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The threshold policy for the restoration of an unreliable server in a service system with bulk input and balking is investigated. The arriving customers in the queueing system are classified into two categories i.e. priority and ordinary customers. The priority customers are assumed to join the system in groups according to Poisson process. The ordinary customers join the system singly and require the essential service as well as optional service on demand and only a limited number of customers can wait in the queue when the server is busy. The service times of both types of customers and life time as well as repair time of the server are governed by the exponential distribution. When the server fails during the service of the ordinary customer, the repair is done following a threshold recovery rule according to which the repair of the failed server is started only when at least q ordinary customers are accumulated in the system. In case of failure while rendering the service to the priority customers, the server is immediately sent for the repair. The matrix geometric method (MGM) has been used to establish the queue size distribution and other performance indices. To validate the suggested MGM approach, numerical simulation is carried out by taking an illustration.
Jain, Madhu 1
@article{RO_2017__51_2_417_0,
author = {Jain, Madhu},
title = {Priority queue with batch arrival, balking, threshold recovery, unreliable server and optimal service},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {417--432},
publisher = {EDP-Sciences},
volume = {51},
number = {2},
year = {2017},
doi = {10.1051/ro/2016032},
mrnumber = {3657432},
zbl = {1367.60113},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ro/2016032/}
}
TY - JOUR AU - Jain, Madhu TI - Priority queue with batch arrival, balking, threshold recovery, unreliable server and optimal service JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2017 SP - 417 EP - 432 VL - 51 IS - 2 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ro/2016032/ DO - 10.1051/ro/2016032 LA - en ID - RO_2017__51_2_417_0 ER -
%0 Journal Article %A Jain, Madhu %T Priority queue with batch arrival, balking, threshold recovery, unreliable server and optimal service %J RAIRO - Operations Research - Recherche Opérationnelle %D 2017 %P 417-432 %V 51 %N 2 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ro/2016032/ %R 10.1051/ro/2016032 %G en %F RO_2017__51_2_417_0
Jain, Madhu. Priority queue with batch arrival, balking, threshold recovery, unreliable server and optimal service. RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 2, pp. 417-432. doi: 10.1051/ro/2016032
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