FYI, there are multiple data analysis engines you can play with when
trying to figure out the math and how it works.

MSJ posted a java program that simulates a lot of clients under
randomized conditions with failure rates here:

https://www.ietf.org/mail-archive/web/dnsop/current/msg21602.html

Additionally, I wrote a javascript based calculator for a single
resolver so you can try to put in "worst case" numbers into form fields
and have it calculate what happens here:

https://www.isi.edu/~hardaker/projects/5011/

-- 
Wes Hardaker
USC/ISI

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