Analysis of a M X /G(a,b)/1 queueing system with vacation interruption
RAIRO - Operations Research - Recherche Opérationnelle, Tome 46 (2012) no. 4, pp. 305-334.

In this paper, a batch arrival general bulk service queueing system with interrupted vacation (secondary job) is considered. At a service completion epoch, if the server finds at least ‘a' customers waiting for service say ξ, he serves a batch of min (ξ, b) customers, where b ≥ a. On the other hand, if the queue length is at the most ‘a-1', the server leaves for a secondary job (vacation) of random length. It is assumed that the secondary job is interrupted abruptly and the server resumes for primary service, if the queue size reaches ‘a', during the secondary job period. On completion of the secondary job, the server remains in the system (dormant period) until the queue length reaches ‘a'. For the proposed model, the probability generating function of the steady state queue size distribution at an arbitrary time is obtained. Various performance measures are derived. A cost model for the queueing system is also developed. To optimize the cost, a numerical illustration is provided.

DOI : 10.1051/ro/2012018
Classification : 60K25, 60K20, 90B22, 68M20
Mots clés : bulk arrival, single server, batch service, vacation, interruption
@article{RO_2012__46_4_305_0,
     author = {Haridass, M. and Arumuganathan, R.},
     title = {Analysis of a {M}$^X$/$\mathrm {G}(a,b)$/$1$ queueing system with vacation interruption},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {305--334},
     publisher = {EDP-Sciences},
     volume = {46},
     number = {4},
     year = {2012},
     doi = {10.1051/ro/2012018},
     zbl = {1268.60113},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ro/2012018/}
}
TY  - JOUR
AU  - Haridass, M.
AU  - Arumuganathan, R.
TI  - Analysis of a M$^X$/$\mathrm {G}(a,b)$/$1$ queueing system with vacation interruption
JO  - RAIRO - Operations Research - Recherche Opérationnelle
PY  - 2012
SP  - 305
EP  - 334
VL  - 46
IS  - 4
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ro/2012018/
DO  - 10.1051/ro/2012018
LA  - en
ID  - RO_2012__46_4_305_0
ER  - 
%0 Journal Article
%A Haridass, M.
%A Arumuganathan, R.
%T Analysis of a M$^X$/$\mathrm {G}(a,b)$/$1$ queueing system with vacation interruption
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 2012
%P 305-334
%V 46
%N 4
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/ro/2012018/
%R 10.1051/ro/2012018
%G en
%F RO_2012__46_4_305_0
Haridass, M.; Arumuganathan, R. Analysis of a M$^X$/$\mathrm {G}(a,b)$/$1$ queueing system with vacation interruption. RAIRO - Operations Research - Recherche Opérationnelle, Tome 46 (2012) no. 4, pp. 305-334. doi : 10.1051/ro/2012018. http://www.numdam.org/articles/10.1051/ro/2012018/

[1] R. Arumuganathan and S. Jeyakumar, 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. | Zbl

[2] M. Balasubramanian, R. Arumuganathan and A. Senthil Vadivu, Steady state analysis of a non-Markovian bulk queueing system with overloading and multiple vacations. Int. J. Oper. Res. 9 (2010) 82-103. | MR | Zbl

[3] M. Balasubramanian and R. Arumuganathan, 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. | MR | Zbl

[4] A. Borthakur and J. Medhi, A queueing system with arrival and services in batches of variable size. Cahiers du. C.E.R.O. 16 (1974) 117-126. | MR | Zbl

[5] M.L. Chaudhry and J.G.C. Templeton, A first course in bulk queues. New York, John Wiley and Sons (1983). | MR | Zbl

[6] B.T. Doshi, Single server queues with vacations : a survey, Queueing Systems. I (1986) 29-66. | Zbl

[7] 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. | MR

[8] M. Haridass and R. Arumuganathan, 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. | MR | Zbl

[9] H. Zhang and D. Shi, The M/M/1 queue with Bernoulli-Schedule-Controlled vacation and vacation interruption. Int. J. Inf. Manag. Sci. 20 (2009) 579-587. | MR | Zbl

[10] Jau-Chuan Ke, Chia-Huang Wu and Wen Lea Pearn, Algorithmic analysis of the multi-server system with a modified Bernoulli vacation schedule. Appl. Math. Model. 35 (2011) 2196-2208. | MR | Zbl

[11] Ji-Hong Li and Nai-Shuo Tian, The M/M/1 queue with working vacations and vacation interruptions. J. Syst. Sci. Eng. 16 (2007) 121-127. | MR | Zbl

[12] Ji-Hong Li, Nai-Shuo Tian and Zhan-You Ma, Performance analysis of GI/M/1 queue with working vacations and vacation interruption. Appl. Math. Model. 32 (2008) 2715-2730. | MR | Zbl

[13] Ji-Hong Li and Nai-Shuo Tian, Performance analysis of a GI/M/1 queue with single working vacation. Appl. Math. Comput. 217 (2001) 4960-4971. | MR | Zbl

[14] G.V Krishna Reddy, R. Nadarajan and R. Arumuganathan, Analysis of a bulk queue with N-policy, multiple vacations and setup times. Comput. Oper. Res. 25 (1998) 957-967. | MR | Zbl

[15] H.W. Lee, S.S Lee, J.O Park and K.C. Chae, Analysis of the Mx / G / 1 queue with N-policy and multiple vacations. J. Appl. Prob. 31 (1994) 476-496. | MR | Zbl

[16] J. Li and N. Tian, The discrete-time GI/Geo/1 queue with working vacations and vacation interruption. Appl. Math. Comput. 185 (2007) 1-10. | MR | Zbl

[17] J. Medhi, Recent Developments in Bulk Queueing Models. Wiley Eastern Ltd. New Delhi (1984). | MR

[18] Mian Zhang and Zhengting Hou, Performance analysis of M/G/1 queue with working vacations and vacation interruption. J. Comput. Appl. Math. 234 (2010) 2977-2985. | MR | Zbl

[19] Mian Zhang and Zhengting Hou, Performance analysis of MAP/G/1 queue with working vacations and vacation interruption. Appl. Math. Modell. 35 (2011) 1551-1560. | MR | Zbl

[20] N. Limnios and Gheorghe Oprisan, Semi-Markov processes and reliability- Statistics for Industry and Technology Birkhauser Boston, Springer (2001). | MR | Zbl

[21] H. Takagi, Queueing Analysis : A foundation of Performance Evaluation, Vacation and Priority Systems. North Holland, Amsterdam (1991), Vol. 1. | MR | Zbl

[22] N. Tian and S.G. Zhang, Vacation Queueing Models : Theory and Applications. Springer, New York (2006). | MR | Zbl

[23] Y. Baba, The M/PH/1 queue with working vacations and vacation interruption. J. Syst. Sci. Eng. 19 (2010) 496-503.

Cité par Sources :