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Model Basic Queueing Systems
4-9
a jammed exit ramp of the freeway. You might model the tollbooth as a server and the
traffic jam as a gate.
Example of a Logical Queue
Suppose you are modeling a queue that can physically hold 100 entities and you want
to determine what proportion of the time the queue length exceeds 10. You can model
the long queue as a pair of shorter queues connected in series. The shorter queues have
length 90 and 10.
Although the division of the long queue into two shorter queues has no basis in physical
reality, it enables you to gather statistics specifically related to one of the shorter queues.
In particular, you can view the queue length signal (#n) of the queue having length 90.
If the signal is positive over a nonzero time interval, then the length-90 queue contains
an entity that cannot advance to the length-10 queue. This means that the length-10
queue is full. As a result, the physical length-100 queue contains more than 10 items.
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