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Supplement to Chapter 11 Analytical queuing models 335
Figure S11.1 Low and high arrival variation
average arrival time is 3 minutes. Therefore to normalize standard deviation, it is divided
by the mean of its distribution. This measure is called the coefficient of variation of the
distribution. So,
c a = coefficient of variation of arrival times = σ a /t a
c e = coefficient of variation of processing times = σ e /t e
Incorporating Little’s law
In Chapter 4 we discussed on of the fundamental laws of processes that describes the relationship
between the cycle time of a process (how often something emerges from the process),
the working in progress in the process and the throughput time of the process (the total time
it takes for an item to move through the whole process including waiting time). It was called
Little’s law and it was denoted by the following simple relationship.
Or,
Work-in-progress = cycle time × throughput time
WIP = C × T
We can make use of Little’s law to help understand queuing behaviour. Consider the queue
in front of a station.
Work-in-progress in the queue = the arrival rate at the queue (equivalent to cycle time)
× waiting time in the queue (equivalent to throughput
time)
and
WIP q = r a × W q
Waiting time in the whole system = the waiting time in the queue + the average process
time at the station
W = W q + t e
We will use this relationship later to investigate queuing behaviour.