folk theorem on queueing delay with applications to routing in networks. J. Assoc. Comput. Mach. 30 (1983) 834-851. Google Scholar
J.J. Hunter, Mathematical techniques of applied probability. Volume 2. Discrete-time models: Techniques and applications. Academic Press, New York (1983).
C. Jiang, T. Yinghui and Y. Miaomiao, The discrete-time bulk service Geo / Geo / 1 queue with multiple working vacations. J. App. Math. (2013) doi.org/10.1155/2013/587269.
G. Latouche and V. Ramaswami, Introdction to matrix analytic method in stochastic modelling. SIAM and ASA, Philadelphia (1990).
Li, J., Tian, N. and Liu, W., Discrete-time GI / Geo /1 queue with multiple working vacations. Queueing Sys. 56 (2007) 53–63. Google Scholar
Li, J. and Tian, N., The discrete-time GI / Geo / 1 queue with working vacations and vacation interruption. App. Math. Comput. 185 (2007) 1–10. Google Scholar
Servi, L.D. and Finn, S.G., M / M / 1 queue with working vacations M / M /1/ N / WV. Perform. Eval. 50 (2002) 41–52. Google Scholar
Tian, N., Ma, Z. and Liu, M., The discrete time Geom / Geom /1 queue with multiple working vacations. App. Math. Modell. 32 (2008) 2941–2953. Google Scholar
H. Takagi, Queueing analysis - A foundation of performance evaluation. Volume 3. Discrete-time systems. North Holland, Amsterdam (1993).
M.E. Woodward, Communication and computer networks: Modelling with discrete-time queues. Los Alamitos, CA: IEEE Computer Society, Press (1994).
Yu, M., Tang, Y., Fu, Y. and Pan, L., GI / Geom / 1 / N / MWV queue with changeover time and searching for the optimum service rate in working vacation period. J. Comput. App. Math. 235 (2011) 2170–2184.Google Scholar