Practical Extensions to Cycle Time Approximations for the $G/G/m$-Queue With Applications

Approximate closed form expressions for the mean cycle time in a G/G/m-queue often serve as practical and intuitive alternatives to more exact but less tractable analyses. However, the G/G/m-queue model may not fully address issues that arise in practical manufacturing systems. Such issues include tools with production parallelism, tools that are idle with work in process, travel to the queue, and the tendency of lots to defect from a failed server and return to the queue even after they have entered production. In this paper, we extend popular approximate mean cycle time formulae to address these practical manufacturing issues. Employing automated data extraction algorithms embedded in software, we test the approximations using parameters gleaned from production tool groups in IBM's 200 mm semiconductor wafer fabricator.