This paper considers a single-server queueing system with server breakdowns. When the server fails, it is sent to repair immediately and its maintenance rate is allowed to be adjustable. The goal is to find the optimal maintenance rates that minimize the long-run average cost of the system. We address the static and dynamic maintenance control problems respectively. For the static control model, we derive the stationary system performances and the explicit solution of the optimal maintenance rate. Then regarding the dynamic maintenance problem, we formulate it as a Markov decision process (MDP) and the optimal dynamic policy is proved to be a threshold policy. Based on the structure of optimal dynamic policy, we construct a performance evaluation for computing efficiently the optimal threshold and average cost. Finally, a comparative study of the dynamic and static policies is presented by numerical experiment which shows the impact of system parameters on the optimal maintenance policies.
Keywords: Queueing system, maintenance rate, MDP, performance evaluation
@article{RO_2021__55_S1_S1339_0,
author = {Chen, Gang and Liu, Zaiming and Chu, Yuqing},
title = {Dynamic vs. static maintenance rate policies for multi-state queueing systems},
journal = {RAIRO. Operations Research},
pages = {S1339--S1354},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
doi = {10.1051/ro/2020034},
mrnumber = {4223153},
zbl = {1469.90055},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2020034/}
}
TY - JOUR AU - Chen, Gang AU - Liu, Zaiming AU - Chu, Yuqing TI - Dynamic vs. static maintenance rate policies for multi-state queueing systems JO - RAIRO. Operations Research PY - 2021 SP - S1339 EP - S1354 VL - 55 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2020034/ DO - 10.1051/ro/2020034 LA - en ID - RO_2021__55_S1_S1339_0 ER -
%0 Journal Article %A Chen, Gang %A Liu, Zaiming %A Chu, Yuqing %T Dynamic vs. static maintenance rate policies for multi-state queueing systems %J RAIRO. Operations Research %D 2021 %P S1339-S1354 %V 55 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ro/2020034/ %R 10.1051/ro/2020034 %G en %F RO_2021__55_S1_S1339_0
Chen, Gang; Liu, Zaiming; Chu, Yuqing. Dynamic vs. static maintenance rate policies for multi-state queueing systems. RAIRO. Operations Research, Tome 55 (2021), pp. S1339-S1354. doi: 10.1051/ro/2020034
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