Performance evaluation of two-machine line with generalized thresholds

An analytical model for evaluating the performance of two-machine continuous flow system with finite capacity, multiple up and down states and generalized thresholds is presented in this paper. The idea is that the system can behave differently above or below certain buffer levels, i.e. thresholds. This means that while crossing one of the thresholds, certain changes of state can happen. The model provides a way to analyze a wide range of two-machine systems, including batching machines, introducing the notion of control by means of thresholds. Moreover, the proposed two-machine line can be used as a building block for the analysis of larger systems, modeling the behavior of loops. In addition, with this model it is possible to analyze all the system that can be studied with the multiple up and down states model, like for example phase-type failure and repair time distributions, series/parallel machines and quality control machines.