If 500 modems communicate credit card information from POS terminals
to a server through landlines, with the potential for some to be
trying to simultaneously communicate- how many modems should be on the
server end?

Thanks for Asking!

You'll need to decide the number of modems for yourself, but an online
Engset calculator will make that job easy.

http://mmc.et.tudelft.nl/~frits/engset9.htm

There's a thorough explanation of the variables on the calculator
webpage, however you can start with the following figures:

Blocking probability: 0.1 (1 busy time unit per 9 idle time units)
Erlang traffic of 10 (10 seconds call length, 10 users per minute)

and of course, Number of users = 500.

Leave the Number of Lines box blank, and click the Calculate button
next to it.

Using these figures, I obtain a result of 12.5 modems. For the
greatest accuracy, you'll need to guess or determine the average call
length, and the expected number of calls per second. Multiply those
two figures to obtain the Erlang traffic variable.

Should you have any questions about using this calculator, please feel
free to ask for clarification.

~larre-ga

Fanatastic Answer! Thank you very much!!!