Cost Analysis of the M/M/R Machine Repair Problem with Multiple Working Vacations

• Main Authors: Shi Jia Chen, 陳詩嘉
• Other Authors: 柯志斌
• Format: Others
• Language: en_US
• Online Access: http://ndltd.ncl.edu.tw/handle/30023770593662177386

碩士 === 國立中興大學 === 應用數學系所 === 97 === In this thesis, we study the M/M/R machine repair problem with working vacation which the servers work with slower repair rate rather than completely terminates repair during a vacation period. We assume that the servers begin a working vacation when they are free of work. The breakdown times, repair times and vacation times are all assumed to be exponentially distributed. We construct the transition rate matrix Q to compute steady-state probabilities and system performance measures by matrix analytic method. A cost model is derived to determine the optimal values of the number of servers and two different repair rates under some constraints. Two methods：Direct search method and Newton-Quasi method are used sequentially to find the minimal total expected cost value within a certain availability level. Some numerical examples are provided to explain the Newton-Quasi method.