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.
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] and , 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] , and , 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] and , 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] and , 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] and , A first course in bulk queues. New York, John Wiley and Sons (1983). | MR | Zbl
[6] , Single server queues with vacations : a survey, Queueing Systems. I (1986) 29-66. | Zbl
[7] , 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] and , 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] and , 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] , and , Algorithmic analysis of the multi-server system with a modified Bernoulli vacation schedule. Appl. Math. Model. 35 (2011) 2196-2208. | MR | Zbl
[11] and , The M/M/1 queue with working vacations and vacation interruptions. J. Syst. Sci. Eng. 16 (2007) 121-127. | MR | Zbl
[12] , and , Performance analysis of GI/M/1 queue with working vacations and vacation interruption. Appl. Math. Model. 32 (2008) 2715-2730. | MR | Zbl
[13] and , Performance analysis of a GI/M/1 queue with single working vacation. Appl. Math. Comput. 217 (2001) 4960-4971. | MR | Zbl
[14] , and , Analysis of a bulk queue with N-policy, multiple vacations and setup times. Comput. Oper. Res. 25 (1998) 957-967. | MR | Zbl
[15] , , and , Analysis of the Mx / G / 1 queue with N-policy and multiple vacations. J. Appl. Prob. 31 (1994) 476-496. | MR | Zbl
[16] and , The discrete-time GI/Geo/1 queue with working vacations and vacation interruption. Appl. Math. Comput. 185 (2007) 1-10. | MR | Zbl
[17] , Recent Developments in Bulk Queueing Models. Wiley Eastern Ltd. New Delhi (1984). | MR
[18] and , Performance analysis of M/G/1 queue with working vacations and vacation interruption. J. Comput. Appl. Math. 234 (2010) 2977-2985. | MR | Zbl
[19] and , Performance analysis of MAP/G/1 queue with working vacations and vacation interruption. Appl. Math. Modell. 35 (2011) 1551-1560. | MR | Zbl
[20] and , Semi-Markov processes and reliability- Statistics for Industry and Technology Birkhauser Boston, Springer (2001). | MR | Zbl
[21] , Queueing Analysis : A foundation of Performance Evaluation, Vacation and Priority Systems. North Holland, Amsterdam (1991), Vol. 1. | MR | Zbl
[22] and , Vacation Queueing Models : Theory and Applications. Springer, New York (2006). | MR | Zbl
[23] , The M/PH/1 queue with working vacations and vacation interruption. J. Syst. Sci. Eng. 19 (2010) 496-503.
Cité par Sources :
