Hello......

As you have noticed i have come with a proof that
makes you feel more that the USL methodology that
makes forecasting of scalability possible is
a success and is an amazing tool..

Why have i done it this way ?

Because Dr. Gunther the author of the USL methodology
didn't spook about why his methodology works using
nonlinear regression or polynomial regression, even
on his book Guerilla capacity planning that explains
his methodology, he didn't explain what why it works..
so this is why i have come with a more precise
proof that makes you feel why the nonlinear regression
of the USL methodology works..

Other than that, i think that we can be confident
because Dr. Gunther is an expert that knows what
he is doing , so this i why i think that the
USL methodology is a success and is an amazing
great tool that predicts sclability.

Here is my contributions of my USL programs..

I have first implemented a solver for my USL program that
is polynomial regression, this solver must make
the a0 coefficient of the mathematical series to 0, but this solver
is not so efficient as my other solver that i have implemented
that is nonlinear regression using the simplex method of
of Nelder and Mead as a function minimization, this nonlinear
solver that i have implemented works perfectly and is more
efficient than the solver that uses polynomial regression,
also my contribution is my USL programs that is called usl_graph
that provides you with a more interractive graphical chart that
permit you to optimize more the criterion of the cost, i think
that the other R package is less powerful on this option.

Also in my USL programs i have calculated and feed my nonlinear solver
with partial derivatives of the USL equation:

C(N) = N/(1 + α (N − 1) + β N (N − 1))

I have calculated the partial derivative with respect to
α of the above USL equation, and i have calculated the partial
derivative with respect to β of the above USL equation, and the
two partial derivatives must be given to my nonlinear solver
that uses the simplex method of of Nelder and Mead as a function
minimization.

Please try my USL programs because they are working great and
they predict scalability !

I have included the 32 bit and 64 bit windows executables of my
programs inside the zip file to easy the job for you.

You can download my USL programs version 3.0 with the source code from:

https://sites.google.com/site/aminer68/universal-scalability-law-for-delphi-and-freepascal


Thank you,
Amine Moulay Ramdane.

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