Exact Analysis of a Continuous Material Merge System with Limited Buffer Capacity and Three Stations

We develop a Markov process model of a flow line consisting of three unreliable machines and one buffer of limited capacity. Two machines upstream of the buffer perform the same operation and feed the same buffer in such a way that one machine has priority over the other when the buffer is full. The third machine removes material from the buffer. Processing times are deterministic and machine-specific. Exponentially distributed times to failure and to repair are also machine-specific. We develop an exact procedure to compute the average production rate and inventory level. The procedure is intended to be used as a building block of decomposition methods for the analysis of flow lines with non-linear flow of material that may, for example, be due to rework loops in flow lines with quality inspections.