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envIn this paper, we analyze an queue operating in multi-phase random environment with vacation policy. In operative phase customers are served according to the discipline of First Come First Served (FCFS). When the system becomes empty, the server takes a vacation under the policy, causing the system to move to vacation phase . At the end of a vacation, if the server finds no customer waiting, another vacation begins. Otherwise, the system jumps from the phase to some operative phase with probability . And whenever the number of the waiting customers in the system reaches , the server interrupts its vacation immediately and the system jumps from the phase to some operative phase with probability , too. Using the method of supplementary variable, we derive the distribution for the stationary system size at arbitrary epoch. We also obtain mean system size, the results of the cycle analysis and the sojourn time distribution. In addition, some special cases and numerical examples are presented.
Keywords: M∕G∕1 queue, vacation, sojourn time, Min(N, V) policy, random environment, queueing theory
Li, Jianjun 1 ; Liu, Liwei 1
@article{RO_2018__52_1_61_0,
author = {Li, Jianjun and Liu, Liwei},
title = {On an $M / G / 1$ queue in random environment with $Min (N , V)$ policy},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {61--77},
publisher = {EDP-Sciences},
volume = {52},
number = {1},
year = {2018},
doi = {10.1051/ro/2018006},
zbl = {1394.60093},
mrnumber = {3812469},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ro/2018006/}
}
TY - JOUR AU - Li, Jianjun AU - Liu, Liwei TI - On an $M / G / 1$ queue in random environment with $Min (N , V)$ policy JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2018 SP - 61 EP - 77 VL - 52 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ro/2018006/ DO - 10.1051/ro/2018006 LA - en ID - RO_2018__52_1_61_0 ER -
%0 Journal Article %A Li, Jianjun %A Liu, Liwei %T On an $M / G / 1$ queue in random environment with $Min (N , V)$ policy %J RAIRO - Operations Research - Recherche Opérationnelle %D 2018 %P 61-77 %V 52 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ro/2018006/ %R 10.1051/ro/2018006 %G en %F RO_2018__52_1_61_0
Li, Jianjun; Liu, Liwei. On an $M / G / 1$ queue in random environment with $Min (N , V)$ policy. RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 1, pp. 61-77. doi: 10.1051/ro/2018006
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