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

Abstract-Approximate closed form expressions for the mean cycle time in a -queue often serve as practical and intuitive alternatives to more exact but less tractable analyses. However, the -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. Note to Practitioners-We develop extensions to intuitive closed-form approximations for the mean cycle time in queueing networks. Such approximations can be used to analyze the tradeoffs between equipment utilization and cycle time in a manufacturing facility. The extensions incorporate issues of practical import that have not been modeled in the literature and were motivated by the inability of existing models to accurately describe the performance of manufacturing in IBM's 200 mm semiconductor wafer fabricator. The utility of our extensions is that, using automated data collection systems, we are able to well model production tools and elucidate the sources of cycle time. Index Terms-Production management, queueing analysis, semiconductor device manufacture