This paper analysis a discrete time infinite capacity queueing system with correlated arrival and negative customers served by two state Markovian server. Positive customers are generated according to the first order Markovian arrival process with geometrically distributed lengths of On periods and Off periods. Further, the geometrically distributed arrival of negative customer removes the positive customers is any, and has no effect when the system is empty. The server state is a two state Markov chain which alternate between Good and Bad states with geometrically distributed service times. Closed-form expressions for mean queue length, unfinished work and sojourn time distributions are obtained. Numerical illustrations are also presented.
Accepté le :
DOI : 10.1051/ro/2015012
Mots clés : On-OffSource, negative customers, two state Markovian server, sojourn time distribution
@article{RO_2016__50_1_67_0,
author = {Senthil Vadivu, A. and Arumuganathan, R. and Senthil Kumar, M.},
title = {Analysis of {Discrete-time} queues with correlated arrivals, negative customers and server interruption},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {67--81},
publisher = {EDP-Sciences},
volume = {50},
number = {1},
year = {2016},
doi = {10.1051/ro/2015012},
zbl = {1335.60175},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ro/2015012/}
}
TY - JOUR AU - Senthil Vadivu, A. AU - Arumuganathan, R. AU - Senthil Kumar, M. TI - Analysis of Discrete-time queues with correlated arrivals, negative customers and server interruption JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2016 SP - 67 EP - 81 VL - 50 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2015012/ DO - 10.1051/ro/2015012 LA - en ID - RO_2016__50_1_67_0 ER -
%0 Journal Article %A Senthil Vadivu, A. %A Arumuganathan, R. %A Senthil Kumar, M. %T Analysis of Discrete-time queues with correlated arrivals, negative customers and server interruption %J RAIRO - Operations Research - Recherche Opérationnelle %D 2016 %P 67-81 %V 50 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2015012/ %R 10.1051/ro/2015012 %G en %F RO_2016__50_1_67_0
Senthil Vadivu, A.; Arumuganathan, R.; Senthil Kumar, M. Analysis of Discrete-time queues with correlated arrivals, negative customers and server interruption. RAIRO - Operations Research - Recherche Opérationnelle, Tome 50 (2016) no. 1, pp. 67-81. doi : 10.1051/ro/2015012. http://www.numdam.org/articles/10.1051/ro/2015012/
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