Ramine
4/18/2016 1:19:00 AM
Hello,
Because Dr. Gunther he author of USL has not explain why
regression analyses works in his methodology, so i will now give my
final mathematical proof...
Here is my final mathematical proof that i will explain...
First you know that Amdahl's law predict scalability using
the serial part S and the parallel part P of a parallel program..
Now i will continu my proof with the Amdahl's law, making some
good approximation by simplifying a little bit the model..
Now here is my proof:
If the serial part of the Amdahl's law is bigger, you have more
chance probabilistically to get contention on the serial part,
and this contention will enable the nonlinear regression to
approximate more the predicted scalability, because this
mathematical fact will deviate the graph of the nonlinear
regression in a more right direction up to a farther predicted
scalability, so this enable the nonlinear regression to predict
scalability farther, so this reasonning will make the USL methodology to
succeed on a more bigger serial parts of the Amdahl's law.
For smaller serial parts, if the serial part is smaller ,
you have less chance probabilistically to get contention on
the serial part, and this mathematical fact will enable
the nonlinear regression to predict farther scalability with
fewer threads and fewer cores.
So this two mathematical facts makes the mathematical probability
distribution of the success of the forecasting of scalability farther
higher, so this is all about mathematical probability, and this
mathematical probability of my proof makes the USL methodology
successful and enable the USL methodology to forecast farther.
Thank you,
Amine Moulay Ramdane.