An analysis of steady-state distribution in M/M/1 queueing system with balking based on concept of statistical mechanics

¹ 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: arizono@okayama-u.ac.jp

Received: 31 October 2018
Accepted: 21 May 2019

Abstract

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.