An M/G/1 retrial queueing system with two phases of service of which the second phase is optional and the server operating under Bernoulli vacation schedule is investigated. Further, the customer is allowed to balk upon arrival if he finds the server unavailable to serve his request immediately. The joint generating functions of orbit size and server status are derived using supplementary variable technique. Some important performance measures like the orbit size, the system size, the server utilisation and the probability that the system is empty are found. Stochastic decomposition law is established when there is no balking permitted. Some existing results are derived as special cases of our model under study. Interestingly, these performance measures are compared for various vacation schedules namely exhaustive service, 1-limited service, Bernoulli vacation and modified Bernoulli vacation schedules. Extensive numerical analysis is carried out to exhibit the effect of the system parameters on the performance measures.
Accepté le :
DOI : 10.1051/ro/2017029
Mots-clés : Retrial queue, two phase service, balking, Bernoulli vacation, modified Bernoulli vacation, supplementary variable, stochastic decomposition
@article{RO_2019__53_2_415_0,
author = {Madheswari, S. Pavai and Krishna Kumar, B. and Suganthi, P.},
title = {Analysis of {M/G/1} retrial queues with second optional service and customer balking under two types of {Bernoulli} vacation schedule},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {415--443},
publisher = {EDP-Sciences},
volume = {53},
number = {2},
year = {2019},
doi = {10.1051/ro/2017029},
zbl = {1423.60143},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ro/2017029/}
}
TY - JOUR AU - Madheswari, S. Pavai AU - Krishna Kumar, B. AU - Suganthi, P. TI - Analysis of M/G/1 retrial queues with second optional service and customer balking under two types of Bernoulli vacation schedule JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2019 SP - 415 EP - 443 VL - 53 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2017029/ DO - 10.1051/ro/2017029 LA - en ID - RO_2019__53_2_415_0 ER -
%0 Journal Article %A Madheswari, S. Pavai %A Krishna Kumar, B. %A Suganthi, P. %T Analysis of M/G/1 retrial queues with second optional service and customer balking under two types of Bernoulli vacation schedule %J RAIRO - Operations Research - Recherche Opérationnelle %D 2019 %P 415-443 %V 53 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2017029/ %R 10.1051/ro/2017029 %G en %F RO_2019__53_2_415_0
Madheswari, S. Pavai; Krishna Kumar, B.; Suganthi, P. Analysis of M/G/1 retrial queues with second optional service and customer balking under two types of Bernoulli vacation schedule. RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 2, pp. 415-443. doi : 10.1051/ro/2017029. http://www.numdam.org/articles/10.1051/ro/2017029/
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