Iterative methods for flexible manufacturing systems

This paper presents an Markovian model for flexible manufacturing systems (FMSs). The model captures two important features of an FMS: the reliability of machines and the capacity of the maintenance facility. A fast numerical algorithm based on preconditioned conjugate gradient (PCG) method is developed to solve the steady state probability distribution of the system. We prove the fast convergence rate of the PCG method. The performance analysis of the FMS can be evaluated by making use of the steady state probability distribution.