Discrete-time model for two-machine one-buffer transfer lines with buffer bypass and two capacity levels

This article deals with the analytical modeling of transfer lines consisting of two machines decoupled by one finite buffer. The innovative contribution of this work consists in representing a particular behavior that can be found in a number of industrial applications, such as in the ceramics and electronics industries. Specifically, the buffer significantly affects the lines performance as, when it is accumulating or releasing material (i.e., when one machine is operational and the other machine is under repair), it forces the operational machine to slow down. Conversely, when both machines are operational they can work at a higher capacity since the buffer is bypassed. Thus, two levels for the machine capacity can be identified, based on the conditions of the machines and, consequently, the state of the buffer. The system is modeled as a discrete-time, discrete-state Markov process. The resulting two-Machine one-Buffer Model with Buffer Bypass is here called 2M-1B-BB model. The analytical solution of the model is obtained and mathematical expressions of the most important performance measures are provided. Finally, some numerical results are discussed.