Performance evaluation of two-machine lines with generalized thresholds

An analytical model for evaluating the performance of two-machine continuous flow systems with finite buffer capacity, multiple up and down states and generalised thresholds is presented in this paper. The idea is that the machines can behave differently above or below certain buffer levels named thresholds. In addition, when the buffer level crosses one of the thresholds, certain changes of state of the machines can happen. With the method presented in the paper it is possible to consider all the different types of two machine lines which can be modelled with multiple up and down states, like for example cases with machines having phase-type failure and repair time distributions, serial/parallel machines and quality control machines. The proposed approach, allows to include system control by means of thresholds in the system model and provides a way to analyse the performance of a wide range of two-machine systems. Some of these cases are proposed in the numerical examples at the end of the paper. Moreover, the proposed two-machine line can be used as a building block for the analysis of larger systems, including systems with loops.