The output processes of serial production lines of exponential machines with finite buffers

Little is known about the interaction among the various manufacturing subsystems in a factory. The output of one manufacturing subsystem is usually the input to one or more downstream subsystems in the plant. Examples include the output of one production line being the input to another manufacturing stage, to a shipping system, or to an automated part conveyor. In all these examples, the output process of the production line forms the arrival process to the next subsystem. This paper develops a technique to analytically describe the output process of a serial production line of N machines with exponential processing time distributions and finite buffer capacities. Extensive exact results are used to examine the effects of line length, buffer capacity, and buffer placement on the interdeparture distribution, correlation structure, and variability of the output process of the production line. These results are used to determine the extent to which buffer allocation can be used to control the variability of the output process (and thereby the amount of work-in-process required to downstream subsystems). In addition, insights are provided to help explain why small buffers in production lines are normally adequate.