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# IE Resources

Gain an in-depth understanding of the issues that cause cycle time problems and learn how to solve them.

For manufacturing systems, queueing formulas can be used to estimate system performance measures such as average cycle time and throughput. For a full-scale wafer fab, these formulas usually become prohibitively complex. Accurate closed form solutions are not readily available — at least not solutions that contain sufficient detail to match actual cycle times in the fab. As a result, most practitioners turn to simulation for estimating cycle times.

Queueing models can be very useful, however, for validating the behavior of individual workstations and workcells. For our customers’ convenience, we have collected a series of relevant queueing formulas. Most of these formulas have also been published in Chance (1999). For more information, we recommend any good queueing textbook. Examples include Gross and Harris’ Fundamentals of Queueing Theory or Asmussen’s Applied Probability and Queues, both published by John Wiley & Sons.

Queueing formulas are usually categorized according to Kendall’s A/B/s notation, where A is the distribution of inter-release times, B is the distribution of service times, and s is the number of servers. Common distributions are M (Markov, or exponential), G (general), and D (deterministic, or constant).

- M/M/1 Queues in Series
- M/M/1 Queue with Loading and Unloading
- M/M/1 Queue with Two Priority Classes
- M/M/1 Queues in Series with Rework
- M/M/1 Queues in Series with Scrap
- M/M/s Queue
- M/G/1 Queue