Continuous versus discrete flow of parts in a production dipole. Exact transient analysis

A simple production line composed of two identical failure prone machines separated by a buffer is studied. In one case, a continuous flux of parts is produced by both machines while in the other case, it is assumed that each machine produces parts one by one with a processing time which is exponentially distributed. By analytically comparing the results obtained in both situations, the operation regime for which the hydrodynamical model is a consistent analytical tool to model discrete flows is characterized. The comparison also indicate that continuous versus production flows coincide for high production rates.