Volume 55, 2021Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
|Page(s)||S327 - S341|
|Published online||09 February 2021|
An analysis of steady-state distribution in M/M/1 queueing system with balking based on concept of statistical mechanics
Okayama University, 3-1-1 Tsushima-naka, Okayama, 700-8530, Japan.
2 Kindai University, 3-4-1 Kowakae, Higashi-Osaka, Osaka, 577-8502, Japan.
* Corresponding author: email@example.com
Accepted: 21 May 2019
The phenomenon of balking has been considered frequently in the steady-state analysis of the M/M/1 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 M/M/1 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 M/M/1 queueing system with balking. As the result, we have defined an extended analysis model for the M/M/1 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 M/M/1 queueing system has been also constructed.
Mathematics Subject Classification: 60K25 / 90B22 / 82B31
Key words: M/M/1 queueing system / balking / statistical mechanics / entropy / potential energy / steady-state analysis
© EDP Sciences, ROADEF, SMAI 2021
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