Queueing Theory - is the study of waiting times in queues (lines). Queueing theory is used to optimizing systems to reduce wait times. An easy example to understand is looking at wait times in line (also know as a queue).
For example, if a store has 7 different service lines then any delay at a specific line means all those in that line have to suffer to a greater extent. If, instead, there is one line that feeds all 7 stations then a delay in one line will mean that a delay at one station does not adversely impact the few unlucky enough to choose that line.
The importance of applying queuing theory is raised due to psychological factors (people will become frustrated if they see no progress, see themselves stuck while other [in other lines] mover forward...). This is an example of the interconnections Dr. Deming laid out in his management theory between, in this case systems improvement and psychology.
Queueing theory is also very important in how the computers we use every day work. The computer is constantly juggling thousands of actions and queueing them to be processed.
The Shmula blog has a series of interesting posts on Queueing Theory.
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