Formulas:
Introduction
M/M/1 Queues in Series
M/M/1 with Load and Unload
M/M/1 with Priority Classes
M/M/1 with Rework
M/M/1 with Scrap
M/M/s Queue
M/G/1 Queue
Formula References



Cycle Time Estimation Formulas
For manufacturing systems, queueing formulas can
be used to estimate system performance measures such as
average cycle time and throughput. For a fullscale 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.
Notation
Queueing formulas are usually categorized according to
Kendall’s A/B/s notation, where A is the distribution
of interrelease 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).
