Performance Analysis of <i>M/G/1/N</i> Machining System with Breakdown, Balking, Imperfect Recovery, and Reboot

ABSTRACT This paper analyzes the M/G/1/N machine repair problem, considering various factors such as an unreliable repairman (server), balking, recovery, and reboot processes. A notable feature of the model is its ability to effectively handle situations where failed machines within the system cannot be successfully recovered for specific reasons. In such cases, the system automatically initiates a reconfiguration process through rebooting, thereby enabling resolution of these issues. This aspect and the consideration of balking and breakdown features commonly observed in practical machining systems significantly enhance the model's realism. We employ a supplementary variable technique corresponding to the remaining repair time to develop steady-state solutions. Various metrics for system performance, such as expected system size, probability of server idle, and probability of server breakdown, are derived using probability distributions in steady state. A sensitivity analysis is also included to explore and validate the model further. Moreover, we frame an optimization problem for the cost function to compute the minimum cost corresponding to the optimal decision variables: system capacity and repair rate.