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Analysis of a MX/G(a,b)/1 queueing system withvacation interruption

Published online by Cambridge University Press:  08 November 2012

M. Haridass  and
R. Arumuganathan
M. Haridass
Affiliation:
Department of Mathematics, PSG College of Technology, 641 004 Coimbatore, Tamil Nadu, India. irahpsg@yahoo.com; psgtech@yahoo.co.in
R. Arumuganathan
Affiliation:
Department of Mathematics, PSG College of Technology, 641 004 Coimbatore, Tamil Nadu, India. irahpsg@yahoo.com; psgtech@yahoo.co.in
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Abstract

In this paper, a batch arrival general bulk service queueing system with interruptedvacation (secondary job) is considered. At a service completion epoch, if the server findsat least ‘a’ customers waiting for service say ξ, heserves a batch of min (ξ, b) customers, whereb ≥ a. On the other hand, if the queue length is atthe most ‘a-1’, the server leaves for a secondary job (vacation) ofrandom length. It is assumed that the secondary job is interrupted abruptly and the serverresumes for primary service, if the queue size reaches ‘a’, during thesecondary job period. On completion of the secondary job, the server remains in the system(dormant period) until the queue length reaches ‘a’. For the proposedmodel, the probability generating function of the steady state queue size distribution atan arbitrary time is obtained. Various performance measures are derived. A cost model forthe queueing system is also developed. To optimize the cost, a numerical illustration isprovided.

Keywords

Bulk arrivalsingle serverbatch servicevacationinterruption
Type
Research Article
Information
RAIRO - Operations Research , Volume 46 , Issue 4 , October 2012 , pp. 305 - 334
Copyright
© EDP Sciences, ROADEF, SMAI, 2012

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References

Arumuganathan, R. and Jeyakumar, S., Steady state analysis of a bulk queue with multiple vacations, setup times with N-policy and closedown times. Appl. Math. Modell. 29 (2005) 972–986. Google Scholar
Balasubramanian, M., Arumuganathan, R. and Senthil Vadivu, A. , Steady state analysis of a non-Markovian bulk queueing system with overloading and multiple vacations. Int. J. Oper. Res. 9 (2010) 82–103. Google Scholar
Balasubramanian, M. and Arumuganathan, R., Steady state analysis of a bulk arrival general bulk service queueing system with modififed M-vacation policy and variant arrival rate. Int. J. Oper. Res. 11 (2011) 383–407. Google Scholar
Borthakur, A. and Medhi, J., A queueing system with arrival and services in batches of variable size. Cahiers du. C.E.R.O. 16 (1974) 117–126. Google Scholar
M.L. Chaudhry and J.G.C. Templeton, A first course in bulk queues. New York, John Wiley and Sons (1983).
Doshi, B.T., Single server queues with vacations : a survey, Queueing Systems. I (1986) 29–66. Google Scholar
B.T. Doshi, Single server queues with vacation, Stochastic Analysis of the Computer and Communication Systems, edited by H. Takagi. North-Holland/Elsevier, Amsterdam (1990) 217–264.
Haridass, M. and Arumuganathan, R., Analysis of a batch arrival general bulk service queueing system with variant threshold policy for secondary jobs. Int. J. Math. Oper. Res. 3 (2011) 56–77. Google Scholar
Zhang, H. and Shi, D., The M/M/1 queue with Bernoulli-Schedule-Controlled vacation and vacation interruption. Int. J. Inf. Manag. Sci. 20 (2009) 579–587. Google Scholar
Ke, Jau-Chuan, Wu, Chia-Huang and Pearn, Wen Lea, Algorithmic analysis of the multi-server system with a modified Bernoulli vacation schedule. Appl. Math. Model. 35 (2011) 2196–2208. Google Scholar
Li, Ji-Hong and Tian, Nai-Shuo, The M/M/1 queue with working vacations and vacation interruptions. J. Syst. Sci. Eng. 16 (2007) 121–127. Google Scholar
Li, Ji-Hong, Tian, Nai-Shuo and Ma, Zhan-You, Performance analysis of GI/M/1 queue with working vacations and vacation interruption. Appl. Math. Model. 32 (2008) 2715–2730. Google Scholar
Li, Ji-Hong and Tian, Nai-Shuo, Performance analysis of a GI/M/1 queue with single working vacation. Appl. Math. Comput. 217 (2001) 4960–4971. Google Scholar
Krishna Reddy, G.V, Nadarajan, R. and Arumuganathan, R., Analysis of a bulk queue with N-policy, multiple vacations and setup times. Comput. Oper. Res. 25 (1998) 957–967. Google Scholar
Lee, H.W., Lee, S.S, Park, J.O and Chae, K.C., Analysis of the M x / G / 1 queue with N-policy and multiple vacations. J. Appl. Prob. 31 (1994) 476–496. Google Scholar
Li, J. and Tian, N., The discrete-time GI/Geo/1 queue with working vacations and vacation interruption. Appl. Math. Comput. 185 (2007) 1–10. Google Scholar
J. Medhi, Recent Developments in Bulk Queueing Models. Wiley Eastern Ltd. New Delhi (1984).
Zhang, Mian and Hou, Zhengting, Performance analysis of M/G/1 queue with working vacations and vacation interruption. J. Comput. Appl. Math. 234 (2010) 2977–2985. Google Scholar
Zhang, Mian and Hou, Zhengting, Performance analysis of MAP/G/1 queue with working vacations and vacation interruption. Appl. Math. Modell. 35 (2011) 1551–1560. Google Scholar
N. Limnios and Gheorghe Oprisan, Semi-Markov processes and reliability- Statistics for Industry and Technology Birkhauser Boston, Springer (2001).
H. Takagi, Queueing Analysis : A foundation of Performance Evaluation, Vacation and Priority Systems. North Holland, Amsterdam (1991), Vol. 1.
N. Tian and S.G. Zhang, Vacation Queueing Models : Theory and Applications. Springer, New York (2006).
Baba, Y., The M/PH/1 queue with working vacations and vacation interruption. J. Syst. Sci. Eng. 19 (2010) 496–503.Google Scholar