Machine repair problem with variable servers considering balking concept

• Main Authors: Yu-Ching Liou, 劉郁青
• Other Authors: 王國雄
• Format: Others
• Language: en_US
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/20017879997620734545

碩士 === 國立中興大學 === 應用數學系所 === 97 === This thesis studies the machine repair problem with variable servers in which failed machines balk (do not enter) with a constant probability 1-bn. We assume that the minimum number of busy servers is one. The failure times and repair times are both assumed to be exponentially distributed. We use a recursive method to develop analytic steady-state solutions and evaluate several system performance measures for three cases. A cost model is developed to determine the optimum number of busy servers and the optimal balking rate. We use the direct search method and the Newton’s method to find the global minimum value until the balking rate constraint is satisfied. Numerical results are provided in which various system performance measures are evaluated under optimal operating conditions. Two numerical examples are provided to illustrate the Newton’s method.