TY - JOUR
T1 - STATISTICAL MECHANICS APPROACH FOR STEADY-STATE ANALYSIS IN M/M/S QUEUEING SYSTEM WITH BALKING
AU - Arizono, Ikuo
AU - Takemoto, Yasuhiko
N1 - Funding Information:
Acknowledgments. We would like to thank the Editor and referees very much for their helpful, useful, and constructive comments and suggestions regarding this article. Further, this work was supported by JSPS KAKENHI Grant Number 18K04611: “Evaluation of system performance and reliability under incomplete information environment”. We would like to appreciate the grant for our research.
Funding Information:
2020 Mathematics Subject Classification. Primary: 60K25; Secondary: 60K20, 60K35. Key words and phrases. M/M/s queueing system, balking, statistical mechanics, entropy, potential energy, steady-state analysis. The authors are supported by Japan Society for the Promotion of Science (JSPS) KAKENHI Grant Number 18K04611: “Evaluation of system performance and reliability under incomplete information environment”. ∗ Corresponding author: Ikuo Arizono.
Publisher Copyright:
© 2022. All Rights Reserved.
PY - 2022/1
Y1 - 2022/1
N2 - Behavior that a customer who has just arrived at a crowded queue-ing system leaves without joining the queue is known as the phenomenon of balking. Queueing systems with balking have been studied continually as one of significant subjects. In this paper, the theoretical approach for the steady-state analysis of the Markovian queueing systems with balking is considered based on the concept of the statistical mechanics. Here, it can be easily seen that the strength of balking is not constant but various in each queueing systems. Note that the strength of balking means how degree a customer who has just arrived at a crowded queueing system leaves without joining the queue. In our approach, under considering the difference of the strength of balking for each queueing systems, we have proposed a statistical mechanics model for analyzing the M/M/s queueing system with balking by introducing a parameter influencing the strength of balking. Further, we define a procedure for estimating the model parameter influencing the strength of balking. In addition, we consider a method of improving the performance of the M/M/s queueing system with balking by utilizing the statistical mechanics approach.
AB - Behavior that a customer who has just arrived at a crowded queue-ing system leaves without joining the queue is known as the phenomenon of balking. Queueing systems with balking have been studied continually as one of significant subjects. In this paper, the theoretical approach for the steady-state analysis of the Markovian queueing systems with balking is considered based on the concept of the statistical mechanics. Here, it can be easily seen that the strength of balking is not constant but various in each queueing systems. Note that the strength of balking means how degree a customer who has just arrived at a crowded queueing system leaves without joining the queue. In our approach, under considering the difference of the strength of balking for each queueing systems, we have proposed a statistical mechanics model for analyzing the M/M/s queueing system with balking by introducing a parameter influencing the strength of balking. Further, we define a procedure for estimating the model parameter influencing the strength of balking. In addition, we consider a method of improving the performance of the M/M/s queueing system with balking by utilizing the statistical mechanics approach.
KW - balking
KW - entropy
KW - M/M/s queueing system
KW - potential energy
KW - statistical mechanics
KW - steady-state analysis
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U2 - 10.3934/jimo.2020141
DO - 10.3934/jimo.2020141
M3 - Article
AN - SCOPUS:85123265809
SN - 1547-5816
VL - 18
SP - 25
EP - 44
JO - Journal of Industrial and Management Optimization
JF - Journal of Industrial and Management Optimization
IS - 1
ER -