The phenomenon of balking has been considered frequently in the steady-state analysis of the queueing system. Balking means the phenomenon that a customer who arrives at a queueing system leaves without joining a queue, since he/she is disgusted with the waiting queue length at the moment of his/her arrival. In the traditional studies for the steady-state analysis of the queueing system with balking, it has been typically assumed that the arrival rates obey an inverse proportional function for the waiting queue length. In this study, based on the concept of the statistical mechanics, we have a challenge to extend the traditional steady-state analysis model for the queueing system with balking. As the result, we have defined an extended analysis model for the queueing system under the consideration of the change in the directivity strength of balking. In addition, the procedure for estimating the strength of balking in this analysis model using the observed data in the queueing system has been also constructed.
Keywords: $M/M/1$ queueing system, balking, statistical mechanics, entropy, potential energy, steady-state analysis
@article{RO_2021__55_S1_S327_0,
author = {Arizono, Ikuo and Takemoto, Yasuhiko},
title = {An analysis of steady-state distribution in $M/M/1$ queueing system with balking based on concept of statistical mechanics},
journal = {RAIRO. Operations Research},
pages = {S327--S341},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
doi = {10.1051/ro/2019064},
mrnumber = {4237379},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2019064/}
}
TY - JOUR AU - Arizono, Ikuo AU - Takemoto, Yasuhiko TI - An analysis of steady-state distribution in $M/M/1$ queueing system with balking based on concept of statistical mechanics JO - RAIRO. Operations Research PY - 2021 SP - S327 EP - S341 VL - 55 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2019064/ DO - 10.1051/ro/2019064 LA - en ID - RO_2021__55_S1_S327_0 ER -
%0 Journal Article %A Arizono, Ikuo %A Takemoto, Yasuhiko %T An analysis of steady-state distribution in $M/M/1$ queueing system with balking based on concept of statistical mechanics %J RAIRO. Operations Research %D 2021 %P S327-S341 %V 55 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ro/2019064/ %R 10.1051/ro/2019064 %G en %F RO_2021__55_S1_S327_0
Arizono, Ikuo; Takemoto, Yasuhiko. An analysis of steady-state distribution in $M/M/1$ queueing system with balking based on concept of statistical mechanics. RAIRO. Operations Research, Tome 55 (2021), pp. S327-S341. doi: 10.1051/ro/2019064
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