Hello......


Here is all my text about my USL programs...

I have to set it more right and more precise..

So here is my other proof again...

If the serial part of the Amdahl's law is bigger, you have
more chance to hit the contention, so there is more chance
that USL will give a good approximation of the predicted
scalability up to 10X the maximum number of cores and threads
of the performance data measurements.., but let say the serial part
of the Amdahl's law is bigger and is 1/4 the parallel part of the
Amdahl's law, and let say the parallel part is variable and it makes the
USL methodology escape the contention at fewer core and fewer threads,
the USL methodology will have much more chance at fewer cores
and fewer threads to give a good approximation up to 10X the maximum
number of cores and threads of the performance data measurements.., you
can feel and confirm it by statistically using more examples of the
follwing above cases and calculating it..

But if the serial part is smaller , so there is more chance that
USL methodology will escape contention at fewer core and fewer
threads. so there is more chance that USL will give a good approximation
of the predicted scalability up to 10X the maximum number of cores and
threads of the performance data measurements..

So overall. the USL methodology will be able to forecast scalability
with a better approximation up to 10X the maximum number of cores and
threads of the performance data measurements..

If you have followed my previous proof of my previous post..
i have said that USL methodology can predict scalability up
to 10X the maximum number of cores and threads of the performance
data measurements..

So now look at this link about the USL methodology about
mixed workload on Ecommerce websites from Dr. Gunther the author
of USL methodology:

http://perfdynamics.blogspot.ca/2009/04/assessing-usl-scalability-with-mixed.html

I think from my proof, i say that Dr. Gunther is making a mistake,
because in this eCommerce example of the link above, since
we can predict scalability of the database server system up
to 10X the maximum number of cores and threads of the
performance data measurements, so the Dr. Gunther solution
is not a general solution , so my solution for this, is that
you have to use the right number of cores and number of threads
in the database system server side that ensure us to have
a more linear scalability when there internet users are using the
database system..and since the internet network have a more linear
scalability, so the USL methodology in my solution will be able to
predict scalability of the eCommerce website, so this is my solution.


About my previous post about mixed workload and eCommerce websites..

You have seen my previous general solution about this case..

I will make it more precise: if you want to apply the
USL methodology with my USL programs to mixed workload
of eCommerce websites, i think here is necessary
conditions:

1- the mean time of the inter-arrivals of the internet users is
assumed to be a good approximation.

2- the webserver database systems must be set with the
right number of cores and the right number of threads
that ensure a more linear scalability.

3- the internet network is assumed to have a more linear
scalability even if its derivative of its linear scalability is
negative.

So those necessary conditions permit the nonlinear regression
of my USL programs to predict scalability of eCommerce websites.

So that makes my USL programs an amazing great tools to foerecast
scalability, and it makes the USL methodology an amazing great tool.

A you have noticed i have given a proof that my USL
programs can forecast scalability up to 10X the maximum number
of cores and threads of the performance data measurements,
this is useful, other than that, this 10X is the right number
that optimizes the criterion of the cost, so when you want
to buy bigger NUMA systems, make sure that you buy them
with the right configuration that permit to add more processors
and more memory, this way you will be able to test again empirically
the Computer NUMA system that you have bought with my USL programs,
to better forecast again farther the scalability and optimize more
the criterion of the cost, so as you have noticed my USL programs
are great tools and important tools !

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 !

Now about my USL programs solvers...

I have used a second implementation of the BFGS Quasi-Newton
second-derivative line search family method as minimization function
for my nonlinear regression solver of USL programs, it is
one of the most powerful methods to solve unconstrained optimization
problem , but it didn't solve all the problems that the simplex method
of Nelder an Mead all solved, so i think i will stay with my nonlinear regression solver that uses the simplex method of Nelder and Mead that
have solved all the problems that i have given to it, i think it is a
good solver for my purpose of my USL programs.

How to validate my USL programs to be sure that they work correctly ?

I have first tested my USL programs with polynomial regression
against the R package of USL with the default solver with the raytracer performance data of the R package and they are giving the same results
that is the peak number of processors at 449 and the same predicted scalability, but my nonlinear solver that uses the simplex method as
a function minimization is giving a very good approximation
of the predicted scalability, i have also tested with other performance
data from my parallel LZMA algorithm and parallel LZ4 algorithm
of my parallel compression library and the R package is giving
the same results as my USL program solvers.

So you can be confident with my USL programs because they are working
great and are great tools for predicting 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.


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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