Setup: A technical support agent answers incoming calls. Average call
duration is 5 minutes. Assuming a normal distribution of calls over a
3-hour peak period, how many calls can you assign to this 3-hour
period to make sure that 90% of the time the hold time is 1 minute or
less? What would the answer be if the time window was 6 hours? 9
hours? Same with 2, 3, 4 ... 10 agents. The answer would be a 3x10
matrix indicating the number of calls that can be accommodated under
these conditions.

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Request for Question Clarification by tox-ga on 28 May 2004 22:58 PDT

Greetings loosh,

This question is that reaches into a field of statistics known as
queuing theory and involves some rather complicated mathematics.  I
could write a program to find the answers for you, similar to the one
provided below.  (There are a few things about that one which doesn't
match your situation.)  Would you like me to provide such a program,
the explanation of the theory and how to solve such a question, or
just the numerical answers?

Best regards,
tox-ga

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Clarification of Question by loosh-ga on 29 May 2004 20:12 PDT

Hi, Tox--

What would help me most is a program along with an explanation that
can be understood by a tech-proficient non-mathematician. These
parameters are merely assumptions, and, it seems, the purely numercal
values have been kindly provided by a couple of folks in the comments.
Although, I can understand how this can seem like a pretty tall order
for the amount offered.

Thank you very much for the interest,
Loosh

I wish you had offered a lower price for this question, because
there's a free calculator that can answer it --
http://www.erlang.com/calculator/call/

You can use it to get the answers you wanted, for free.

And then, when your parameters change, you can get revised answers.

I used the free calculator on the website (the one I linked, above) to
make the matrix you requested.  See
http://mcraefamily.com/MathHelp/AlgebraOnline/m040528CallCenterDistributionErlangC.htm

Dear Graememcrae--

Thank you very very much for your comment and for the link. This is,
perhaps, a problem with the system as it stands--that is, it's hard to
split the retainer between several answerers. This is my first
experience with Google Answers and I am still feeling my way around
the system. In posting the pricing I followed the advice of the
developers and indicated what a good answer is worth to me... Now, it
seems, aside from just the numbers, I am getting an introduction into
a very interesting field. Yum.

Loosh, I'm not a researcher, so I can never get a fee in any case.  If
a researcher feels he can give you the value you are looking for
(fifty dollar's worth) then he'll lock the question, and give you a
really, really good answer.  Maybe that will be Mr. Tox, who has asked
you for a clarification.  Or maybe no researcher will feel able to
answer the question fully, in which case it will expire (or you may
withdraw it) before it ever gets answered.