Theory rarely translates exactly into reality. There are too many variables. This is notably true in High Performance Computing (HPC) where system performance measurements of Theoretical Peak and Real Peak are commonplace. A colleague of my from Dell Dr. Jeff Layton recently wrote an article in Admin HPC called A Failure to Scale that addressing scalability limits. The limits to improved performance and scalability can run counter to logic. For example, many HPC administrators have added cores and CPUs, but stop receiving performance boosts.

Jeff points out Amdahl's Law, which seemingly injects logic to this illogical behavior:

Underlying the scalability limit is something called Amdahl’s Law, proposed by Gene Amdahl in 1967. ... This law illustrates the theoretical speedup of an application when running with more processes and how it is limited by the serial performance of the application. At some point, your application will not run appreciable faster unless you have a very small serial portion.

Gene Amdahl

As always, Jeff's article is loaded with detailed information on the subject, back up formulas and charts, as well as tidbits of interesting information. Reading this article will outline where the term FUD came from, as an example. Most importantly, Jeff provides guidance to help system administrators who are facing performance and scalability limits due to Amdahl's Law, or even I/O.

You can read the full article here: A Failure to Scale.