Compatibility of Queueing Theory, Manufacturing Systems and SEMI Standards

Queueing theory is a powerful method to evaluate the performance of a manufacturing system. However, when applying it to a real system, both practical and theoretical issues arise. The practical issues are how to determine the parameter values for queuing models from the data available in real manufacturing systems. We explore this issue by comparing the data needed by queueing models to SEMI standards definitions. The theoretical issues are the selection of a specific queuing model and its proper use. In order to illustrate this, we design a specific situation for the applications of an M/M/1/Unreliable Machine queue, and compare the performances of two other approaches with it. The results show that, depending on the approach chosen, the differences in approximation error for cycle time can be over 30% at lower utilization levels.