Dr. Neil Gunther has undertaken an important work, that of teaching to IT professionals the basics of measuring and modeling the scalability of parallel computer systems. The model that he develops in his book is a useful starting point; however, this model fails to provide a sufficiently general basis for modeling the behavior of the wide variety of current parallel computer systems.
The "universal scalability law" that he describes in section 4.4, and for which he provides figure 4.8 and equation 4.31, extends Amdahl's Law via the addition of a "coherency" term that models effects such as data exchange between parallel processes. And although Dr. Gunther suggests that this coherency term ought to grow linearly with the number of parallel processes, and hence should appear as a quadratic term in equation 4.31, this coherency term depends on the specific communication architecture of the computer system and can grow non-linearly, for example, as log to the base two of the number of processes.
This logarithmic growth law may occur because one processor may not communicate directly with all other processors. Instead, one processor may send information to two other processors, and each of those two processors may send information to two more processors, and so forth. Therefore, in order to model the communication that occurs in such a communication cascade, the quadratic n(n-1) coherency term in equation 4.31 should be replaced by an n*log(n) term.
Moreover, performance data that are obtained from current parallel computer systems do not always conform to Dr. Gunther's "universal" scalability "law" under other conditions. For example, a large volume of data that exceeds the capacity of the total cache memory when distributed across a few processors may well fit into total cache memory when distributed across a larger number of processors. Under these conditions, the scalability for the larger number of processors appears to grow "super-linearly" relative to the scalability of a few processors. However, Dr. Guther's model specifically disallows this "super-linear" scaling that is commonly observed. Thus, although Dr. Gunther's book is a useful introduction to the subject of measuring and modeling the behavior of parallel computer architectures, his universal scalability law should not be considered to be universal.