Journal Published Online: 06 October 2014
Volume 43, Issue 1

Diffusion Approximation for G/G/R Machine Repair Problems with Balking and Reneging



This paper analyzes the G/G/R machine repair problems with balking and reneging via diffusion approximation. Failed machines balk (do not enter) with a constant probability and renege (leave the queue after entering) according to a general distribution. Failure and repair times of the machines are also generally distributed. We obtain steady-state diffusion equations from the Fokker-Planck equations. In heavy traffic conditions, the approximate expressions for the diffusion parameters of the diffusion equations are obtained by the renewal theory. The analysis assumes heavy traffic conditions, that is, the number of failed machines in the repair state is nonempty in most cases all the time. We develop the expressions for the approximate probability density functions of the number of failed machines in the system. An accuracy comparison is performed between the diffusion approximation results and exact results of the M/M/R machine repair model with balking and exponential reneging times. Finally, numerical examples are given for illustration.

Author Information

Wang, Kuo-Hsiung
Dept. of Computer Science and Information Management, Providence Univ., Taichung, TW
Chung, Chi-Yuan
Dept. of Applied Mathematics, National Chung-Hsing Univ., Taichung, TW
Yang, Dong-Yuh
Institute of Information and Decision Sciences, National Taipei College of Business, Taipei, TW
Pages: 12
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Stock #: JTE20130155
ISSN: 0090-3973
DOI: 10.1520/JTE20130155