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is correct that the assumption need not be the case in either. However, with 'sufficiently large' populations, assuming an infinite population doesn't reduce the accuracy of analytical investigations of the process but does make such investigations much more tractable - that is, it makes such
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which is constant reguardless of the number of queueing customers, however the blocking probability changes for the infinite population (Erlang C formula) in the finite case (Engset formula), this make it computationally simpler then having to place a weight on
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model. Suppose you are looking at the failure rate of light bulbs in your home. If several are blown out while you're replacing the first one, you will see a slow down in the rate of light bulb failure because many lamps are "in line" for service. As
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investigations both easier to conduct and, when numbers are involved, the computations of the flow equations are much simpler and fast. Largely for this reason, the predictive power rather than the exact match to reality, the M/M/C/K/
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With respect to your discussion of how to model a finite pool of users when a 'small' pool of potential callers exists, i.e., when an approximation with an infinite population is inappropriate, I agree with
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For general consumption: If you have a population so small that, for instance, the number of people in line impacts the arrival rate of new 'customers' then it is poorly fit with an M/M/c/K/</math: -->
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which may violate copyright. Even if not, the copyng stage seemed to have resulted in many errors and would need to be done more carefully. I note the same addition was attempted in both
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parameters can depend on the number of customers in the queue, which is easily related to the number of customers not in the queue when the population is finite.
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If this is supposed to represent the size of a population, should we just make lambda 0 be equal to 0 since it would be an absorbing state?
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I have deleted the recent addition of Dec 30 which had all the missing and misformatted equations. It seems to have been copied from
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notes, the model must be modified to account for the fact that the number in queue will impact the arrival rate.
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The default assumption in both Birth-Death and
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If you have a finite calling population, rather than infinite one, you can have constant parameters
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The article says "In queueing theory the birth-death process is the most fundamental example of a
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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for all levels of the queue, but the blocking probability changes. Have a look at
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that you'd likely be better off just using the Birth-Death process directly.
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
