Practical extensions to cycle time approximations for the G/G/m-queue with applications

James R. Morrison, Donald P. Martin

Research output: Contribution to journalArticlepeer-review

40 Scopus citations


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.

Original languageEnglish
Pages (from-to)523-532
Number of pages10
JournalIEEE Transactions on Automation Science and Engineering
Issue number4
StatePublished - Oct 2007


  • Production management
  • Queueing analysis
  • Semiconductor device manufacture


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