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

2019 ◽  
Author(s):  
IKUO ARIZONO ◽  
Yasuhiko Takemoto
Keyword(s):  
Steady State ◽  
Statistical Mechanics ◽  
Queue Length ◽  
Queueing System ◽  
Analysis Model ◽  
Steady State Distribution ◽  
Steady State Analysis ◽  
Extended Analysis ◽  
The Moment ◽  
State Analysis

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.

scholarly journals Temperature rise characteristics for angular-contact ball bearings with oil-air lubrication based on fluid-solid conjugate heat transfer

2021 ◽  
Vol 13 (1) ◽  
pp. 168781402199092
Author(s):  
Miaomiao Li ◽  
Yu Wang ◽  
Weifang Chen ◽  
Rupeng Zhu
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Flow Field ◽  
Temperature Rise ◽  
Conjugate Heat Transfer ◽  
Operating Conditions ◽  
Ball Bearings ◽  
Analysis Model ◽  
Steady State Analysis ◽  
State Analysis

At present, the thermal analysis of oil-air-lubricated angular-contact ball bearings uses empirical heat transfer coefficients to calculate heat transfer. This approach presents problems such as simulating the actual lubrication flow field and ignoring the internal heat conduction in the bearing ring. This paper proposes a CFD steady-state analysis model of oil-air-lubricated angular-contact ball bearings based on fluid-solid conjugate heat transfer to analyze the flow field and temperature field. A temperature rise test of oil-air-lubricated angular-contact ball bearings was carried out to verify the positive determination of the simulation analysis results. Based on a fluid-solid conjugate heat transfer steady-state analysis model, the effects of lubrication parameters, operating conditions, and rolling element materials on the temperature rise characteristics of oil-air-lubricated angular-contact ball bearings were studied. The research results provide a method for analyzing the temperature rise characteristics of oil-lubricated bearings and provide a basis for the analysis of oil-lubricated bearing life.

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